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\title{Final Design and Implementation of the KAGRA green lock system}
\date{v2: 2021/June/20th}
\author{Kiwamu Izumi for the GRE team}
\institution{Institute of Space and Astronautical Science}


\begin{document}
\setstretch{1.2}

\setcounter{tocdepth}{2}
\tableofcontents

\newpage

%%%%%%%%%%%%%%%%%%%%%%
\section{Overview}
\subsection{Overview of this document}
This document summarizes the design and current implementation of the green lock (GRE) system or ALS (Arm Length Stabilization) system as a snapshot. For historical reasons, we refer this particular system either ALS system or green lock system, interchangeably.

\subsection{Notes on version updates}
This document is version 2, meant for capturing the latest implementation as of June 2021.

\subsection{Scope of this document}
The scope of this document covers the following items.
	\begin{itemize}
		\item Design concept and associated considerations
		\item Final design and actual implementation
		\item Lessons learned
	\end{itemize}
The performance achieved by the actual implementation is not described in this document. Please refer to Refs.~\cite{Sugimoto2020, Enomoto2019, Yokogawathesis2019} and references therein.


\section{Related documents and development history}
\subsection{Related documents}
\scriptsize
\setstretch{1.0}
%%%%%%%%%%%%%%%%%%%%%%%
\begin{thebibliography}{9}
	\bibitem{DocTree}
	``Document Tree for Arm Length Stabilization System,'' JGW document, JGW-E1807769,
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=7769}{Link to JGW-E1807769}
	\bibitem{Sugimoto2020}
	R.~Sugimoto, ``Development of Auxiliary Locking System in Gravitational Wave Telescope KAGRA,'' Master thesis, Univ. Toyama (2020)
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=12605}{Link to JGW-P2012605}
	\bibitem{Enomoto2019}
	Y.~Enmoto {\it et al.,}  journal paper in preparation (2019)
	\bibitem{Yokogawathesis2019}
	K.~Yokogawa, ``Arm length stabilization system in KAGRA,'' (in Japanese) master thesis, Univ. of Toyama (2019)
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=9919}{Link to JGW-P1909919}
	\bibitem{5735}
	Y.~Enomoto, ``Modification of RFPD for Green Lock PDH,'' klog 5735, (2018),
	\href{https://klog.icrr.u-tokyo.ac.jp/osl/?r=5735}{Link to klog 5735}
	\bibitem{rfpd}
	Y.~Enomoto, ``Proposal: Modification of LSC RFPD for Green PDH,'' JGW-D1808442-v1 (2018)
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=8442}{JGW-G1808442-v1}
	\bibitem{vco}
	Y.~Enomoto, ``Prototype Low Noise VCO Chassis Top Assembly,'' JGW--D1808968 (2018), \href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=8968}{JGW--D1808968}
	\bibitem{5785}
	K. Izumi et al., ``ALS/PSL installation update: fibers are successfully pulled,'' klog 5785 (2018), 
	\href{https://klog.icrr.u-tokyo.ac.jp/osl/?r=5785}{Link to klog 5785}
	\bibitem{routing}
	``[CONFIDENTIAL] ALS optical fiber routing,'' (in Japanese) JGW-D1813050 (2018)
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=13050}{Link to JGW-D1813050}
	\bibitem{Review2018}
	K.~Yokoagaw and Y.~Moriwaki, ``Material for the review about green laser (2018.Mar.28),' JGW-T180103-v3 (2018
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=8103}{Link to JGW-T180103}
	\bibitem{CD2017}
	K.~Doi {\it et al.,} ``ALS meeting material (2017.Nov.13),'' JGW-E1707416-v1 (2017)
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=7416}{Link to JGW-E1707416}
	\bibitem{CD2016}
	Y.~Michimura, ``Arm length stabilization conceptual design,'' JGW-T1605353-v12 (2016)\\
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=5353}{JGW-T1605353}
	\bibitem{ServoDesign2011}
	D.~Tatsumi {\it et al.,} ``Servo designs for green lock, '' in Japanese, JGW-T1200788-v1 (2011)\\
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=788}{JGW-T1200877}
	
