Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications

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 on the same spatial point at exactly the same time. One possible situation where such a coincidence may be useful is in the driving of Raman transitions 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 355nm 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. The project first aims to find such a metal and design a set-up to perform this experiment; after which, we intend to measure the timing resolution such a method is limited to. If time permits, we then intend to try to use this method to perhaps characterise the density/surface smoothness and other possible features of the metal object used.

Theory

Photoelectric Effect

The photoelectric effect is a simple yet revolutionary phenomena, being one of the first experiments to show the quantisation of energy. Every metal surface has a characteristic feature known as the work function ($\varphi$) which describes the amount of energy required for an electron to be ejected from its crystal structure into the continuum. If one illuminates such a metal surface using some light source, the energies of the electrons that are emitted are characterised by a simple equation:

$E_{electron}=hf-\varphi$

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

There are three possible results based on the frequency of light.

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

A typical set-up used to test the model described above goes as the following (obtained from https://physicscatalyst.com/chemistry/photoelectric-effect.php, but will make our own later on):

A light source is used to illuminate a metal surface. If the frequency of the light is high enough, electrons are ejected from the surface. These ejected electrons are accelerated onto a detector via the application of an external potential. Once these electrons fall upon the detector, they travel through the wires, causing a current to be detected. As such, depending on the lack or presence of a current, one could tell if the frequency of light used is sufficiently high to overcome the work function of the metal.One additional note regarding this experiment is that the amount of current detected is not proportional to the frequency, but rather the intensity of light. While a higher frequency of light would provide the electrons with higher kinetic energies, this does not lead to a rise in current. However, a larger intensity, corresponding to a larger number of photons, would mean that more electrons are emitted, causing higher currents.

Pulsed Lasers

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

In addition to the usual parameters that characterises a laser; the wavelength and the power, pulsed lasers have two additional important numbers. The first is the pulse duration, which refers to how long each pulse lasts in the time domain. The second is the repetition rate, or how many pulses are emitted per second.

Electron Multiplication & Secondary Emission

Unfortunately, for us to actually measure a photoelectric current, a simple photoelectric set-up would not be sufficient. This is simply because the number of photons and thus number of electrons emitted only gives very small currents, which require amplifications for successful detection. This analogue electron amplification is done via what's known as the electron multiplier, using the theory of secondary emission.

A sample diagram of an electron multipler is shown below:

The bulk of the electron multiplier is formed by dynodes, which are basically metallic plates that are subjected to high voltages. The first of such dynodes, referred to as the primary dynode, is at the highest voltage, with subsequent dynodes at lower voltages in steps of about a 100V. The high voltage helps to accelerate the electrons towards the electron multiplier, ensuring high "capture rates" of photoelectrons.

The theory of secondary emission is then very similar to that of the photoelectric effect. The incoming photoelectron, having been accelrated by the high voltage of the primary dynode, carries a lot of energy. This is sufficient to "knock" electrons out of the metal of the dynode. The number of such secondary electrons depends on several parameters of the metals used for the dynodes, but 3~4 secondary electrons seem to be a very plausible number at not super-high voltages.

These secondary electrons, which still have a lot of energy, are then accelerated to the subsequent dynode, which then produces more electrons. In effect, the number of electrons collected at the final dynode at 0V is simply the number of secondary electrons per dynode, denoted $\delta$, to the power of however many dynodes are available, N. Or, simply put, $n_{electons}=n_{photoelectrons}\times {\delta }^N$

Experiment

Consider a situation where one has a pulsed laser split into two beam paths, which are then directed to coincide on a single metal plate. The material of the metal plate is chosen such that a single photon from one of the paths of the pulsed laser is insufficient to produce an electron ($hf<\varphi$). However, if both photons from each beam path is incident upon the metal plate, there is then sufficient energy for a photoelectron emission ($2hf>\varphi$). Since a pulsed laser is used, this will only happen when the pulses from each of the arms arrive at the metal plate at the same time. This would form the so-called "coincidence time measurement of pulsed lasers".

The main motivation and purpose of having such a set-up would be exactly when one requires the lengths of two or more beam paths to be exactly the same. Only when the lengths are approximately (depending on the pulse duration) equal to each other would a photoelectron be observed, allowing for precise measurements of distances.

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 3.7eV

Vacuum - Acrylic Enclosure

Details: Vacuum seal is achieved by using Torr seal.

High Voltage Source - Matusada Precision TM-3N

Details: A negative 3000 volts power supply.

Dynode - Stainless Steel

Details: Flat sheets of about 3mm thickness

Steps Towards Success

This project has been broken down into the following steps:

  1) Design and Construction of DIY electron multiplier
  2) Design and Consturction of vaccum chamber (mainly an issue of getting things to fit inside nicely)
  3) Evacuation of vaccum chamber
  4) Start experiments.

But to ensure that the experiment would work, we first perform some simple simulations to estimate what would be the resources required to generate a high enough signal that may be detected.

Simulations

This project is generally heavily limited by the resources that we have on hand. As such, we initially perform some simple simulations to ensure that whatever resources we have are sufficient for the actual experiment to work.

Part 1: Photoemission

The energy associated to a wavelength of 355nm is given by

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

Compared to the work function of copper, ${\varphi }_{Cu}=4.7eV$, we can see 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:

$E_e=2hf-4.7\approx 2.285eV$

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 $2eV$. These photoelectrons can be emitted in all directions from the region of the surface illuminated with light.

Part 2: Primary Dynode

Having obtained a 3kV high voltage supply, we assume that the cathode is placed at a voltage of 2kV, and the first dynode is placed at 1kV, with a subsequent decrease in voltage of 100V per dynode. The last dynode will then be at 0V. This will mean that we have a total of 11 dynodes and 10 stages of multiplication.

In which case, due to the acceleration of the photoelectron towards the lower potential pf the dynode, the kinetic energy of the electron at the primary dynode is

$E_{e,dynode}=2.285+V\times e=1002.285eV$

The value of which tells us that the kinetic energy at which the electrons are emitted do not actually matter much.

The number of secondary electrons emitted from the primary dynode depends on the energy of the incoming primary electron and the voltage the dynode is put at. For steel, with a primary electron energy of around a 1000V, this secondary electron emission coefficient factor is about 1.5 (https://accelconf.web.cern.ch/e00/PAPERS/THXF102.pdf). The maximum of this value occurs when the electron energy is about 250V.

Part 3: Electron Multiplication

The number of electrons at the end of the multiplier is simply given by the number of secondary electrons emitted at each dynode (which is approximately the same as the number of electrons emitted at the primary dynode) to the power of how many dynodes are available.

There is a 100V potential difference between the 10 dynodes. This means that with a maximum voltage of 1kV, we should have 10 dynodes for multiplication and the 11th dynode will act as the anode for the collection of all the electrons emitted.

With 2 secondary electrons per dynode, this would mean that we would have 2**10 = 1024 electrons at the anode for each photoelectron produced at the copper cathode.

Part 4: 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 5: 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.

Proposed vacuum design

Below are screenshots 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.

Proposed vacuum design

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. It turns out that the number of secondary electrons do not simply scale with the primary electron's energy. Instead, the relation between the primary electron's energy and the number of secondary electrons emitted look as such: