QT5201U wiki - User contributions [en]

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T16:03:03Z

WenYi: /* Coincidence Time of Pulsed Lasers */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>TriScroll<math>^{TM}</math> 300 Series Dry Scroll Vacuum Pump. (2003, May). Varian. https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection<ref>Model RGC-100 Series Digital Vacuum Gauge. (2010, May). Agilent Technologies. https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>.

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>High Voltage power supplies | TM series. Matsusada Precision. https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>Keithley DMM7510: 7½-Digit Graphical Sampling Digital Multimeter. (n.d.). DMM7510 | Tektronix. https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>UV Fused Silica High-Precision Windows. (n.d.). Thorlabs. https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below <ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T16:02:25Z

WenYi: /* Part 1: Photoemission */

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T16:01:33Z

WenYi: /* Part 2: Primary Emission */

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T16:00:45Z

WenYi: /* Part 4: Detection */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>TriScroll<math>^{TM}</math> 300 Series Dry Scroll Vacuum Pump. (2003, May). Varian. https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection<ref>Model RGC-100 Series Digital Vacuum Gauge. (2010, May). Agilent Technologies. https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>.

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>High Voltage power supplies | TM series. Matsusada Precision. https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>Keithley DMM7510: 7½-Digit Graphical Sampling Digital Multimeter. (n.d.). DMM7510 | Tektronix. https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>UV Fused Silica High-Precision Windows. (n.d.). Thorlabs. https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below <ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T16:00:05Z

WenYi: /* Proposed Vacuum Design */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>TriScroll<math>^{TM}</math> 300 Series Dry Scroll Vacuum Pump. (2003, May). Varian. https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection<ref>Model RGC-100 Series Digital Vacuum Gauge. (2010, May). Agilent Technologies. https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>.

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>High Voltage power supplies | TM series. Matsusada Precision. https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>Keithley DMM7510: 7½-Digit Graphical Sampling Digital Multimeter. (n.d.). DMM7510 | Tektronix. https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>UV Fused Silica High-Precision Windows. (n.d.). Thorlabs. https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below <ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:58:38Z

WenYi: /* Completed Vacuum Chamber */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>TriScrollTM 300 Series Dry Scroll Vacuum Pump. (2003, May). Varian. https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection<ref>Model RGC-100 Series Digital Vacuum Gauge. (2010, May). Agilent Technologies. https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>.

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>High Voltage power supplies | TM series. Matsusada Precision. https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>Keithley DMM7510: 7½-Digit Graphical Sampling Digital Multimeter. (n.d.). DMM7510 | Tektronix. https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>UV Fused Silica High-Precision Windows. (n.d.). Thorlabs. https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below <ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:58:06Z

WenYi: /* High Voltage Supply */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>TriScrollTM 300 Series Dry Scroll Vacuum Pump. (2003, May). Varian. https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection<ref>Model RGC-100 Series Digital Vacuum Gauge. (2010, May). Agilent Technologies. https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>.

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>High Voltage power supplies | TM series. Matsusada Precision. https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>Keithley DMM7510: 7½-Digit Graphical Sampling Digital Multimeter. (n.d.). DMM7510 | Tektronix. https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>UV Fused Silica High-Precision Windows. (n.d.). Thorlabs. https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below <ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:57:34Z

WenYi: /* Conclusion & Difficulties */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>TriScrollTM 300 Series Dry Scroll Vacuum Pump. (2003, May). Varian. https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection<ref>Model RGC-100 Series Digital Vacuum Gauge. (2010, May). Agilent Technologies. https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>.

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>High Voltage power supplies | TM series. Matsusada Precision. https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>Keithley DMM7510: 7½-Digit Graphical Sampling Digital Multimeter. (n.d.). DMM7510 | Tektronix. https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>UV Fused Silica High-Precision Windows. (n.d.). Thorlabs. https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below <ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:55:25Z

WenYi: /* Electron Multiplier Design Considerations */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>TriScrollTM 300 Series Dry Scroll Vacuum Pump. (2003, May). Varian. https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection<ref>Model RGC-100 Series Digital Vacuum Gauge. (2010, May). Agilent Technologies. https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>.

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>High Voltage power supplies | TM series. Matsusada Precision. https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>Keithley DMM7510: 7½-Digit Graphical Sampling Digital Multimeter. (n.d.). DMM7510 | Tektronix. https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>UV Fused Silica High-Precision Windows. (n.d.). Thorlabs. https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below <ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>J.J Scholtz, D. Dijkkamp and R.W.A. Schmitz, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:54:03Z

WenYi: /* Cathode & First Dynode Voltages */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>TriScrollTM 300 Series Dry Scroll Vacuum Pump. (2003, May). Varian. https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection<ref>Model RGC-100 Series Digital Vacuum Gauge. (2010, May). Agilent Technologies. https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>.

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>Matsusada Precision Inc. (n.d.). High Voltage power supplies | TM series. Matsusada Precision. https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below <ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>J.J. SCHOLTZ, D. DIJKKAMP and R.W.A. SCHMITZ, Secondary electron emission properties. Phillips Journal of Research, Vol 50, No. 3/4, 1996, https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:49:29Z

WenYi: /* Cathode & First Dynode Voltages */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>TriScrollTM 300 Series Dry Scroll Vacuum Pump. (2003, May). Varian. https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below <ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:48:05Z

WenYi: /* Cathode & First Dynode Voltages */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>V. Baglin, J. Bojko
, O. Gröbner, B. Henrist, N. Hilleret, C. Scheuerlein, M. Taborelli. The secondary electron yield of technical materials and its variation with surface treatments, Proceedings of EPAC 2000, Vienna, Austria, https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:46:41Z

WenYi: /* Cathode & First Dynode Voltages */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>Electron Multipliers. (2019, January). Hamamatsu. https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>Yoshida, S., Takeda, I., Igarashi, Y., & Arata, H. (1953). Secondary Electron Emission of Copper-Beryllium Alloy The Surface Products of the Alloys and their Secondary Electron Emission Characteristic under Different Oxygen Pressures and Temperatures. Journal of the Physical Society of Japan, 8(3), 318–323. https://doi.org/10.1143/jpsj.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>Guo, J., Wang, D., Xu, Y., Zhu, X., Wen, K., Miao, G., Cao, W., Si, J., Lu, M., & Guo, H. (2019). Secondary electron emission characteristics of Al2O3 coatings prepared by atomic layer deposition. AIP Advances, 9(9), 095303. https://doi.org/10.1063/1.5113671</ref>, and finally steel of about 2<ref>Baglin, V., Bozhko, Y., Grobner, O., Henrist, B., & Hilleret, N. (2000). The secondary electron yield of technical materials and its variation with surface treatments. 7th European Particle Accelerator Conference, 1–3, 217–221. https://inspirehep.net/literature/535205</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>Kang, Y., Wu, G., Zhang, X., Liu, Y., Shi, C., Wei, W., & Gao, G. (2019). Verification and analysis of flowing gas discharge – Part II. IEEE Transactions on Dielectrics and Electrical Insulation, 26(4), 1056–1064. https://doi.org/10.1109/tdei.2019.007833</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>Mitchell, E., & Mitchell, J. (1951). The work functions of copper, silver and aluminium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1100), 70–84. https://doi.org/10.1098/rspa.1951.0231.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>V. Baglin, J. Bojko1
, O. Gröbner, B. Henrist, N. Hilleret, C. Scheuerlein, M. Taborelli. THE SECONDARY ELECTRON YIELD OF TECHNICAL MATERIALS
AND ITS VARIATION WITH SURFACE TREATMENT, https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

= Conclusion & Difficulties =
In conclusion, we did not manage to make the electron multiplier work. We know for a fact that the vacuum chamber was entirely unsuccessful; however, whether our dynode electron multiplications system works remain unclear.

We faced a lot of difficulties during this project. Trying to rely on existing hardware lying around our labs made planning and designing things in ahead extremely difficult. One clear example would be the high voltage supply, which we initially expected to get a source which we can immediately connect our wires to. Finding the 3000V supply and the MHV connector after the box was already cut was a pretty bad experience; especially given that the final leak preventing vacuum from being successful was the hole we made for the MHV connector.

Also, we lacked prior experience in working with vacuum. Many fundamental things in constructing and working with a vacuum was only picked up along the way during this project. Unfortunately, we picked this knowledge up too slowly to finish the project in a timely manner. With a successful vacuum, we could then determine whether the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser is working as intended. But again, very sadly, we were not able to get to this stage.

Regardless, it was a pretty fun and interesting project to have worked on. The knowledge we had to pick up along the way will definitely be of help to us someday in PhD or further in the future. No regrets on attempting this!

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:20:58Z

WenYi: /* Michelson Interferometer */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams are sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
We then attempted to evacuate the vacuum chamber. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

== Difficulties and challenges ==

Due to a lack of prior experience working with vacuum, we faced many unexpected challenges in setting up the entire setup for the experiment. This resulted in us not having enough time to be able to test the vacuum chamber properly and to fix any issues that arise during the process. The torr seal takes 24 hours to cure and this is a significant amount of time as time is very much scarce for the project. Given more time, we wish to be able to test out the vacuum and be able to properly seal any leaks. With it, we would also like to be able to devise ways through which we can know that the individual components of the experiments, namely the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser. Through this, in the process of putting everything together, we can then know and pinpoint the specific part that might not be working.