	\bibitem{8535} K.~Izumi, ``Landing point for the messenger wire for pulling the GRE fibers,'' (2018)\\
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=8535}{JGW-G1808535-v1}
	
	\bibitem{5626}
	Y.~Michimura, ``ALS Sideband Frequency'', T1605626-v3 (2018)
	\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=5626}{JGW-T1605626-v3}
	
\end{thebibliography}
\normalsize
\setstretch{1.2}

\subsection{Brief history}
\subsubsection{Conceptual design phase (2011-2016)}
The conceptual design was initiated in 2011 by Tatsumi~\cite{ServoDesign2011} with input from K.~Arai. Several main features were already introduced, such as the use of the Prometheus lasers, injection of the green light from the corner volume and the use of an AOM to lock green light to an arm cavity. Further study had been carried out by the group in the University of Toyama and the KAGRA MIF team since 2016. The studies include experimental verifications, fiber selection and circuit designs based on the conceptual design~\cite{CD2016}.

\subsubsection{Implementation phase (2017-2019)}
Later in 2017, the team proceeded with the implementation designs as well as procurement where the design of the optical layouts and hardware parts began being consolidated. In August 2017 and March, 2018, the team underwent review processes where the installation route of the fibers and the fiber selection were identified as main concerns. 

\subsubsection{Upgrade phase 2021}
The fiber noise cancellation loops were upgraded.





\section{Conceptual Designs}
\subsection{Role of the green lock system}
The ALS system shall be able to control the resonance conditions of the arm cavities with respect to the infrared science laser independently of the resonance condition in the central dual-recycled Michelson interferometer. The ALS serves as extra sensors and controllers to make the lock acquisition process much less stochastic.

\subsection{Requirements}
The ALS system shall have the following functions.
	\begin{itemize}
		\item Sensing the displacement of the arm cavities\footnote{or equivalently, relative shift in the frequency of science laser.} for a sufficiently wide range
		\item Controlling the length of the arm cavities and laser frequency at a precision level required for lock acquisition.
		\item The sensing and control must be insensitive to the resonant condition of the dual-recycled Michelson interferometer.
	\end{itemize} 

In order to achieve a repeatable process in lock acquisition, we set the following requirement values for the ALS system.
	\begin{itemize}
		\item Range for controlling each of the cavity length shall be greater than \textcolor{magenta}{XXX}~m.
		\item Precision for controlling each cavity length shall be \textcolor{magenta}{YYY}~nm in root mean square (rms).
	\end{itemize}

\subsection{Architecture}
\textcolor{magenta}{A simple diagram will be here.}

\subsubsection{RF modulation frequencies}
The sideband frequencies are selected to be 32 and 33 MHz. See \cite{5626}.

\subsection{Difference against aLIGO}
The biggest difference is that the auxiliary lasers are injected from the corner volume as opposed to the injection from the end stations. This choice completely removes the need for kilometer-long optical fibers. 

Another difference is that the signals for cavity lengths are extracted electronically as opposed to the one via optical beatnote measurements. The electronic signal extraction is less involved in terms of the optical setup while no drastic improvement or degradation in the noise performance is expected compared against the aLIGO scheme.

\section{Final design and Implementation}

\subsection{Test mass coatings}
\subsubsection{Specification}
The coatings of the test masses are designed such that high reflectivity is achieved for both 532 and 1064~nm. The lower finesse is for 532~nm, the easier resonance acquisition becomes. However, if the finesse was too small, it would introduce the spurious coupling of the TEM01/10 and other higher odd-number order modes into the TEM00 modes, leading to degraded performance in control precision. For this reason, the nominal finesse value was targeted to be approximately 50.
The specification calls for the values shown in table~\ref{tab:coatings}. The complete set of design parameters are available in JGW wiki at \url{http://gwwiki.icrr.u-tokyo.ac.jp/JGWwiki/LCGT/subgroup/ifo/MIF/OptParam}.

