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 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. 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 one illuminates such a metal surface 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 used.

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.

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 multiple 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 from, 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), 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; Al2O3 of about 4, and finally steel of about 2.

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, ne 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, 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

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:

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:

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

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

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

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: 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 $2\ast \ast 9$

[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 $1\times 120\times 10^6\times 2^{10}$ electrons will arrive at the final anode. This will result in a current of $1.96\times 10^{-8}A$.

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

$N_e=N_{photon}=\frac{I\times A}{h\times f}$

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

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.

Actual vacuum chamber made from acrylic

The 6 faces of the box are held together using M? 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.

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.

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.

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 V monitor connector to an multi-meter and compared the multi-meter 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 $10M\Omega$, 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.

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 ohm 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.

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 HV 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 also using adhesive.

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$\Omega$ 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 directly connected between the live and ground pin of the miniature high voltage (MHV) connector. Running the high voltage supply at 1000V and 2500V, we measured the voltage across each resistor. The data recorded is shown below:

Voltage Divider Test

Resistor	1000V	2500V
Resistor 1	Voltage 1
Resistor 2	Pie
Resistor 3	Ice cream
Resistor 4	Ice cream
Resistor 5	Ice cream
Resistor 6	Ice cream
Resistor 7	Ice cream
Resistor 8	Ice cream
Resistor 9	Ice cream
Resistor 10	Ice cream

Once again, we were unable to have the voltage divider working appropriately. It seems that the final resistor always has a voltage drop across it of a value that is half that of the total voltage applied. The remaining voltage is then divided evenly across the remaining resistors.