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:19:43Z

WenYi: /* Copper cathode */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. This is to ensure that the laser light is directed onto copper instead of its oxides, whose work function is different from that of copper. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams is sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

While the beam shape and the resulting interference pattern in not the nicest to say the least, this is of little concern for the applications of this project and thus was ignored.

== Non-Vacuum Attempt ==
We first attempted the experiment in non-vacuum conditions. As expected as per the mean free path of electrons in air as [[#Electron Multipliers & Vacuum|previously discussed]], no significant readings were observed.

== Vacuum Attempt ==
The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

Despite our best efforts to get the vacuum chamber to work, we were unfortunately unable to achieve any kind of vacuum. The reason was simply due to leaks, caused by imperfect applications of torr seal at some key areas. Attempts to patch such leaks were unsuccessful, as we did not have any more time to wait for the newly-applied torr seal to fully cure.

== Difficulties and challenges ==

Due to a lack of prior experience working with vacuum, we faced many unexpected challenges in setting up the entire setup for the experiment. This resulted in us not having enough time to be able to test the vacuum chamber properly and to fix any issues that arise during the process. The torr seal takes 24 hours to cure and this is a significant amount of time as time is very much scarce for the project. Given more time, we wish to be able to test out the vacuum and be able to properly seal any leaks. With it, we would also like to be able to devise ways through which we can know that the individual components of the experiments, namely the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser. Through this, in the process of putting everything together, we can then know and pinpoint the specific part that might not be working.

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:12:16Z

WenYi: /* Copper cathode */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8cm x 4cm) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors in series. Running a standard voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect the 10V applied be divided evenly between each of the 10 resistors; resulting in 1V across each resistor. We performed this measurement, and the data is presented in the table below. We also repeated the experiment for standard R = 500k<math> \Omega</math> resistors to see if there were any differences between the two.

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

We notice that the voltage across each of the 10M<math>\Omega</math> resistor is only 0.5V. The theory that the resistors are not meant for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists.

Eventually it was discovered that this discrepancy was probably due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved.
The second set of data for resistors of R = 500k<math> \Omega</math>, verifies this conclusion. As the resistors under test now have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is mostly gone.

==Michelson Interferometer==
The optical set-up is a simple Michelson interferometer, as shown in the picture below. An additional telescope formed by a f=50mm and f=250mm lens pair was used to magnify the beam diameter from 1mm to 5mm. The beam is then split into the two arms of the interferometer via a 50-50 beam splitter, after which the recombined beams is sent into the copper target in the vacuum chamber.

[[File:optics_table.png|center|500px]]

The resulting interference pattern was recorded via a camera, and is replicated below.

[[File:interference.png|center|500px]]

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down. While this is expected based on the [[#Electron Multipliers & Vacuum|previous discussion]] of the mean free path of the electrons in air, we are unable to verify whether other parts of the experiment are working fine.

== Vacuum Attempt ==
The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

The vacuum attempt was however also unsuccessful as there appears to be a leak located at where the hole for the miniature high voltage connector is.

== Difficulties and challenges ==

Due to a lack of prior experience working with vacuum, we faced many unexpected challenges in setting up the entire setup for the experiment. This resulted in us not having enough time to be able to test the vacuum chamber properly and to fix any issues that arise during the process. The torr seal takes 24 hours to cure and this is a significant amount of time as time is very much scarce for the project. Given more time, we wish to be able to test out the vacuum and be able to properly seal any leaks. With it, we would also like to be able to devise ways through which we can know that the individual components of the experiments, namely the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser. Through this, in the process of putting everything together, we can then know and pinpoint the specific part that might not be working.

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T15:00:40Z

WenYi: /* Difficulties and challenges */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down. While this is expected based on the [[#Electron Multipliers & Vacuum|previous discussion]] of the mean free path of the electrons in air, we are unable to verify whether other parts of the experiment are working fine.

== Vacuum Attempt ==
The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

The vacuum attempt was however also unsuccessful as there appears to be a leak located at where the hole for the miniature high voltage connector is.

== Difficulties and challenges ==

Due to a lack of prior experience working with vacuum, we faced many unexpected challenges in setting up the entire setup for the experiment. This resulted in us not having enough time to be able to test the vacuum chamber properly and to fix any issues that arise during the process. The torr seal takes 24 hours to cure and this is a significant amount of time as time is very much scarce for the project. Given more time, we wish to be able to test out the vacuum and be able to properly seal any leaks. With it, we would also like to be able to devise ways through which we can know that the individual components of the experiments, namely the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser. Through this, in the process of putting everything together, we can then know and pinpoint the specific part that might not be working.

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:58:18Z

WenYi: /* Non-Vacuum Attempt */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down. While this is expected based on the [[#Electron Multipliers & Vacuum|previous discussion]] of the mean free path of the electrons in air, we are unable to verify whether other parts of the experiment are working fine.

== Vacuum Attempt ==
The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

The vacuum attempt was however also unsuccessful as there appears to be a leak located at where the hole for the miniature high voltage connector is.

== Difficulties and challenges ==

Due to a lack of prior experience working with vacuum, we faced many unexpected challenges in setting up the entire setup for the experiment. This resulted in us not having enough time to be able to test the vacuum chamber properly and to fix any issues that arises during the process. The torr seal takes 24 hours to cure and this is a significant amount of time as time is very much scarce for the project. Given more time, we wish to be able to test out the vacuum and be able to properly seal any leaks. With it, we would also like to be able to devise ways through which we can know that the individual components of the experiments, namely the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser. Through this, in the process of putting everything together, we can then know and pinpoint the specific part that might not be working.

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:55:18Z

WenYi: /* Difficulties and challenges */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes. Unfortunately, the wires could not be soldered onto the stainless steel dynodes effectively (spot welding was our initial choice, but we didn't have the time to learn how to use it). Thus, we bent the steel around the wires and secured them in place via applying pressure and crimping the wire in place. We then checked for electrical contact before soldering the wires such that they made a loop around the bent. The wires were also superglued to the walls to ensure that they do not come into contact with each other during operation.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down.

== Vacuum Attempt ==
The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

The vacuum attempt was however also unsuccessful as there appears to be a leak located at where the hole for the miniature high voltage connector is.

== Difficulties and challenges ==

Due to a lack of prior experience working with vacuum, we faced many unexpected challenges in setting up the entire setup for the experiment. This resulted in us not having enough time to be able to test the vacuum chamber properly and to fix any issues that arises during the process. The torr seal takes 24 hours to cure and this is a significant amount of time as time is very much scarce for the project. Given more time, we wish to be able to test out the vacuum and be able to properly seal any leaks. With it, we would also like to be able to devise ways through which we can know that the individual components of the experiments, namely the electron multiplication chain using the dynodes and the 2-photon photoelectric effect using the pulsed laser. Through this, in the process of putting everything together, we can then know and pinpoint the specific part that might not be working.

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:49:13Z

WenYi: /* Measurements & Data */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down.

== Vacuum Attempt ==
The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

The vacuum attempt was however also unsuccessful as there appears to be a leak located at where the hole for the miniature high voltage connector is.

== Difficulties and challenges ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:47:01Z

WenYi: /* Vacuum Attempt */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, our 3000V supply can only reliably run at 2500V (confusing I know), and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid. The final layout of the dynodes is shown below:

[[File:dynode_setup.png|center|500px|]

Due to the box not having originally been designed to accept a MHV connector, we had to drill an additional hole and torr seal a MHV female connector into the box as well. To also allow for a current read-out, an additional small hole was made through which a single wire was sent through to set the last dynode to ground.

The voltage divider is made of ten 10 <math>M\Omega</math> resistors soldered together in series. The chain of resistors are then secured to the inner surfaces of the acrylic box using superglue. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down.

== Vacuum Attempt ==
The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

The vacuum attempt was however also unsuccessful as there appears to be a leak located at where the hole for the miniature high voltage connector is.

== Background Reading ==

== Success? ==

=References=
<references />

File:Vacuum box.jpg

2021-04-30T14:46:15Z

WenYi: WenYi uploaded a new version of File:Vacuum box.jpg

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:38:28Z

WenYi: /* Vacuum Attempt */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, out 3000V supply can only reliably run at 2500V, and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid.

The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down.

== Vacuum Attempt ==

The vacuum attempt was however also unsuccessful as there appears to be a leak located at where the hole for the miniature high voltage connector is. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|300px]]

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:38:00Z

WenYi: /* Vacuum Attempt */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, out 3000V supply can only reliably run at 2500V, and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid.

The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down.

== Vacuum Attempt ==

The vacuum attempt was however also unsuccessful as there appears to be a leak located at where the hole for the miniature high voltage connector is. The picture below shows the vacuum chamber secured to the optical table and attached to the pump.

[[File:vacuum_box.jpg|center|500px]]

== Background Reading ==

== Success? ==

=References=
<references />

File:Vacuum box.jpg

2021-04-30T14:37:06Z

WenYi:

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:36:39Z

WenYi: /* Measurements & Data */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, out 3000V supply can only reliably run at 2500V, and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid.

