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%%\title{CH.6 Laser stabilization for 6D isolation injection}
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%\begin{document}
\chapter{Laser stabilization for 6D isolation system device}
In this chapter I will introduce the 6D device, a new technology for inertial isolation. This project has been presented to the scientific community at the 10th ET Symposium in 2019 \cite{poster}. My contribution to the development of this technique focussed on the sensing side: a laser will be injected into the device and will need to be stabilized in frequency. We will see here why and how.\\
This work has been done entirely at UoB during the pandemic period: the design of the project has been conducted from home during the lockdown in 2020, while the experiment has been built and tested from September 2020, when the University accorded me the permission to return to the lab.

\section{6D inertial isolation system overview}
The 6D inertial isolation system is a device based on a new technology under development at University of Birmingham and at Vrije Univestiteit in Amsterdam, which could enable detection of gravitational waves at 10 Hz and below \cite{6d}. We have already seen the importance for this frequency window to be opened (chap 2): this facility can be installed on Earth-based interferometers of every type, on or under ground, allowing the different instruments to easily use the same device.\\
As the name reminds, the 6D investigates the motion of a reference mass in all 6 degrees of freedom, using 6 interferometers. In Fig. \ref{6d} it is shown a sketch of the design of the facility. \\

\begin{figure}[h!]
\centering
\includegraphics[scale=1.2]{images/6d.png}
\caption[6D design.]{Sketch of the 6D device (Figure taken from \cite{6d}). The working principle is based on a isolated, suspended reference mass which is monitored by position sensors detecting the relative motion between the ground and the platform; actuators apply corrections to the platform and the whole apparatus is in vacuum.}
\label{6d}
\end{figure}
\noindent
All six degrees of freedom are simultaneously low-noise, reducing the cross-coupling affecting low force-noise measurements.\\
The reference mass, suspended from a single, thin, fused-silica fibre and a metal spring, provides supports in the vertical (Z) degree of freedom. An interferometric readout provides control in the X and Y tilting degrees of freedom.\\
The interesting advantage is that this system provides isolation in all the degrees of freedom with the use of only one device: currently aLIGO is seismically isolated by three seismometers and twelve geophones \cite{lisa}.\\
\noindent
What we expect from 6D is isolation at low frequencies and reduction of fundamental noises: the thermal noise of the suspension is suppressed by the quasi-monolithic, fused-silica fibre; temperature gradients are kept under control thanks to the vacuum enclosure.\\
We expect a reduction of the platform motion at aLIGO and the bandwidth of the control loop by a factor of about 5 \cite{6d}.\\
The expected performance is shown in Fig. \ref{6dsens}: at low frequency 6D isolator provides two order of magnitude better results with respect to the current devices. The time of observation is expected to be increased from 66\% to 81\% for each detector.\\
The control noise will become negligible above 5Hz because the bandwidth for the control loops will be reduced to 0.5 Hz.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.7]{images/6dsens.PNG}
\caption[6D sensitivity curve]{A comparison of the expected performance of the 6D isolator and that of current STS-2 seismometers (Figure taken from \cite{6d}).}
\label{6dsens}
\end{figure}

\subsection{HoQI technology}
The 6 interferometers dedicated to the sensing role of the facility are the HoQI devices (Homodyne Quadrature Interferometer) developed at UoB \cite{hoqi}.\\
HoQI is a compact, fibre-coupled interferometer with high sensitivity and large working range. In Fig. \ref{hoqi1} you can see the optical layout of the device:

\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{images/hoqi1.png}
\caption[HoQI optical layout]{HoQI optical layout (Figure taken from \cite{hoqi}). The working principle is based on a Mach-Zender interferometer which uses two different beam splitters to recombine the beam independently. Moreover, the required differential phase shift is generated by a polarization scheme conveniently designed.}
\label{hoqi1}
\end{figure}
\noindent
This device has been designed to sense motion at low frequency, with a sensitivity of 2 $\times$ 10$^{-14}$ m/ $\sqrt(Hz)$ at 70 Hz and 7 $\times$ 10$^{-11}$ m/ $\sqrt(Hz)$ at 10 mHz \cite{hoqi}. This is a result obtained when combining HoQI devices to inertial sensors to create an "interferometric inertial sensor" \cite{sam}. In the frame of compact devices, HoQIs are designed to be very small in size, so can can easily be attached to sensors. They are then ideal for 6D purposes, not only for their high sensitivity, but also for their small size.

