Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

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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. Every metal surface has a characteristic number known as the work function, $\varphi$. 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:

$E_{electron}=hf-\varphi$

Where $h$ is the Planck's constant and $f$ is the frequency of light.

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

$\{\begin{array}{c}hf<\varphi \to E_{electron}<0\to \text{No electrons emitted}\\ hf=\varphi \to E_{electron}=0\to \text{Surface electrons}\\ hf>\varphi \to E_{electron}>0\to \text{Electrons are emitted with kinetic energy}{E}_{electron}\end{array}$

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:

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:

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

$d_2-d_1\equiv d=n\times \lambda /2$

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:

$|d|<c\times t_{\text{Pulse Duration}}$

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:

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 ($A{l}_2{O}_3$), 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; $A{l}_2{O}_3$ of about 4, and finally steel of about 2.

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, 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

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 $1.0\times 10^{-2}$ Torr. Pumping speed of $12.6m^3/hr$

Vacuum Gauge - Agilent RGC-100

Details: Measures from $1\times 10^{-3}$ Torr till 1 atm. Works via temperature measurement of a thermistor. KF connection.

High Voltage Source - Matusada Precision TM-3N

Details: A negative 3000 volts power supply.

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.

Window - Thorlabs WG41050

Details: >90% transmission at 355nm

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:

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. 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:

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

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.

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

$E_{\lambda }=hf=h\times c/\lambda \approx 3.493eV$

Compared to the work function of copper, ${\varphi }_{Cu}=4.6eV$, 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:

$E_e=2hf-4.6\approx 2.385eV$

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 $2.4eV$.

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:

$N_{\text{photons}}=\frac{P}{\pi r^2}\times \frac{\pi r^2}{hf}\approx 7.1\times 10^{10}$

Where $h$ is Planck's constant.

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

$N_{\text{electrons}}=\frac{1}{2}\times N_{\text{photons}}\approx 3.55\times 10^{10}$

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 $2^{10}$.

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 $0.5859\mu A$. 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.

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.

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

Completed Vacuum Chamber

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

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.

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

The voltage divider is made of ten 10M$\Omega$ 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 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.

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$\Omega$ 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$\Omega$ 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 $V_R$ 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$\Omega$, the same as the value of the resistance used. Thus, when we connect the multimeter across a single resistor of 10M$\Omega$ 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$\Omega$. 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:

Voltage Divider Test @ 10V

Resistor	$V_{R=10M\Omega }(V)$	$V_{R=500k\Omega }(V)$
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