The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down.

== Vacuum Attempt ==

The vacuum attempt was however also unsuccessful as there appears to be a leak located at where the hole for the miniature high voltage connector is.

[[File:vacuum_box.jpg|center|500px]]

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:35:03Z

WenYi: /* Vacuum Attempt */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, out 3000V supply can only reliably run at 2500V, and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid.

The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down.

== Vacuum Attempt ==

The vacuum attempt was however also unsuccessful as there appears to be a leak located at where the hole for the miniature high voltage connector is.

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:29:07Z

WenYi: /* Non-Vacuum Attempt */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, out 3000V supply can only reliably run at 2500V, and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid.

The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==
We attempted the experiment without the vacuum to see if this is possible without it. We were unable however to get any significant readings without the vacuum pumped down.

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:24:35Z

WenYi: /* Measurements & Data */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, out 3000V supply can only reliably run at 2500V, and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid.

The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

In the following sections we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

File:Optics table.png

2021-04-30T14:24:00Z

WenYi:

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:22:16Z

WenYi: /* Measurements & Data */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, out 3000V supply can only reliably run at 2500V, and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid.

The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optics_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T14:21:24Z

WenYi: /* Measurements & Data */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons are), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the 50-50 beam splitter, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center><math>|d| < c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below<ref>By Nikob7 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=77906837</ref>:

[[File:em.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (<math>Cu-BeO</math>), aluminimum oxide (<math>Al_2O_3</math>)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, <math>Cu-BeO</math> has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; <math>Al_2O_3</math> of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers multiple dynode to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how the electrons are to be propagated from one dynode to the next in a systematic and controller manner, such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards subsequent dynodes due to electrostatic attraction, which will ensure a systemic and controlled propagation. However, due to safety concerns, the final dynode at the end of the multiplication chain should be at zero potential. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

'''Current Measurement Device - Tektronix DMM7510'''

Details: Capable of current measurements down to 1pA<ref>https://sg.tek.com/tektronix-and-keithley-digital-multimeter/dmm7510</ref>.

''' Window - Thorlabs WG41050'''

Details: >90% transmission at 355nm<ref>https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3983</ref>

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

Across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decays back down. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. The maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode needs to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. A graph of the energy distribution of secondary electrons emitted from stainless steel is shown below<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>:

[[File:secondary_electron_energy.png|center|500px]]

Which tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to avoid any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode. A 3D sketch we had of the planned dynode geometry is shown below.

[[File:dynode_combined.png|center|500px]]

While we did go on to construct dynodes of such geometry (by hand-cutting and hand-folding them), we found that mounting them securely onto the already-cut mounting base (shown in a later section) was not possible. While the dynodes themselves did fit into the holes in the mounting base, they were only loosely hanging and thus susceptible to falling off. Due to a lack of time, we then decided to move away from these nicely-shaped dynodes and instead build the electron multiple with flat, rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Primary Emission===
As mentioned, the amount of power available for use of the 355nm laser is about 400mW (P). While the original beam diameter is about 1mm, we telescoped this to magnify the beam diameter on the copper to be about 5mm (r) instead. Then, the number of photons incident on the copper per unit time is given by:

<math> N_{\text{photons}} = \frac{P}{\pi r^2} \times \frac{\pi r^2}{hf} \approx 7.1\times 10^{10} </math>

Where <math>h</math> is Planck's constant.

Since two photons are required for a photoemission, the net number of primary electrons produced would then be:

<math> N_{\text{electrons}} = \frac{1}{2} \times N_{\text{photons}} \approx 3.55\times 10^{10} </math>

===Part 3: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients of steel as studied above, we expect about two secondary electrons to be emitted for every primary electron incident on a dynode. We assume a 10-dynode electron multiplier, based on which the total gain would be <math>2^{10}</math>.

===Part 4: Detection===
We now need to account for losses in the system. There are many possible loss mechanisms: electron losses due to collisions with background gas, finite capture rate of the emitted electrons and so forth. Putting all the losses together, we assume that we only obtain 10% of the maximally possible current that could be generated in the optimal scenario.

Given the number of primary electrons and the gain, we can then convert the final number of electrons to a current. Performing the calculations shows that we should expect currents on the order of <math> 0.5859\mu A</math>. This is well above the resolution of the current measurement device we are using, and thus the project's logic sounds sound so far.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed Vacuum Design===
Below is a screenshot of the proposed vacuum design (without the dynodes). The box will be made out of acrylic of 10mm thickness. The internal dimensions of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

[[File:Box2.png|center|600px]]

Some important design aspects are as follows:
* Front Wall:
** A hole for the window to sit in. A window is necessary since acrylic generally does not deal well with UV, and the laser we're using happens to be a UV laser. The window will allow the beam to then almost fully transmit into the vacuum chamber and onto the copper target.
* Left Wall:
** 4 M2 screw holes for mounting the dynode mounting plates.
* Right Wall:
** One hole for the valve and vacuum pump to connect to
** One hole for a connection to a pressure gauge
*Dynode Plates:
** Mounting plates for the dynodes. They are rectangular pieces with rectangular holes cut into them where the dynodes should seat. The holes on the top and bottom plates are slightly displaced.

===Initial Vacuum Chamber===
The actual box that Imran was kind enough to help us make is almost exactly like the drawing in SolidWorks. The only difference lies in the hole that was meant for a mirror to sit in. The original design included two concentric holes of two different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of one size that is smaller than that of the window. This turned out to be not much of an issue, as shown in a later section.

[[File:box.png|center|500px]]

The 6 faces of the box are held together using M3 screws, which dug into tapped holes in the acrylic itself.

===Completed Vacuum Chamber===
[[File:Completed_setup.png|center|500px]]

A few changes had to be made between the time that the vacuum box was cut, and when we finally put it together. The main changes are mentioned below.

'''Window'''

Since the window could not fit into the hole made in the acrylic, we placed the window over the designated hole instead. To prevent airflow, we then sealed the window onto the acrylic using Torr seal.


'''Vacuum pump'''

Since there was no way we could attach a pump directly onto the acrylic, we instead used a pipe system with a valve. One end of the pipe was inserted into the box, while the valve itself was Torr sealed to the surface to prevent airflow. The other end of the pipe was a KF connector, which we could then connect to the vacuum pump.


'''Vacuum Gauge'''

Due to the lack of hardware (all of these vacuum parts were found lying around in the lab, and we didn't have anything else we could use unfortunately), we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then close the valve, disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how reliable the vacuum valve is. After which, we will replace the gauge with the pump again and leave it to run for a couple of hours.

==The Electron-Multiplier Setup==
===High Voltage Supply===
[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

The high voltage (HV) supply that we have is a Matusada Precision TM-3N, -3000V supply. The board was previously constructed by someone else. Though the supply itself is rated for 3000V, the previous user also added a warning sticker saying not to exceed 2500V. To ensure that the HV supply survived the entirety of this project, we decided not to go above 2500V and risk potentially damaging the supply permanently.

We performed some simply characterization of the supply. We first made sure that the supply was actually capable of supplying 2500V by measuring the voltage across a small resistance in a voltage divider. Performing the calculations showed us that the supply was indeed outputting 2500V. We also ensured that the reading on the LCD screen actually corresponded to the output voltage. While this was an issue at lower voltages (<100V), the reading on the LCD was pretty much accurate at the voltages we were working at.
The output of the HV supply was also a miniature high voltage (MHV) connector, which we fortunately had cables around for. This, however, brought about some changes to the vacuum chamber as detailed below. [If you're wondering why we didn't think of this beforehand, its because we didn't know that this HV supply existed when we made the box.]

===Dynodes===
The 3mm thick strips of stainless steel dynodes were secured to the mounting plates using superglue. They are arranged in a staggered manner such that the first dynode is placed on the top plate, closest to the copper cathode while the second is on the bottom plate and slightly further (5mm) away from the target. The third dynode is again on the top plate, which is placed 10mm away from the target, and so on. The original reason for this staggering of the dynodes was to accommodate for the fact that the dynodes were supposed to be curved, with a radius of curvature of 5mm. As such, this staggering would have helped to increase the capture rate of the electrons for each of the dynodes. While we had to move away from the curved dynodes due to the difficulty in securely attaching them to the mounting plates, the staggering was still done with the flat dynodes as well.

The strips were cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper of dimensions (8 x 4) as the cathode, onto which the laser light is directed. The copper was smoothed using sandpaper (down to P400) to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent under running water before securing it to the top of the box using superglue.

===Voltage divider===
You might recall (if you're still reading) that 300V was the optimal dynode-dynode voltage separation. With 10 dynodes, this would require a 3000V supply. Unfortunately, out 3000V supply can only reliably run at 2500V, and so we had no choice but to run the copper target and the dynodes in 250V intervals. Fortunately, the secondary emission coefficient is still approximately 2, and so the numbers obtained in the simulations should still be valid.

The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

File:Optical table.png

2021-04-30T14:18:33Z

WenYi: WenYi uploaded a new version of File:Optical table.png

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T09:29:14Z

WenYi: /* Completed Setup */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons is), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the photodetector, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center>Positional Accuracy: <math>\quad c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[[File:dynode_combined.png|center|500px]]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2^{10}</math>.

===Part 3: Detection===
We now need to see if the current generated by the multiplied electrons is at a detectable scale.

The average power of the laser is 400mW. We approximate the beam size of our laser to have a diameter of 5mm. This corresponds to a total <math> 7.1\times 10^{10}</math> of photons arriving at the photocathode. This will result in a <math> 3.55\times 10^{10}</math> electrons being emitted per second as 2 photons are required for the two-photon photoelectric effect. Assuming that the electron multiplication yields a gain of <math> 2^{10}</math>, we then have a current of <math> 5.859\mu</math>A. The scaling goes as <math>1A = 6.242 \times 10^{18}</math> electrons per second.

===Part 4: Scaling===
In all of the above calculations, we have assumed that we have captured all of the electrons and secondary electrons emitted. This is often not the case. We assume that we can only achieve a capture rate of 10%. This would mean that we are looking for a current that is on the order of <math> 0.5859\mu A</math>.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Box2.png|400px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|left|thumb|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|right|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|400px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T09:28:16Z

WenYi: /* Proposed vacuum design */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons is), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the photodetector, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center>Positional Accuracy: <math>\quad c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[[File:dynode_combined.png|center|500px]]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2^{10}</math>.

===Part 3: Detection===
We now need to see if the current generated by the multiplied electrons is at a detectable scale.

The average power of the laser is 400mW. We approximate the beam size of our laser to have a diameter of 5mm. This corresponds to a total <math> 7.1\times 10^{10}</math> of photons arriving at the photocathode. This will result in a <math> 3.55\times 10^{10}</math> electrons being emitted per second as 2 photons are required for the two-photon photoelectric effect. Assuming that the electron multiplication yields a gain of <math> 2^{10}</math>, we then have a current of <math> 5.859\mu</math>A. The scaling goes as <math>1A = 6.242 \times 10^{18}</math> electrons per second.

===Part 4: Scaling===
In all of the above calculations, we have assumed that we have captured all of the electrons and secondary electrons emitted. This is often not the case. We assume that we can only achieve a capture rate of 10%. This would mean that we are looking for a current that is on the order of <math> 0.5859\mu A</math>.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Box2.png|400px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|left|thumb|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|right|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T09:27:31Z

WenYi: /* Actual vacuum chamber */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons is), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the photodetector, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center>Positional Accuracy: <math>\quad c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[[File:dynode_combined.png|center|500px]]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2^{10}</math>.

===Part 3: Detection===
We now need to see if the current generated by the multiplied electrons is at a detectable scale.

The average power of the laser is 400mW. We approximate the beam size of our laser to have a diameter of 5mm. This corresponds to a total <math> 7.1\times 10^{10}</math> of photons arriving at the photocathode. This will result in a <math> 3.55\times 10^{10}</math> electrons being emitted per second as 2 photons are required for the two-photon photoelectric effect. Assuming that the electron multiplication yields a gain of <math> 2^{10}</math>, we then have a current of <math> 5.859\mu</math>A. The scaling goes as <math>1A = 6.242 \times 10^{18}</math> electrons per second.

===Part 4: Scaling===
In all of the above calculations, we have assumed that we have captured all of the electrons and secondary electrons emitted. This is often not the case. We assume that we can only achieve a capture rate of 10%. This would mean that we are looking for a current that is on the order of <math> 0.5859\mu A</math>.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Box2.png|450px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|left|thumb|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|right|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T09:26:39Z

WenYi: /* Vacuum System */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons is), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the photodetector, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center>Positional Accuracy: <math>\quad c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[[File:dynode_combined.png|center|500px]]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2^{10}</math>.

===Part 3: Detection===
We now need to see if the current generated by the multiplied electrons is at a detectable scale.

The average power of the laser is 400mW. We approximate the beam size of our laser to have a diameter of 5mm. This corresponds to a total <math> 7.1\times 10^{10}</math> of photons arriving at the photocathode. This will result in a <math> 3.55\times 10^{10}</math> electrons being emitted per second as 2 photons are required for the two-photon photoelectric effect. Assuming that the electron multiplication yields a gain of <math> 2^{10}</math>, we then have a current of <math> 5.859\mu</math>A. The scaling goes as <math>1A = 6.242 \times 10^{18}</math> electrons per second.

===Part 4: Scaling===
In all of the above calculations, we have assumed that we have captured all of the electrons and secondary electrons emitted. This is often not the case. We assume that we can only achieve a capture rate of 10%. This would mean that we are looking for a current that is on the order of <math> 0.5859\mu A</math>.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Box2.png|450px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|center|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|right|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T09:25:56Z

WenYi: /* Actual vacuum chamber */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons is), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the photodetector, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center>Positional Accuracy: <math>\quad c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[[File:dynode_combined.png|center|500px]]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2^{10}</math>.

===Part 3: Detection===
We now need to see if the current generated by the multiplied electrons is at a detectable scale.

The average power of the laser is 400mW. We approximate the beam size of our laser to have a diameter of 5mm. This corresponds to a total <math> 7.1\times 10^{10}</math> of photons arriving at the photocathode. This will result in a <math> 3.55\times 10^{10}</math> electrons being emitted per second as 2 photons are required for the two-photon photoelectric effect. Assuming that the electron multiplication yields a gain of <math> 2^{10}</math>, we then have a current of <math> 5.859\mu</math>A. The scaling goes as <math>1A = 6.242 \times 10^{18}</math> electrons per second.

===Part 4: Scaling===
In all of the above calculations, we have assumed that we have captured all of the electrons and secondary electrons emitted. This is often not the case. We assume that we can only achieve a capture rate of 10%. This would mean that we are looking for a current that is on the order of <math> 0.5859\mu A</math>.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Box2.png|450px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|center|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|left|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T09:25:05Z

WenYi: /* Proposed vacuum design */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons is), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the photodetector, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center>Positional Accuracy: <math>\quad c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[[File:dynode_combined.png|center|500px]]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2^{10}</math>.

===Part 3: Detection===
We now need to see if the current generated by the multiplied electrons is at a detectable scale.

The average power of the laser is 400mW. We approximate the beam size of our laser to have a diameter of 5mm. This corresponds to a total <math> 7.1\times 10^{10}</math> of photons arriving at the photocathode. This will result in a <math> 3.55\times 10^{10}</math> electrons being emitted per second as 2 photons are required for the two-photon photoelectric effect. Assuming that the electron multiplication yields a gain of <math> 2^{10}</math>, we then have a current of <math> 5.859\mu</math>A. The scaling goes as <math>1A = 6.242 \times 10^{18}</math> electrons per second.

===Part 4: Scaling===
In all of the above calculations, we have assumed that we have captured all of the electrons and secondary electrons emitted. This is often not the case. We assume that we can only achieve a capture rate of 10%. This would mean that we are looking for a current that is on the order of <math> 0.5859\mu A</math>.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Box2.png|450px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|thumb|right|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|left|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

File:Box2.png

2021-04-30T09:23:28Z

WenYi:

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T09:22:35Z

WenYi: /* Vacuum System */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons is), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the photodetector, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center>Positional Accuracy: <math>\quad c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[[File:dynode_combined.png|center|500px]]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2^{10}</math>.

===Part 3: Detection===
We now need to see if the current generated by the multiplied electrons is at a detectable scale.

The average power of the laser is 400mW. We approximate the beam size of our laser to have a diameter of 5mm. This corresponds to a total <math> 7.1\times 10^{10}</math> of photons arriving at the photocathode. This will result in a <math> 3.55\times 10^{10}</math> electrons being emitted per second as 2 photons are required for the two-photon photoelectric effect. Assuming that the electron multiplication yields a gain of <math> 2^{10}</math>, we then have a current of <math> 5.859\mu</math>A. The scaling goes as <math>1A = 6.242 \times 10^{18}</math> electrons per second.

===Part 4: Scaling===
In all of the above calculations, we have assumed that we have captured all of the electrons and secondary electrons emitted. This is often not the case. We assume that we can only achieve a capture rate of 10%. This would mean that we are looking for a current that is on the order of <math> 0.5859\mu A</math>.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Box2.png|250px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|thumb|right|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|left|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

File:Vacuum1.png

2021-04-30T09:21:37Z

WenYi: WenYi uploaded a new version of File:Vacuum1.png

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-30T09:16:25Z

WenYi: /* Vacuum System */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a DYI system to perform a precise coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If such a metal surface is illuminated using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.

===Coincidence Time of Pulsed Lasers===
Consider the following optical setup of a simple Michelson interferometer:

[[File:interferometer.png|center|300px]]
Where the detector is a specially designed one such that it only ticks when two photons land on it at the same time.

For a cw laser, the detector will only tick when the laser beams along two paths of the Michelson interferometer interfere constructively at the detector. This is given by

<center><math>d_2 - d_1 \equiv d = n\times \lambda/2</math></center>

However, when we make the transition to pulsed lasers, things become a bit more exciting. For slow detectors that are not able to resolve the pulses (that is, their frequency bandwidth is lower than the repetition rate of the pulsed laser), the pulsed laser looks effectively like a cw laser. So, for example, if we were to check for constructive interference by using a camera (which has a typical frequency bandwidth of tens of Hertz at best), we would see a cw-like interference pattern.