\noindent
The six HoQIs used for the 6D device need to be fed by a laser source that is sent into the vacuum chamber: my project focussed on this source, specifically how to stabilize it in frequency.

\section{Laser stabilization: requirements and key technology}
The laser chosen as source for 6D is a 1064 nm RIO ORION Laser Module (see Fig. \ref{rio}). This has been chosen for its low frequency noise, inexpensiveness and small size, relatively to other options. The key point in the stabilization of the frequency noise of this source is that the technology will be based on HoQIs: the same devices used by the 6D are sensitive enough to be installed also to stabilize the laser source. This solution is very convenient in terms of costs and presents practical advantages: the HoQIs are known devices, compact in size and, as we will see, they allow the setup to be moved easily (in vacuum or in air), according to the main 6D tank requirements.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{images/rio.jpg}
\caption[Rio Orion laser modules]{Picture of the RIO Orion laser mounted on a breadboard.}
\label{rio}
\end{figure}
\noindent
What we want from this source is a low-noise readout for the HoQIs inside the 6D tank, and thus the laser source needs to be as low noise in frequency fluctuations as possible at frequencies below 1Hz, because this is the range of frequencies where the 6D isolator is aimed to detect and control seismic noise: we are going to use two Rio Orion lase modules to obtain a frequency stabilization suitable for 6D requirements. Constraints to these requirements are mainly given by the HoQIs. For 6D readout, HoQIs are built in such a way that the arm length is L$_{6D}$ $<$ 3 mm. Limitations to this number are given by BOSEM size ($\pm$ 2 mm) and the ability to adjust it, once the devices are in vacuum. Another parameter to take into account is the ADC noise of HoQIs, which is ADC = 2 $\times$ 10$^{-14}$ m/$\surd{Hz}$ at about 10 Hz \cite{hoqi}. Frequency fluctuations depend on both these parameters and we want it to meet the following requirement:

\begin{equation}
\centering
\delta f_{6D} \ll f \times \frac{ADC}{L_{6D}} = 2000 \frac{Hz}{\surd{Hz}}.
\end{equation}\\
The technique we are going to adopt to stabilize the laser in frequency, as anticipated, is to use HoQIs, because we can associate frequency fluctuations to fluctuations of arm length:\\
\begin{equation}
\centering
\delta f = \frac{\delta L}{L}\cdot f,
\label{df}
\end{equation}\\
and this arm length can belong to a HoQI placed on the optical bench. The use of compact interferometers to stabilize solid-state lasers in frequency is new and allows the whole set up to be small in size. This technique, in combination with cheap laser sources, makes the set up competitive with other more expensive products.\\
We can then apply the same relation of. eq. \ref{df} to the arm length of the HoQI used for the laser stabilization, remembering that the requirement of $\delta$f $\ll$ 2000 Hz/$\surd{Hz}$ must remain valid. So, constraints to the arm length in this case are due also to the size of the bench and the whole set up.\\ We said we want a compact setup, but the arm length of this HoQI (say L$_{stab}$) can have a wider range of sizes to fit the requirement. For example, for L$_{stab}$ = 0.1 m we have:\\
\begin{equation}
\centering
\delta f_{stab} = f \times \frac{ADC}{L_{stab}} \simeq 55 \frac{Hz}{\surd{Hz}},
\end{equation}\\
which is still much lower than the threshold.\\
Since we want the setup to be as much compact as possible, we need to find the lowest possible L$_{stab}$ which gives an interesting $\delta f_{stab}$, compared to the current performances of RIO Orion and the best products available.\\
In the plot in Fig. \ref{perf} there is the analysis and comparison with two of the best products available.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/perf.png}
\caption{Analysis and comparison of RIO Orion laser with other products and with the configuration involving HoQIs.}
\label{perf}
\end{figure}
\noindent
It is evident that we cannot build a HoQI with L=10 m. If we want our device to be competitive even with the best product (ADJUSTIK X15, shown in blue line), we will need a L=30 cm. However, our purpose is to make the set up \textit{compact} and \textit{competitive} with most of the available products, so the best compromise is choosing L=10 cm. With this configuration, the device will still be competitive with ADJUSTIK X15 in terms of price.\\
Fig. \ref{free} shows a plot of the measured frequency noise of the Rio Orion laser modules and the level of stabilization required by the 6D with the chosen L$_{stab}$.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/free.png}
\caption[Free running noise and requirements]{Measured free running frequency noise of the Rio Orion laser modules compared with the frequency noise of the Mephisto Light laser module. The dotted line is the threshold of the 6D requirements for stabilization of its laser source, which is the goal we aim to achieve with the proposed setup. This threshold has been built using L$_{stab}$=10 cm and the HoQI noise and ADC floors as in \cite{hoqi}.}
\label{free}
\end{figure}