%%%%%%%%%%%%%%%%%%%%%%%
%% begin table
%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[t]
\begin{center}
\begin{tabular}{r| r |r}
{\bf Parameter} & {\bf Value} & {\bf Notes} \\
\hline
ITMs\\
\hline \hline
Transmission for 532~nm & 0.06 +0/-0.005&  larger than ETM for 532~nm\\
Asymmetry in transmission for 532~nm & No requirement\\
HR loss for 532~nm & $<$ 1\% &\\
AR reflectivity for 532~nm& $<$ 5\% & as small as possible \\
\hline
ETMs\\
\hline \hline
Transmission for 532~nm & 0.06 +0/-0.005&  smaller than ITM for 532~nm\\
Asymmetry in transmission for 532~nm & No requirement\\
HR loss for 532~nm & $<$ 1\% &\\
AR reflectivity for 532~nm& $<$ 5\% & as small as possible \\


\hline
\end{tabular}
\end{center}

\caption{Coating specifications for the test masses}
\label{tab:coatings}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%
%% end table
%%%%%%%%%%%%%%%%%%%%%%%


\subsection{Lasers}
\subsubsection{Specifications}
The two lasers are both \textit{Prometheus-532-100-CP} from Coherent Inc. The output power for the 532~nm light is 100 mW.

The lasers in the GRE must to produce the second harmonic fields of the main science laser at 1064~nm.
In order not to use significant amount of the optical power out of the main laser, we chose to use independent lasers radiating the 1064~nm laser light. The cost of this scheme is that we must introduce the phase-locked loop system to tie the frequencies of the GRE lasers to the main one.


\subsubsection{Implementation}
\textit{\textbf{Laser units---}} Three Prometheus lasers were purchased; two for the actual use in KAGRA and the other for spare and prototyping. As of writing, the spare unit is in the University of Toyama for carrying out extra experiments.
The part numbers for the two lasers installed in the PSL room are summarized in the table below.

\textit{\textbf{UPS unit---}} In addition, a UPS unit was installed in Jan. 2019 for supplying stable power voltages for the two lasers. The UPS unit is SMT1500RMJ2U from APC. The UPS unit resides in the same electronic rack as the laser controllers.

\textit{\textbf{Temperature settings---}}The temperature settings for the laser crystals were carefully adjusted such that the frequency difference of each GRE laser with respect to the science laser is 80~MHz. The absolute wavelengths as functions of the crystals' temperatures are summarized in figure~\ref{fig:absfreq}. The PLS runs nominally at a crystal temperature of 46.4~deg as noted in the IOO manual (\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=8998}{JGW-T1808998-v3}).

%%%%%%%%%%%%%%%%%%%%%%%
%% begin table
%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[t]
\begin{center}
\begin{tabular}{r| r |r | r}
{\bf Description} & {\bf Laser S/N} & {\bf Diode current}  & {\bf Xstal temperature}\\
\hline \hline
Prometheus for ALS X& 2143A & 2.05~A & 23.51~deg\\
Prometheus for ALS Y& 2143B & 2.20~A & 22.42~deg\\
Prometheus for spare& 7023 & 2.01~A & --\\
\hline
\end{tabular}
\end{center}

\caption{A summary of the Prometheus lasers currently installed. Both lasers receive power voltage from the UPS unit.}
\label{tab:lasers}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%
%% end table
%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%
% begin figure
%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
		\begin{center}
			\includegraphics[width= \columnwidth]{../../figures/AbsFreq.png}
		\end{center}
		\caption{Measurement of absolute frequencies as functions of the crystal temperature. The measurement was done in 2018 and 2019.  ``New Prometheus'' shown as green dots are the spare unit. }
		\label{fig:absfreq}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%
% end figure
%%%%%%%%%%%%%%%%%%%%%%%


\subsection{Optical fibers}
\subsubsection{Specifications}
To deliver the green light onto the POP and POS tables, two fibers with different lengths are necessary. The lengths for these fibers are summarized in table~\ref{tab:fibers}. Taking the advantage of this installation opportunity, we decided to install the IR fibers too for future use.