If we use a fast enough detector however (which the copper target and the emitted photoelectrons is), the resonance condition changes. Consider a case where we have one incoming pulse. The pulse gets split into two at the photodetector, and each arm of the interferometer has one pulse each. Then, for the detector to tick, we need the two pulses to reach the detector within a pulse duration of each other. This thus gives us the positional accuracy we require:

<center>Positional Accuracy: <math>\quad c \times t_{\text{Pulse Duration}}</math></center>

===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here (in fact, based on the limited reading we have done, the actual mechanism behind secondary electron emissions seem to be not yet well-understood until now). In our case, the most important factor is the so-called "secondary electron emission coefficient"; a number which describes how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron emission coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply<ref>https://www.matsusada.com/product/hvps2/onboard/tm/#download</ref>.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness. Obtained from Mechanical Workshop. Thank you Bob!

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While many variables such as geometry and polishing can be optimised for this purpose, resource and time constraints meant that only the electron energy at which the primary electron hits the first dynode was a controllable variable.

In general, the plot of secondary electron emission coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy. However, regardless how deep the primary electron may penetrate, only those secondary electrons produced within the 10nm depth of the dynode are able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced<ref>https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf</ref>. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[[File:dynode_combined.png|center|500px]]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2^{10}</math>.

===Part 3: Detection===
We now need to see if the current generated by the multiplied electrons is at a detectable scale.

The average power of the laser is 400mW. We approximate the beam size of our laser to have a diameter of 5mm. This corresponds to a total <math> 7.1\times 10^{10}</math> of photons arriving at the photocathode. This will result in a <math> 3.55\times 10^{10}</math> electrons being emitted per second as 2 photons are required for the two-photon photoelectric effect. Assuming that the electron multiplication yields a gain of <math> 2^{10}</math>, we then have a current of <math> 5.859\mu</math>A. The scaling goes as <math>1A = 6.242 \times 10^{18}</math> electrons per second.

===Part 4: Scaling===
In all of the above calculations, we have assumed that we have captured all of the electrons and secondary electrons emitted. This is often not the case. We assume that we can only achieve a capture rate of 10%. This would mean that we are looking for a current that is on the order of <math> 0.5859\mu A</math>.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Vacuum1.png|250px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm. [[File:Box2.png|250px|thumb|right|Proposed vacuum design]]

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|thumb|right|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|left|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-29T13:02:48Z

WenYi: /* Measurements & Data */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a system to perform a coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If one illuminates such a metal surface using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light used.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.


===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here. In our case, the most important factor is the so-called "secondary electron coefficient", which determines how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

Brief explanation on how secondary emission occurs here?

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While there are many variables which can be optimised such that this secondary electron coefficient is maximised, resource constraints meant that only the electron energy was a variable within control.

In general, the plot of secondary electron coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy.However, regardless how deep the primary electron may penetrate, it turns out that only those secondary electrons produced within the 10nm depth of the dynode is able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[Insert 3D sketch of dynode here]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2**9</math>

[UPDATE FROM HERE ON]
===Part 3: Detection===
We now need to see if the current generated by the multipled electrons is at a detectable scale.

Our laser has a repetition rate of 120MHz. This implies that in 1 second, 120e6 number of pulses are directed at the copper cathode. Assuming that each of these pulses emit 1 electron (numbers can be changed later), a total of <math> 1 \times 120 \times 10^6 \times 2^{10} </math> electrons will arrive at the final anode. This will result in a current of <math> 1.96\times 10^{-8} A </math>.

The scaling goes as 1A = 6.242 \times 10^(18) electrons per second, meaning 32 electrons would give about 5*10**(-18) Amps.

===Part 4: Scaling===
In all of the above calculations, we have assumed that there is only one photoelectron emitted per pulse. However, the number of photoelectrons emitted is proportional to the intensity of the incident light. The exact scaling goes by

<math>N_{e} = N_{photon} = \frac{I\times A}{h\times f} </math>

Taking I = 400mW, r = 0.mm (beam radius), the number of electrons emitted would be about 561 million. The amount of current generated would scale proportionally with the number of electrons captured by the electron multiplier.

In this case, if we take 1nA to be a detectable current, we would thus need 10^(-18)/10^(-9) = 10^9 electons, or about 100 million electrons. That would mean we need about 1/5 capture of the emitted photoelectrons.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Vacuum1.png|250px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|thumb|right|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|left|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-29T13:00:50Z

WenYi: /* Measurements & Data */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a system to perform a coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If one illuminates such a metal surface using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light used.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.


===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here. In our case, the most important factor is the so-called "secondary electron coefficient", which determines how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

Brief explanation on how secondary emission occurs here?

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While there are many variables which can be optimised such that this secondary electron coefficient is maximised, resource constraints meant that only the electron energy was a variable within control.

In general, the plot of secondary electron coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy.However, regardless how deep the primary electron may penetrate, it turns out that only those secondary electrons produced within the 10nm depth of the dynode is able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[Insert 3D sketch of dynode here]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2**9</math>

[UPDATE FROM HERE ON]
===Part 3: Detection===
We now need to see if the current generated by the multipled electrons is at a detectable scale.

Our laser has a repetition rate of 120MHz. This implies that in 1 second, 120e6 number of pulses are directed at the copper cathode. Assuming that each of these pulses emit 1 electron (numbers can be changed later), a total of <math> 1 \times 120 \times 10^6 \times 2^{10} </math> electrons will arrive at the final anode. This will result in a current of <math> 1.96\times 10^{-8} A </math>.

The scaling goes as 1A = 6.242 \times 10^(18) electrons per second, meaning 32 electrons would give about 5*10**(-18) Amps.

===Part 4: Scaling===
In all of the above calculations, we have assumed that there is only one photoelectron emitted per pulse. However, the number of photoelectrons emitted is proportional to the intensity of the incident light. The exact scaling goes by

<math>N_{e} = N_{photon} = \frac{I\times A}{h\times f} </math>

Taking I = 400mW, r = 0.mm (beam radius), the number of electrons emitted would be about 561 million. The amount of current generated would scale proportionally with the number of electrons captured by the electron multiplier.

In this case, if we take 1nA to be a detectable current, we would thus need 10^(-18)/10^(-9) = 10^9 electons, or about 100 million electrons. That would mean we need about 1/5 capture of the emitted photoelectrons.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Vacuum1.png|250px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|thumb|right|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|left|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Non-Vacuum Attempt ==

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

File:Optical table.png

2021-04-29T13:00:05Z

WenYi:

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-29T12:59:35Z

WenYi: /* Measurements & Data */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a system to perform a coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If one illuminates such a metal surface using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light used.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.


===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here. In our case, the most important factor is the so-called "secondary electron coefficient", which determines how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

Brief explanation on how secondary emission occurs here?

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While there are many variables which can be optimised such that this secondary electron coefficient is maximised, resource constraints meant that only the electron energy was a variable within control.

In general, the plot of secondary electron coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy.However, regardless how deep the primary electron may penetrate, it turns out that only those secondary electrons produced within the 10nm depth of the dynode is able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[Insert 3D sketch of dynode here]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2**9</math>

[UPDATE FROM HERE ON]
===Part 3: Detection===
We now need to see if the current generated by the multipled electrons is at a detectable scale.

Our laser has a repetition rate of 120MHz. This implies that in 1 second, 120e6 number of pulses are directed at the copper cathode. Assuming that each of these pulses emit 1 electron (numbers can be changed later), a total of <math> 1 \times 120 \times 10^6 \times 2^{10} </math> electrons will arrive at the final anode. This will result in a current of <math> 1.96\times 10^{-8} A </math>.

The scaling goes as 1A = 6.242 \times 10^(18) electrons per second, meaning 32 electrons would give about 5*10**(-18) Amps.

===Part 4: Scaling===
In all of the above calculations, we have assumed that there is only one photoelectron emitted per pulse. However, the number of photoelectrons emitted is proportional to the intensity of the incident light. The exact scaling goes by

<math>N_{e} = N_{photon} = \frac{I\times A}{h\times f} </math>

Taking I = 400mW, r = 0.mm (beam radius), the number of electrons emitted would be about 561 million. The amount of current generated would scale proportionally with the number of electrons captured by the electron multiplier.

In this case, if we take 1nA to be a detectable current, we would thus need 10^(-18)/10^(-9) = 10^9 electons, or about 100 million electrons. That would mean we need about 1/5 capture of the emitted photoelectrons.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Vacuum1.png|250px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|thumb|right|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|left|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

[[File:optical_table.png|center|500px]]

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-29T12:50:12Z

WenYi: /* Measurements & Data */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a system to perform a coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If one illuminates such a metal surface using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light used.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.


===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here. In our case, the most important factor is the so-called "secondary electron coefficient", which determines how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

Brief explanation on how secondary emission occurs here?

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While there are many variables which can be optimised such that this secondary electron coefficient is maximised, resource constraints meant that only the electron energy was a variable within control.