\section{Experiment design}
The optical set up for the stabilization of the laser source is built on a 800 mm $\times$ 650 mm breadboard: this choice allows to adjust the position of the laser source easier when the light is sent to the 6D vacuum chamber. The setup includes two RIO Orion lasers with output power 12 mW each, and a double-check of the light signal through an optical heterodyne detection: the beat frequency is monitored to assure that the two light frequencies are as much similar as possible.\\
The frequency of the lasers is tunable via temperature and input modulation: in the first case, the Thermo-Electric-Controller (TEC) is driven by a software provided by the manufacturer, while in the second case the module can be integrated to any software code to apply a modulation voltage between +4 V and - 4 V.\\
To minimise airflows, the optical setup has been enclosed into a box made of foam.

\paragraph*{Opto-mechanical design}
The optical layout is shown in Fig. \ref{las}: the two lasers have a twin optical layout. There is a Faraday Isolator (FI) at each output and then a 1 to 4 fibre beam splitter (BS) which separates the beam into 4 outputs of equal power: 3 outputs go into the vacuum chamber (for a total of 6 laser inputs, one for each 6D HoQI into the vacuum chamber). The remaining output is sent through a fibre coupler to a Schafter-Kirchhoff collimator and gives an output of about 1.2 mW for each laser; this proceeds freely on the breadboard towards a 1 inch, 10/90 (R/T) beam splitter: 10$\%$ of the light is sent to a fast DC coupled 125-MHz photoreceiver (PD) acted to sense the beat-note of the two lasers; two 1 inch mirrors deviate one of the two laser beams towards the transmitting surface of another 1 inch beam splitter, which combines the light from both lasers towards the photoreceiver; the other 90$\%$ of it is sent to the HoQIs, one for each laser. The optical path lengths (OPL) have been set to be equal, to assure the same beam size from both lasers at the photoreceiver.\\
The photoreceiver has strict constraints about the beam size and the input power: a focussing lens in front of the active area assures that the beam size is suitable to fit the 0.3 mm active area. Damping filters are added along the OPL, because the maximum input power of the device is 55 $\mu$W.\\
The whole optical setup lies on the bradboard and it is relatively easy to align because all the optomechanical components have been manufactured to make the beams out of the collimator to travel at the same height as HoQI components and the photoreceiver, so that there is no need of pitch tuning.

\begin{figure}[h!]
\centering
\includegraphics[scale=1]{images/layout.png}
\caption[Optical layout]{Optical layout of the laser stabilization experiment.}
\label{las}
\end{figure}

\paragraph*{HoQI design}
HoQIs for 6D laser stabilization have been built to fit the requirements, as shown previously: the adjustable arm length is of 10 cm; the photodiodes have a bigger active area with respect to the one of the HoQIs inside the 6D vacuum chamber, because the laser spot size is larger than the one travelling into the 6D device. Moreover, this type of HoQI is independent from any inertial sensor, so both the arms end with a steering mirror. Table \ref{hoqi} shows other small details that have been adapted for this experiment.\\

\begin{table}[h!]
\centering
\begin{tabular}{|c|| c| c| }
\hline
 & \textbf{Original} & \textbf{HoQI stab}\\
\hline
Platform thickness & 6 mm & 1 cm\\
\hline
Size &65$\times$75mm &65$\times$200mm\\
\hline
Corner Cubes & 2 & 0 \\
\hline
PD active area &3.6$\times$3.6mm &5.8 $\times$5.8mm\\
\hline
Steering mirrors & 1 & 2\\
\hline
\end{tabular}
\caption{Main differences between the original HoQI and the one used for 6D laser stabilization.}
\label{hoqi}
\end{table}

\noindent
In Fig. \ref{chia} there is a photo of the HoQI built for this experiment.\\

\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{images/HoQIChia.png}
\caption[Photo of a HoQI]{Photo of one of the HoQIs built for the laser stabilization experiment.}
\label{chia}
\end{figure}
\noindent
The photodiodes are Hamamatsu S2386-8K and the optical layout is similar to the one shown in the figure \ref{hoqi1}: there are commercial 0.5 inch cubic beam splitters (three polarizing and 1 non polarising) mounted on custom cubic bases, two 0.5 inch mirrors on steering mounts, one 0.5 inch $\lambda$/2 waveplate and one 0.5 inch $\lambda$/4 waveplate, both mounted on a custom base allowing them to rotate for fine tuning. The whole optical set up is placed on a 75 mm $\times$ 200 mm $\times$ 10 mm baseplate.\\
The two HoQIs have been tuned to obtain the best fringe visibility, which is 0.8 for HoQI1 and 0.6 for HoQI2. The technique used to measure the fringe visibility is based on measured power on a sin vs cos plot, once the beams have been aligned to overlap in far field and produce interference, and tuning the steering mirrors for fine alignment and the waveplates for power adjustments (Fig. \ref{fringes}).

\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/fringes.png}
\caption[HoQI fringes alignment.]{Example of how we set the fringes of the HoQIs to obtain the desired alignment. Every photodiode detects the fringes independently from the others: to obtain the same response, we adjusted the offsets and the gains of each diode on the pre-amplifier and via software.}
\label{fringes}
\end{figure}

\section{AC-coupled control loop}
To acquire our data, we need to connect the HoQIs and the beat-note receiver to a data acquisition system. At UoB we have 3 CDS racks and one of them is dedicated to 6D. As shown in Fig. \ref{signals}, HoQIs will need a pre-amplifier, an Anti-Aliasing (AA) device and an Analog to Digital Converter (ADC) before connecting to CDS (Fig. \ref{signals}).\\
The sensing and control system of the experiment is based on the HoQIs: the software code manipulating the HOQIs signal and driving the input modulation is written with Matlab Simulink and controlled by the CDS. The controller filter has been built taking into account all the features of the loop and implemented into the CDS. The lasers can then be controlled via input modulation through a feedback control loop where HoQIs act as the sensors and feedback devices for frequency stability. 

\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{images/signals.png}
\caption[Scheme of the signals]{Basic scheme of the row signals for laser frequency control: the power detected by the photodiodes is converted into $\mu$A and sent to a pre-amp, one for each HoQI; the pre-amps convert the signal in double-ended voltage to be sent to an ADC. The output of the CDS is a $\pm$ 10 V double-ended signal out of the DAC: since the lasers require a $\pm$ 4 V single-ended input, the double-ended signal is converted into single with a custom differential- to single-ended amplifier of gain 2.5. The calibration of the CDS gives 0.00061 V/counts, which allows to digit into the CDS the right counts divided by the gain of the differential- to single-ended  amplifier to obtain the desired voltage to send to the lasers.}
\label{signals}
\end{figure}
\noindent
The beat-note receiver is 15 V powered and connected to a frequency counter, and then to the CDS. A detailed scheme of the electronics is shown in Fig. \ref{cables}.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.7]{images/cables.png}
\caption[Scheme of the electronics]{Detailed scheme of the electronics designed for this experiment. The different colors of the arrows represents different types of cables. Bacardi and Peapsy are the CDS and the computer controlling it, as we named them at UoB. Differential to single ended converters (Diff2SE) are needed because the CDS supports single ended outputs while the pre-amps are double ended. The Mokulab is the device used as an oscilloscope and/or as a spectrum analyser, connected to the beat-note fast photoreceiver. Green arrows indicate power supplies. The frequency counter can be connected to a computer to acquire data or a USB drive can be inserted to save data directly from the device. The temperature modulation requires the use of a software provided by the manufacturer and installed on computers. Each laser needs its own software connection. }
\label{cables}
\end{figure}
\noindent
Models of our system are designed with Symulink and the controller filters is designed using the tools provided by the CDS in Birmingham laboratory (Fig. \ref{filter}).

\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/filter.png}
\caption[Controller filter]{Bode plot of the controller filter installed into the CDS (blue) and of the closed-loop expected gain when this filter is applied (red). Since we want to lower the frequency noise below 1 Hz, the filter has been designed with a pole at 0.1 Hz: this design should push the gain from below 10 Hz, with the maximum gain at 0.1 Hz, assuring stability.}
\label{filter}
\end{figure}

\section{Noise hunting}
\paragraph*{Noise budget}
The performances of the setup depend strongly on the HoQIs because they are the sensing and feedback devices of the setup: the noise budget in Fig. \ref{noiseb} shows that the measured HoQI readut follows the free running frequency noise of the lasers detected by the frequency counter at low frequencies, and then it sits on the ADC noise (estimated as in \cite{hoqi}) at frequencies above 100 Hz. What we are interested in is getting the lowest possible frequency noise from the lasers, reducing the noises affecting the HoQIs. The improvement of HoQIs sensitivity is crucial to obtain the best performances in sensing frequency fluctuations, in order to provide the correct and stable control and feedback to the setup.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/noisebudget.png}
\caption[Noise budget]{Noise budget of the laser stabilization setup. The paper which provided the HoQI noise and the ADC noise is given by \cite{hoqi}.}
\label{noiseb}
\end{figure}

\paragraph*{Tested noise sources}
There are several noise sources to take into account: air currents and vibrations from electronics and cables have been reduced placing the optical setup into a foam box and moving the electronic devices suitably. Cables have been isolated from the table and the breadboard by rubber feet.\\
\noindent
The test in Fig. \ref{sound} shows that the setup is sensitive to acoustic noise: we injected a sound at 75 Hz and both HoQIs clearly detected it. Moreover, we found out that HoQI1 is detected some noise around 22 Hz that HoQI2 is not able to sense: the two peaks in the figure are present in every condition of the laboratory and part of the day. The source of this noise is still under investigation: it could be a permanent sound in the lab non audible by humans. The fact that only HoQI1 can detected could be due to its position with respect to the noise source: it might be closer to it than HoQI2. Imperfections in the optics and general setup of the HoQIs are also taken into account.\\

\begin{figure}[h!]
\centering
\includegraphics[scale=0.33]{images/sound75hz.png}
\caption[Test of the setup to sound stimulation.]{Test of the setup to sound stimulation. The peaks at 75 Hz shows that both HoQIs are sensitive to acoustic stimulation; HoQI1 is also detecting another noise around 22 Hz, which is instead non-visible by HoQI2.}
\label{sound}
\end{figure}

\noindent
Temperature changes affected dramatically the measurements: the two lasers can be driven also via temperature modulation. This method has been used to move the beat-note peak along the frequencies and set it around 60 Hz, being this the setpoint we decided for it. However, both laser modules are sensitive to changes of the room temperature, which make the peak move out from the setpoint on large time scales (~hours): this affects long time measurements. The stabilization of the room temperature requires the use of the air conditioning, which in turn creates air currents visible by the setup below 1 Hz.\\
Temperature changes are also responsible for deformations of metals; this induces noises into the HoQI platforms because of the different materials they are built of: platform, screws, post holders expand in different ways with temperature changes, and this produces deformations and friction between the metals, which translate into displacement noise visible by the HoQIs. This issue has been reduce by inserting rubber rings between the junctions where different metals are mounted.\\

\noindent
Another noise we noticed from the datasheets of the laser modules is the intensity fluctuations: in particular, laser2 is more affected by this noise than laser1 (compare the datasheets reports in Fig. ...). This in part explains why HoQI2 is in general noisier than HoQI1, as shown in the following sections.