As for the fibers for the 532~nm wavelength, the below is a list of the common specifications.
\begin{itemize}
	\item Wavelength: 532~nm
	\item End caps: 330+/-30~$\mu$m long end caps (at the both ends)
	\item Sheath: $\phi$~3~mm OD Doplex Zipcoard tubing
	\item Fiber type: Nufern PM-S405-XP
	\item End connectors: FC/APC, narrow key
	\item Connector key: Slow axis
\end{itemize}
The fiber ends are protected by the end caps in order to reduce the risk of damaging the end parts in case high optical power was applied to the fibers.
The minimum required power for 532~nm was set to \textcolor{magenta}{XXX}~mW. Each fiber has a duplication fiber and they are collectively assembled as a single bundle, called duplex, for redundancy. 


As for the fibers for the 1064~nm, the below is a list of the common specifications.
\begin{itemize}
	\item Wavelength: 532~nm
	\item End caps: N/A
	\item Sheath: $\phi$~3~mm OD Doplex Zipcoard tubing
	\item Fiber type: Nufern PM-S405-XP
	\item End connectors: FC/APC, narrow key
	\item Connector key: Slow axis
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%
%% begin table
%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[t]
\begin{center}
\begin{tabular}{r| r |r | r}
{\bf Descriptions} & {\bf fiber P/N} & {\bf Fiber length}  & {\bf \# of fibers}\\
\hline \hline
PSL-POP table fibers for 532~nm& Nufern PM-S405-XP & 58~m& 2 (Duplex cable)\\
PSL-POP table fibers for 1064~nm& Nufern PM980-XP & 58~m & 2 (Duplex cable)\\
PSL-POS table fibers for 532~nm& Nufern PM-S405-XP & 63~m& 2 (Duplex cable)\\
PSL-POS table fibers for 1064~nm& Nufern PM980-XP & 63~m & 2 (Duplex cable)\\

\hline
\end{tabular}
\end{center}

\caption{A summary of the Prometheus lasers currently installed. Both lasers receive power voltage from the UPS unit.}
\label{tab:fibers}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%
%% end table
%%%%%%%%%%%%%%%%%%%%%%%


\subsubsection{Implementation}
Bundles of the optical fibers were installed on August 11th in 2018 by Fujitsu Fsas Inc.~\cite{5785}.

\textit{\textbf{Fiber protection---}} To protect the fibers from water and other possible corrosion materials, the fibers in the experimental area are put in PF tubing (Plastic Flexible Conduit tubing). Figure~\ref{fig:tubing} shows an illustration of how it was implemented. Figure~\ref{fig:fbinstallation} shows a picture of the actual work done by Fujitsu Fsas. The portion, that are in the PSL room and the clean area around PR2 and SR2 areas, do not have the PF protection. In addition, in order to stably hold the fibers within the PF tubing, shock-absorbing material\footnote{A spongy material -- the details not specified or confirmed.}.

%%%%%%%%%%%%%%%%%%%%%%
% begin figure
%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
		\begin{center}
			\includegraphics[width= 0.7\columnwidth]{../../figures/fbtubing.pdf}
		\end{center}
		\caption{An illustration of the PF tubing for protection. The shock absorbers are placed approximately ever 1~meter or so.}
		\label{fig:tubing}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%
% end figure
%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%
% begin figure
%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
		\begin{center}
			\includegraphics[width= 0.7\columnwidth]{../../figures/FBinstallation.jpg}
		\end{center}
		\caption{A picture of the fiber installation work around the PR2 chamber in August, 2018. The yellow cables are the optical fibers being inserted into the light blue PF tubing. The black spongy materials are attached to the optical fibers before the insertion.}
		\label{fig:fbinstallation}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%
% end figure
%%%%%%%%%%%%%%%%%%%%%%%



\textit{\textbf{Fiber routing---}} The routing paths were decided based on the discussion with the industrial contractor. Details can be found in Refs.~\cite{routing, 8535}.

\textit{\textbf{Fiber core transmission tests---}}
Table~\ref{tab:coretrans} summarizes the transmission tests performed right after the completion of the installation to confirm that the fibers did not have any damage~\cite{5785}. The measurements were done only for the fibers for 532~nm and we did not evaluate the core transmittance for the 1064~nm fibers. 

%%%%%%%%%%%%%%%%%%%%%%%
%% begin table
%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[t]
\begin{center}
\begin{tabular}{r| r |r | r}
{\bf Fiber} & {\bf Output} & {\bf Core trans. }  & {\bf Trans. ratio}\\
\hline \hline
CCH-948-63 A (63 m duplex fiber, A)& 27~mW & 66\% & 110\%\\
CCH-948-63 B (63 m duplex fiber, B)& 22~mW & 54\% & 105\%\\
CCH-948-58 A (63 m duplex fiber, A)& 24~mW & 59\% & 87\%\\
CCH-948-58 B (63 m duplex fiber, B)& 25~mW & 61\% & 90\%\\
\hline
\end{tabular}
\end{center}

\caption{A summary of the core transmittance tests. The input light power was 68~mW in this measurement. The coupling efficiency was assumed to be a typical value of 60\%. The transimittance ratio is defined as the ratio of the output power after the installation over the one before the installation.}
\label{tab:coretrans}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%
%% end table
%%%%%%%%%%%%%%%%%%%%%%%


\subsection{Low-noise voltage controlled oscillators}
\subsubsection{Specification}
The low noise VCOs (voltage controlled oscillators) are required for driving the AOMs with sufficiently low frequency noise. The tentative specification was set such that the unit essentially duplicates the architecture for aLIGO's low noise VCOs (\href{https://dcc.ligo.org/LIGO-E1200120}{LIGO-E1200120-x0}) where a tunable oscillator signal is mixed with stable seed RF signal.

\subsubsection{Implementation}
See the top assembly document~\cite{vco} and related documents therein. This unit is meant to be prototype in the sense that the noise performance has not fully understood. Two units were made and installed.

\subsection{Phase-Frequency Discriminator}
\subsubsection{Specification}
The tentative specifications are set such that the phase frequency discriminator achieves the readout noise as good as that built for aLIGO (\href{https://dcc.ligo.org/LIGO-D1002476}{LIGO-D1002476}). The architecture is essentially the same --- the combination of AD96687 and AD9901 for phase-frequency discrimination.

\subsubsection{Implementation}
The unit was designed, assembled and tested in the University of Toyama. See the documents listed below for the details.



\subsection{AOM}
\subsubsection{Specifications}
The AOM is necessary to continuously control the laser frequencies of the 532~nm light for keeping the green light resonating in the arm cavities. AOMO 3080-125 from Gooch and Housego was selected for the AOMs.

\subsubsection{Implementation}
Two units are installed in the PSL optical bench --- one for ALS X and the other for ALS Y. Currently the mounts are temporary ones and could be replaced with a dedicated block-mount made by University of Toyama.

\subsection{EOM}
\subsubsection{Specification}
EO-T30M3-VIS fro Qbig was chosen for the EOM.

\subsubsection{Implementation}
Similarly to the AOMs, the current mounts can be replaced with a more rigid mount if necessary.

\subsection{Mirror holders}
\textcolor{magenta}{TBW.}


\subsection{Small optics}
\textcolor{magenta}{TBW.}

\subsection{In-vac oberisks}
\textcolor{magenta}{TBW}

\subsection{Photodetectors}
\subsubsection{The beatnote photodetectors}
818-BB-21A was selected for the photodetectors monitoring the beatnote.

\subsubsection{The PDH photodetectors}
The units were custom-made RFPDs (\href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=1280}{JGW-D1201280}) with manual adjustments applied on the circuit. A set of modifications is applied to the existing PCB including the replacement of the photodiode with a Hamamatsu S3399 and adjustment of LC network~\cite{rfpd}. In addition, the removal of the C31 capacitor was necessary~\cite{5735}.

The units currently in use are:
	\begin{itemize}
		\item \href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=8690}{JGW-S1808690-v1} for the X arm, tuned for 33~MHz.
		\item \href{https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=8567}{JGW-S1808567-v1} for the Y arm, tuned for 32~MHz.
	\end{itemize}


\subsection{Picomotors}
\textcolor{magenta}{TBW}



\subsection{Realtime digital system}
\subsubsection{Signal I/Os}

\subsubsection{Guardians for automation}


\section{Lessons learned}
\subsection{Fiber vibration noise}
\subsection{AC100V power supply}
\subsection{VCO offset}
	



\end{document}