In general, the plot of secondary electron coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy.However, regardless how deep the primary electron may penetrate, it turns out that only those secondary electrons produced within the 10nm depth of the dynode is able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[Insert 3D sketch of dynode here]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2**9</math>

[UPDATE FROM HERE ON]
===Part 3: Detection===
We now need to see if the current generated by the multipled electrons is at a detectable scale.

Our laser has a repetition rate of 120MHz. This implies that in 1 second, 120e6 number of pulses are directed at the copper cathode. Assuming that each of these pulses emit 1 electron (numbers can be changed later), a total of <math> 1 \times 120 \times 10^6 \times 2^{10} </math> electrons will arrive at the final anode. This will result in a current of <math> 1.96\times 10^{-8} A </math>.

The scaling goes as 1A = 6.242 \times 10^(18) electrons per second, meaning 32 electrons would give about 5*10**(-18) Amps.

===Part 4: Scaling===
In all of the above calculations, we have assumed that there is only one photoelectron emitted per pulse. However, the number of photoelectrons emitted is proportional to the intensity of the incident light. The exact scaling goes by

<math>N_{e} = N_{photon} = \frac{I\times A}{h\times f} </math>

Taking I = 400mW, r = 0.mm (beam radius), the number of electrons emitted would be about 561 million. The amount of current generated would scale proportionally with the number of electrons captured by the electron multiplier.

In this case, if we take 1nA to be a detectable current, we would thus need 10^(-18)/10^(-9) = 10^9 electons, or about 100 million electrons. That would mean we need about 1/5 capture of the emitted photoelectrons.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Vacuum1.png|250px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|thumb|right|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|left|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =

The completed setup is placed on the optical table and tested. On the right is a photo of the set up of the optical table. The laser beam of beam size 1mm is magnified to 5mm by 2 lenses before being split into two paths. They are recombined again before being directed at the box.

Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-29T07:01:47Z

WenYi: /* Voltage Divider Characterisation */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a system to perform a coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If one illuminates such a metal surface using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light used.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.


===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here. In our case, the most important factor is the so-called "secondary electron coefficient", which determines how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

Brief explanation on how secondary emission occurs here?

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While there are many variables which can be optimised such that this secondary electron coefficient is maximised, resource constraints meant that only the electron energy was a variable within control.

In general, the plot of secondary electron coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy.However, regardless how deep the primary electron may penetrate, it turns out that only those secondary electrons produced within the 10nm depth of the dynode is able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[Insert 3D sketch of dynode here]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2**9</math>

[UPDATE FROM HERE ON]
===Part 3: Detection===
We now need to see if the current generated by the multipled electrons is at a detectable scale.

Our laser has a repetition rate of 120MHz. This implies that in 1 second, 120e6 number of pulses are directed at the copper cathode. Assuming that each of these pulses emit 1 electron (numbers can be changed later), a total of <math> 1 \times 120 \times 10^6 \times 2^{10} </math> electrons will arrive at the final anode. This will result in a current of <math> 1.96\times 10^{-8} A </math>.

The scaling goes as 1A = 6.242 \times 10^(18) electrons per second, meaning 32 electrons would give about 5*10**(-18) Amps.

===Part 4: Scaling===
In all of the above calculations, we have assumed that there is only one photoelectron emitted per pulse. However, the number of photoelectrons emitted is proportional to the intensity of the incident light. The exact scaling goes by

<math>N_{e} = N_{photon} = \frac{I\times A}{h\times f} </math>

Taking I = 400mW, r = 0.mm (beam radius), the number of electrons emitted would be about 561 million. The amount of current generated would scale proportionally with the number of electrons captured by the electron multiplier.

In this case, if we take 1nA to be a detectable current, we would thus need 10^(-18)/10^(-9) = 10^9 electons, or about 100 million electrons. That would mean we need about 1/5 capture of the emitted photoelectrons.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Vacuum1.png|250px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|thumb|right|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|left|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =
Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors. Running the voltage supply at 10V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />

Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

2021-04-29T06:48:36Z

WenYi: /* Electron Multiplier & Secondary Emission */

===Members===
Tan Wen Yi, Kim Mu Young

==Abstract==
Given two paths through a which a pulsed laser propagates, one might be interested in ensuring that the pulses coincide at the same spatial point at the same time. One possible situation where such a coincidence measurement may be useful is in the driving of Raman transitions in an atom via a pulsed laser. We intend to perform such a coincidence time measurement using commonly-available metals. By choosing a material with a work function on the order of the energies of two photons, the detection of a photocurrent through a metal would then indicate that both laser pulses arrived at the metal at approximately the same time. However, the amount of current generated directly from these photoelectrons is minimal at best, and thus very hard to detect. In this project, we use a copper target along with a home-build electron multiplier in a vacuum chamber to look at the possibility of using such a system to perform a coincidence time measurement.

=Theory=

===Photoelectric Effect===
The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of light<ref>Photoelectric effect. (2021, March 17). Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect</ref>. Every metal surface has a characteristic number known as the work function, <math> \phi </math>. This number describes the amount of energy required for an electron to be ejected from a metal's crystal structure into the continuum. If one illuminates such a metal surface using some light, the energy of an emitted electron is characterised by the following equation:

<math>\qquad E_{electron} = hf - \phi</math>

Where <math>h</math> is the Planck's constant and <math>f</math> is the frequency of light used.

There are three possible cases depending on the frequency of light used:

<math>
\begin{cases}
hf < \phi \rightarrow E_{electron} < 0 \quad \rightarrow \quad \text{No electrons emitted} \\
hf = \phi \rightarrow E_{electron} = 0 \quad \rightarrow \quad \text{Surface electrons}\\
hf > \phi \rightarrow E_{electron} > 0 \quad \rightarrow \quad \text{Electrons are emitted with kinetic energy} \, E_{electron}
\end{cases}
</math>

Importantly, the frequency of light only determines the kinetic energy of the emitted photoelectron. To increase the number of photoelectrons produced, one has to increase the intensity of light. A higher intensity would mean that more photons are incident on the metal surface, meaning more electrons will be excited to the continuum.


===Pulsed Lasers===
Pulsed lasers differ from the more commonly found continuous wave (cw) lasers in that they emit light in a discrete manner in time. The difference between the two can be understood from the following picture:

[[File:pulsevscw.png|center|500px]]

Lasers are usually charactersied by two properties: the wavelength and output power. In the case of pulsed lasers, pulse duration (how long each pulse lasts in time) and repetition rate (how many pulses are emitted per second) are additional properties that one has to take note of.


===Electron Multiplier & Secondary Emission===
Electron multipliers, as their name suggests, are devices which amplify the number of electrons present in a given system. This amplification is necessary as the photoelectrons emitted generates minimal currents, which are very difficult to measure. The use of an electron multiplier results in more electrons and thus larger currents, which may then be measured without the need for special circuits. A diagram of an electron multiplier is shown below:

[[File:pmt.png|center|700px]]

An electron multiplier is typically formed by the following components: a target from which photoelectrons are emitted, dynodes which perform the actual electron multiplication, a high voltage source to drive the dynodes, and finally a resistor chain to distribute the voltages appropriately to the dynodes. The last three components are discussed in detail below.

====Dynodes====
Dynodes are typically thin metal sheets which perform the actual multiplication in an electron multiplier. Typical materials used for dynodes include copper beryllium oxide (Cu-BeO), aluminimum oxide (Al2O3)<ref>https://www.hamamatsu.com/resources/pdf/etd/EMT_TPMH1354E.pdf</ref>, and, in our case, steel (iron alloys). The factors which determine what materials are best suited as a dynode is complicated and will not be discussed here. In our case, the most important factor is the so-called "secondary electron coefficient", which determines how many electrons are produced when an electron is incident on the surface of the material. To give a sense of scale, Cu-BeO has a secondary electron coefficient of about 7<ref>https://journals-jps-jp.libproxy1.nus.edu.sg/doi/pdf/10.1143/JPSJ.8.318</ref>; Al2O3 of about 4<ref>https://aip-scitation-org.libproxy1.nus.edu.sg/doi/pdf/10.1063/1.5113671</ref>, and finally steel of about 2<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>.

Brief explanation on how secondary emission occurs here?

==== High Voltage & Resistor Chain ====
Typically, electron multipliers have about 10 dynodes to perform sufficient amplification for a detectable amount of current to be generated at the end of the multiplication chain. Thus, the design of an electron multiplier also requires consideration of how electrons are to be propagated from one dynode to the next in a systematic and controller manner such that the overall gain is a constant value. This is where a high voltage supply and a resistor chain becomes necessary.

The first solution that would probably come to mind would be to place the dynodes in steadily increasing positive voltages. The increasing voltages will attract the electron towards the dynodes due to electrostatic attraction, which will thus ensure a systemic and controlled propagation. However, one constraint that the voltage assignments face is that the final dynode at the end of the multiplication chain should be at zero potential. While this is not technically necessary since we are only interested in detecting a current, the safety concerns that arise due to high-voltage wires flying about in air is too severe to be ignored. This subsequently means that the dynodes must be operated at steadily decreasing negative voltages.

==== Electron Multipliers & Vacuum ====
Electron multipliers are typically operated in vacuum. This is necessary due to the fact that the mean free path of electron in air is on the order of sub-micrometers<ref>https://ieeexplore.ieee.org/document/8785907</ref>, and thus requires the dynodes to be very close to each other for the electrons to successfully move from one dynode from another. However, the proximity of dynodes causes construction and field emissions to be a possible significant issue. By operating the entire system in vacuum, the mean free path of electrons is much longer, and thus the dynodes can be placed at reasonable distances apart from each other.

=Project Breakdown=

==Parameters of Key Devices==
'''Laser: Coherent Paladin Compact'''

Details: 355nm, 15ps pulse duration, 120MHz repetition rate, 4W output power but about 400mW is actually available.

'''Photocathode - Copper sheet'''

Details: Work function of approximately 4.6eV<ref>https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0231#:~:text=The%20work%20functions%20of%20surfaces,%C2%B1%200%C2%B705%20eV%20respectively.</ref>

'''Vacuum - Acrylic Enclosure'''

Details: Thank you Imran!

'''Vacuum Pump - Agilent Varian TriScroll 300'''

Details: Dry scroll vacuum pump with maximum inlet pressure of 1 atm and ultimate pressure of <math>1.0 \times 10^{-2}</math> Torr. Pumping speed of <math>12.6 \, m^3/hr</math><ref>https://www.ajvs.com/library/Agilent_Varian_Triscroll_300_Manual.pdf</ref><ref>https://www.ajvs.com/library/Varian_Triscroll_300_600_Broshure.pdf</ref>

'''Vacuum Gauge - Agilent RGC-100'''

Details: Measures from <math>1 \times 10^{-3}</math> Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection. <ref>https://www.idealvac.com/files/manuals/Agilent-Varian_RGC-100Gauge_DataS.pdf</ref><ref>https://www.agilent.com/cs/library/usermanuals/public/RGC-100%20Model%20RGC-100%20Series%20Digital%20Vacuum%20Gauge%20Installation%20and%20%20Operation%20Manual.pdf</ref>

'''High Voltage Source - Matusada Precision TM-3N'''

Details: A negative 3000 volts power supply.

'''Dynode - Stainless Steel'''

Details: Flat sheets of about 3mm thickness

== Electron Multiplier Design Considerations ==
The main concern in the design of the electron multiplier is the voltages to apply to the cathode (copper target) and the subsequent dynodes. We examine these two considerations one by one.

===Cathode & First Dynode Voltages===
In order to maximise the signal strength at the end of the electron multiplication stage, we need to ensure that the primary electron (the photoelectrons emitted from the cathode) generates the maximum amount of secondary electrons at the first dynode. While there are many variables which can be optimised such that this secondary electron coefficient is maximised, resource constraints meant that only the electron energy was a variable within control.

In general, the plot of secondary electron coefficient against primary electron energy takes the form below<ref>https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf</ref>:

[[File:secondary_electron_emission_coefficient.png|center|500px]]

In general, across most dynode materials, there is an initial increase in secondary electron emissions with voltage. However, after reaching a maximum value, the number of emitted secondary electrons decay back down to low, undesired levels. The physical reason for the above graph is as follows.

The energy of the incident primary electron dictates how deep through the dynode the electron can penetrate before it losses its momentum and is unable to cause any secondary electron production. This explains the low-energy regime of the above plot, where one observes a increase in secondary electron production with increase in primary electron energy.However, regardless how deep the primary electron may penetrate, it turns out that only those secondary electrons produced within the 10nm depth of the dynode is able to escape. As such, if the primary electron penetrates any deeper than this depth, there are no additional secondary electrons produced. While we have not been able to find any definite literature explaining why there is a drop in secondary electron production, our guess is that due to the faster velocity of the primary electron, the interaction time between the electron and the metal within the first 10nm decreases. This thus may result in fewer secondary electrons being emitted, as most of the interaction occurs when the primary electron is slow enough, which only occurs when the electron is already beyond the 10nm depth from the surface.

Unfortunately, there seems to be no agreed-on relation between secondary electron emission and primary electron energy for stainless steel. As such, we have decided to go ahead with the information presented from the graph above. According to that source, the maximum secondary electron emission of around 2 occurs at a primary electron energy of 300eV. This thus consequently means that the potential difference between the cathode and the first dynode need to be about 300V as well.

===Subsequent Dynodes===
When we go onto the secondary dynodes, the objective remains the same. We wish to apply appropriate voltages to the dynodes such that the further electron emissions are maximised. The difference here comes from the fact that the incoming electrons are now secondary electrons emitted from the first dynode. As such, we need to figure out what kind of energies these secondary electrons are emitted at. (https://www.classe.cornell.edu/~critten/cesrta/ecloud/doc/PhilJRes50_1996_375.pdf) measured the energy distribution of the secondary electron emissions from stainless steel and found the following plot:

[[File:secondary_electron_energy.png|center|500px]]

Which thus tells us that, unfortunately, the secondary electrons are only ejected with an every of around 4eV. This is very much lower than the optimal 300eV we require for further electron amplification. As such, this suggested to us that the dynodes themselves need to be separated by around 300V as well.

===Dynode Geometry===
[[File:dynode_setup.png|500px|thumb|right|Sketch of the dynodes and their respective voltages]]

There are two things that we considered with regards to the geometry of the dynodes. First, to minimise field emissions, we had to minimise any sharp edges of the dynodes along the electron path. Second, to maximise the capture rate of the produced electrons, we were considering a concentric circle design for the dynodes such that the emitted electrons would be "focused" to the next dynode and so on till the final dynode.

[Insert 3D sketch of dynode here]

Unfortunately, again due to the lack of time, we could not come up with a mounting base good enough to rigidly hold the above-drawn dynodes up. We ended up using a simple flat rectangular dynodes instead.

==Basic Calculations==
We present here some key calculations required for the design and construction of this experimental setup.

===Part 1: Photoemission===
The energy associated to a wavelength of 355nm is given by

<math>E_{\lambda} = hf = h\times c/\lambda \approx 3.493 \, eV </math>

Compared to the work function of copper, <math>\phi_{Cu} = 4.6 \, eV</math>, we conclude that one photon is insufficient for the release of a photoelectron. We assume here that there are no additional energies due to thermal excitations within the copper itself, the validity of which remains to be seen.

For two photons at 355nm:

<math>E_{e} = 2hf - 4.6 \approx 2.385 \, eV</math>

This consequently means that should two 355nm pulses arrive at the copper at the same time, photoelectrons can indeed be emitted with a kinetic energy of about <math> 2.4 \, eV</math>.

===Part 2: Dynodes & Electron Multiplication===
Based on the secondary electron emission coefficients as studied above, we came to the conclusion that the cathode and the dynodes all need to be separated by the same potential difference. Also mentioned above, the high voltage supply we have obtained has a maximum output of 2500V. This would consequently mean that it would not be possible to run the copper and the dynodes at voltage separations of 300V. Fortunately, the secondary electron coefficient is about the same at a lower energy of 250V. This supply would thus be exactly sufficient to run the copper cathode and the dynodes at a voltage separations of 250V between each element. In total, this would thus allow for 10 dynodes, with the last one being at zero potential.

With each dynode providing a electron multiplication factor of 2, the total gain would then be given by <math>2**9</math>

[UPDATE FROM HERE ON]
===Part 3: Detection===
We now need to see if the current generated by the multipled electrons is at a detectable scale.

Our laser has a repetition rate of 120MHz. This implies that in 1 second, 120e6 number of pulses are directed at the copper cathode. Assuming that each of these pulses emit 1 electron (numbers can be changed later), a total of <math> 1 \times 120 \times 10^6 \times 2^{10} </math> electrons will arrive at the final anode. This will result in a current of <math> 1.96\times 10^{-8} A </math>.

The scaling goes as 1A = 6.242 \times 10^(18) electrons per second, meaning 32 electrons would give about 5*10**(-18) Amps.

===Part 4: Scaling===
In all of the above calculations, we have assumed that there is only one photoelectron emitted per pulse. However, the number of photoelectrons emitted is proportional to the intensity of the incident light. The exact scaling goes by

<math>N_{e} = N_{photon} = \frac{I\times A}{h\times f} </math>

Taking I = 400mW, r = 0.mm (beam radius), the number of electrons emitted would be about 561 million. The amount of current generated would scale proportionally with the number of electrons captured by the electron multiplier.

In this case, if we take 1nA to be a detectable current, we would thus need 10^(-18)/10^(-9) = 10^9 electons, or about 100 million electrons. That would mean we need about 1/5 capture of the emitted photoelectrons.

=Construction of Setup=
The entire setup consists of three main parts; the vacuum system, the high voltage setup and the electron-multiplier setup. Here we outline the work done for each of these before presenting the completed setup.

==Vacuum System==

===Proposed vacuum design===
[[File:Vacuum1.png|250px|thumb|right|Proposed vacuum design]]
On the right is a screenshot of the proposed vacuum design. The box for the vacuum will be made out of acrylic of 10mm thick. The internal of the box will measure 10cm x 10cm x 10cm, making the entire box 12cm x 12cm x 12cm.