\paragraph*{Loop performances}
The behaviour of the two HoQIs has been tested in loop and out of loop, to check if they are detecting and responding correctly to the injection of the controller filters through the input modulation of the laser modules. The expectation is that the HoQIs output in out-of-loop mode should show the injection of the gain: Fig. \ref{looptest} shows that the expectations are satisfied.\\
This test shows that HoQI2 is in general noisier than HoQI1, especially above 1 Hz: this affects laser stabilization measurement and loop stability, thus it has been deeply investigated. The higher intensity fluctuations of laser2 can partially explain the reason of HoQI2 noise.

\begin{figure}[h!]
%\centering
\includegraphics[scale=0.3]{images/hoqisOLCL.png}
\caption[In-loop test of HoQIs performances.]{In-loop test of HoQIs performances. The out-of-loop traces (cyan and purple) are following the free running frequency noise trace (blue) as expected, while when the loop is closed the HoQI outputs (green and red) show that the controllers are pushing the expected gain (orange). There is an evident un-match with the orange trace below 0.4 Hz and this is likely due to loop leakage.}
\label{looptest}
\end{figure}

\section{Laser stabilization: tests and results}
The tests have been performed measuring the stability of the beat-note peak around the 60 Hz setpoint: the frequency counter used for this measurements is a Keysight 53230A 350 MHz - 20 ps. The output of the fast photoreceiver is DC-coupled and can be directly connected to the counter. The measurements has been recorded on a USB drive: the data provided by the counter are in frequency (Hz).\\
Several tests have been taken in different conditions for noise hunting along the frequency range of interest. QUI CI VANNO I TEST COL COUNTER DI CUI PARLAVA CONOR: LO SCOPO E' DIMOSTRARE CHE IL SETUP E' STATO ADEGUATAMENTE TESTATO

\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/result.png}
\caption{Results of frequency stabilization: the in-loop red trace shows the frequency stabilization process as detected by the frequency counter monitoring the beat-note between the two lasers; the black trace is the expected gain activated by the controllers, which is set to maximise the stabilization below 1 Hz.}
\label{test}
\end{figure}

\section{Alternative test}
An alternative test has been made to make sure that the input modulation is effectively reducing the frequency noise of the lasers. Since we found that HoQI2 is noisier than HoQI1 and that laser2 has larger intensity fluctuations, we decided to use laser1 to feed both lasers. The new concept is to let only HoQI1 be the in-loop sensor, while HoQI2 will act as the out-of-loop sensor.\\
Results are shown in Fig. \ref{alt} and are encouraging: the frequency noise of the out-of-loop sensor is lowered by about one order of magnitude when the controller on laser1 is active. This means that the control loop works well and that there are still more external noise sources that are reducing the performances of the HoQIs, impacting also on the measurement through the heterodyne detection.\\
This test highlights also that HoQI2 is still noisier than HoQI1, despite the use of the laser with less intensity fluctuations: this clarify that HoQI2 noise arises from other external sources that HoQI1 is non-sensitive to or imperfections into the optics. A test in vacuum could solve the doubts about the external sources.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/CLOLtest2907.png}
\caption[Alternative stabilization test]{Alternative test for frequency stabilization: the out-of-loop sensor (HoQI2) is less noisy by an order of magnitude when the in-loop sensor is actuated by the controller filter. This is a proof that the frequency noise of the laser is reduced by the control loop.}
\label{alt}
\end{figure}

\section*{Conclusions}
%installation into 6D

%\begin{thebibliography}{9}
%
%\bibitem{poster} \textit{https://dcc.ligo.org/LIGO-G1900741}
%
%\bibitem{6d} C.M. Mow-Lowry, D. Martinov, \textit{A 6D interferometric inertial isolation system}, 2019 Class. Quantum Grav. 36, 24 
%
%\bibitem{hoqi} S. Cooper et. al, \textit{A compact, large-range interferometer for precision measurement and inertial sensing}, 2018 Class. Quantum Grav. 35 095007
%
%\bibitem{sam} S. Cooper, \textit{Breaking the Seismic Wall: How to Improve Gravitational Wave Detectors at Low Frequency}, PhD thesis, University of Birmingham, 2019
%
%\bibitem{rio} $https://rio-lasers.com/1064-nm-laser-module/$
%
%\bibitem{adj} $https://www.photonicsolutions.co.uk/upfiles/ADJUSTIKFiberLaserLG13Dec17.pdf$
%
%\bibitem{mephi} $https://edge.coherent.com/assets/pdf/COHR\_ MephistoNPRO\_ WP\_ 9\_ 24\_ 19.pdf$
%
%
%\end{thebibliography}
%
%\end{document}