Referencing the photo of the proposed vacuum design, the front wall of the box is the one that has a different transparency compared to the others. It also has a hole designed with a ledge for a window to sit in. We can then direct the laser through the window without having any refraction problems that may occur should we choose to direct the laser through the acrylic. The wall on the left of the front wall has 4 small holes designated to be the screw holes for the two plates on which the dynodes are attached. The plates will sit flushed to the wall on the inside of the chamber and thus the holes and the screws are not exposed to the vacuum.

There are also 2 holes on the wall on the right. They are meant to be the hole through which we have a pressure gauge and a tube for the connection to the vacuum pump.

===Actual vacuum chamber===
The box for the vacuum was made almost exactly like the drawing in SolidWorks. The major difference lies in the hole that was meant for a mirror to sit in. The original design included 2 concentric holes of 2 different diameters cut to different depth. The mirror is supposed to sit in the hole with the larger diameter so that it can sit flushed against the outer side of the box. During production we were informed that this was not doable. The end product only has a through hole of 1 diameter that is smaller than that of the window.

[[File:box.png|250px|thumb|right|Actual vacuum chamber made from acrylic]]

The 6 faces of the box are held together using M3 screws. It is to be noted that the screws should not be overly tightened as it will cause the acrylic box to crack. All of the screws are not exposed to the vacuum. We have also labelled the outer face of each wall using a marker.

===Window===
As mentioned before, the ledge in the hole designated for the window can't be cut out and thus there is no ledge for the window to sit inside the hole and flushed against the box. To get around this, we placed the window over the designated hole, outside of the box and torr sealed it. The idea is that when the box is being pumped down, the lower pressure inside of the box will cause a force to act on the window over the hole, thereby sealing it properly. A photo of this can be found on the left.

[[File:window_2.jpg|250px|thumb|left|Window is placed over the hole and torr sealed.]]

===Vacuum pump===
For the vacuum pump, we have a hole the size of an steel tube cut out on one of the walls of the box. The tube is then connected and secured to a valve which can then be attached to the vacuum pump. The valve is of a larger size than that of the hole on the face of the box. Thus, similar to the window, we flushed it against the wall of the box and over the hole and torr sealed it. The tube extends into the box and is of a length of 5cm.

[[File:valve.jpg|250px|thumb|left|Valve and tube torr sealed for the vacuum pump.]]

===Vacuum Gauge===
Due to the lack of hardware, we were not able to find a way to mount the above-mentioned Agilent vacuum gauge onto the vacuum chamber. As we still need to perform some sort of pressure measurement, we are intending to share the vacuum pump tube with the vacuum gauge.

Specifically, we shall first pump down the chamber for about an hour or two. We will then disconnect the pump and replace it with the vacuum gauge, following which we will monitor the pressure for another hour or two. This monitoring over time should give us an idea of how "tight" the vacuum valve is. After which, we will replace the gauge with the pump again and completely pump down.

==The High Voltage Supply==
The high voltage supply that we have is a Matusada Precision TM-3N, negative 3000V supply.

It has a high voltage (HV) output and a HV monitor labelled Vmon.

The output of the HV is controlled by a knob which has a total of 10 turns. We assumed that each turn corresponds to a voltage of 300V. We connected a BNC cable from the Vmon connector to an multimeter and compared the multimeter reading to the display on the front of the HV supply. We found that for a range of voltage below kV, they differ by a factor of 1000. We were unable to verify the operation of the power supply at high voltage (above 800?V) as the multi-meter can only take up to 1kV. We then attempted to test the voltage output of this supply by connecting a series of 4 metal-film resistors with values of 10M<math> \Omega </math>, essentially forming a potential divider, and measuring the voltage across each resistors. What we expected was that at 2kV, the potential drop across each resistor should be of an equal and consistent value of 500V. This was however not the case and after checking the data sheet, we concluded that this is likely due to the fact that the metal film resistors cannot be operated at such high voltages. The characterization of the voltage divider will be discussed in a following [[#Voltage Divider Characterisation|section]].

[[File:HV.jpg|200px|thumb|right|Front panel of the high voltage supply.]]

Just as a side-note. According to https://www.diyaudio.com/forums/parts/248300-resistor-maximum-voltage-rating.html, the maximum voltage rating of a resistor is not defined as the absolute voltage input into a circuit but rather the maximum voltage drop across a resistor. Now, this potentially doesn't make sense with the 30M<math> \Omega </math> resistor circuit we used to test the high voltage supply earlier, but at this point we can only hope for the best and trust that the 1.5k voltage rating on the bought resistors is sufficient to withstand whatever we're going to be throwing at them and give appropriate voltage divisions.

==The Electron-Multiplier Setup==
===Dynodes===
Strips of stainless steel of a 3mm thickness are used as the dynodes for the electron-multiplier. Using an adhesive, we secured the dynodes to the plates that are attached to the side of the vacuum chamber. They are arranged in a staggered manner such that the first dynode is placed on the top and closest to the copper cathode while the second is on the bottom plate and so on. We moved away from a curved design as that proved to be difficult when securing the dynodes and thus the stainless steel strips are pasted flat on the two plates. The strips are cleaned with detergent in an ultrasonic bath prior to setting up.

===Copper cathode===
We used a piece of copper as the cathode, onto which the laser light is directed. The copper is 8cm in height and a 4cm width. The copper is sanded using sandpaper to remove any copper oxide that may have formed on the surface. We then cleaned it with detergent before securing it to the top of the box using adhesive.

===Voltage divider===
The voltage divider is made of ten 10M<math> \Omega</math> resistors soldered together in series. We drilled an additional hole in the acrylic the size of the miniature high voltage (MHV) connector to allow it to be put through the acrylic. We then torr sealed it using a similar idea as the vacuum valve. The chain of resistors are then secured to the inner walls of the acrylic box using adhesive. The wires from the voltage dividers are then attached to the dynodes according to the setup [[#Dynode Geometry|discussed previously]]. Unfortunately, the wires cannot be soldered onto the stainless steel dynodes effectively. Thus we made a bent at the end of the stainless steel and threaded the wire through them. We then checked for electrical contact before crimping down on the bent and soldering the wires such that they made a loop around the bent. The wires are also adhered to the walls to ensure that they do not come into contact with each other during operation.

The wire that is connected to the last dynode also extends out of the box through a tiny hole drilled at the side of the hole meant for the MHV conncector. This wire is designated for detecting the current after the electron multiplication.

==Completed Setup==
The completed setup is as shown below. The photo is taken when the torr seal (white paste) is being cured for 24 hours.

[[File:Completed_setup.png|center|500px]]

= Measurements & Data =
Here we record some of the measurement collected throughout this project. This include the characterisation of the voltage divider and the vacuum.
== Voltage Divider Characterisation ==
Due to the very high voltages employed in this set-up, we had problems with using the resistors available in the electrical workshop. With four equal resistors of 10M<math> \Omega</math> connected in series from live to ground directly, the voltage was not split equally into four across the four resistors. We believed that this was due to the driving voltage being higher than the maximum voltage rating for the resistors. Thus, we proceeded to purchase 10M<math> \Omega</math> resistors rated for 1500V for use in this project.

To ensure that these resistors were indeed working properly, we set-up a simple resistor chain consisting of 10 such resistors directly connected between the live and ground pin of the miniature high voltage (MHV) connector. Running the high voltage supply at 10V and 2500V, we measured the voltage <math>V_{R}</math> across each resistor. We should expect that the 10V applied be divided even between each of the 10 resistors, resulting in 1V each. Yet we noticed that the voltage across each resistor is only 0.5V. The theory was that the resistors are not mean for high voltage operation is not valid here as the voltage applied across the entire chain is only 10V, yet the discrepancy still persists. Eventually it was discovered that this discrepancy was due to the fact that there is an internal resistance in the multimeter for the measurement of voltages. This internal resistance coincidentally also is of a value of 10M<math> \Omega</math>, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M<math> \Omega</math> resistance, the supposed voltage drop across the resistor is now divided between it and the internal resistance of the multimeter, resulting in a voltage reading that is halved. To verify this, we redid the test with a chain of resistors of values R = 500k<math> \Omega</math>. As now the resistors under test have a resistance value that is an order of magnitude smaller than the internal resistance of the multimeter, the discrepancy is gone. The data recorded is shown below:

{| class="wikitable"
|+Voltage Divider Test @ 10V
|-
!Resistor
!<math>V_{R = 10M\Omega} (V)</math>
!<math>V_{R = 500k\Omega} (V)</math>
|-
|Resistor 1
|0.549
|0.987
|-
|Resistor 2
|0.550
|0.986
|-
|Resistor 3
|0.549
|0.986
|-
|Resistor 4
|0.550
|0.990
|-
|Resistor 5
|0.556
|0.983
|-
|Resistor 6
|0.558
|0.985
|-
|Resistor 7
|0.576
|0.986
|-
|Resistor 8
|0.576
|0.987
|-
|Resistor 9
|0.574
|0.987
|-
|Resistor 10
|0.563
|0.987
|}

== Vacuum Attempt ==

== Background Reading ==

== Success? ==

=References=
<references />