1. A study of Arm Length Stabilization in KAGRA
Shogo Kambara University of Toyama Aug 26, 2016
Hello. I’m Shogo Kambara. I’m master student in University of Toyama.
Today I’ll talk about “A study of Arm Length Stabilization in KAGRA”
2016/8/27
F2F Meeting in University of Toyama

2. F2F Meeting in University of Toyama
Reference
Fiber Phase NoiseMeasurements at LHO [1] LIGO-T v1 Development of Auxiliary Lock Acquisition Procedures at the Caltech 40m Interferometer [2] Study by Tatsumi-san et al. in [3] [4] [5] Arm Length Stabilizaton Conceptual Design [6]
2016/8/27
F2F Meeting in University of Toyama

3. F2F Meeting in University of Toyama
Contents
Overview
Arm length stabilization(ALS) Configuration
Noise simulation by Noise Budget
Conclusion
Future works
Contents is this.
2016/8/27
F2F Meeting in University of Toyama

4. Overview ~To lock is too difficult!!! ~
Difficulty of locking interferometer with 5 degree of freedom
Y-Arm cavity
Michelson Interferometer
We need to lock in order
Power Recycling cavity
When Locking Power or Signal Recycling Cavity,
Avoiding accidental resonance of Arm cavity
X-Arm cavity
It is very difficult to lock the interferometer with 5 degree of freedom by using only IR laser. We need to lock the Interferometer in order, first we will lock the “Power recycling cavity” or “Signal recycling cavity”, at this time we need to avoid accidental resonance of IR laser.
Signal Recycling cavity
5 degree of freedom
2016/8/27
F2F Meeting in University of Toyama

5. Overview ~Arm Length Stabilization(ALS)~
Difficulty of locking interferometer with 5 degree of freedom
GREEN
Lock!!!
Y-Arm cavity
We need to lock in order
When Locking Power or Signal Recycling Cavity,
Avoiding accidental resonance of Arm cavity
Power Recycling cavity
X-Arm cavity
Locking arm cavity by Green laser using PDH
Frequency of Green laser stabilized by PLL
To keep arm cavity no resonance at IR, we lock arm cavity by Green laser using PDH, and we need to stabilize the frequency of Green laser by phase lock loop. These system are called Arm Length Stabilization system.
Signal Recycling cavity
Arm Length Stabilization System(ALS)!!!!!!
3degree of freedom!!
2016/8/27
F2F Meeting in University of Toyama

6. ALS Configuration(Y-arm)
Laser room
PDH PD
40Mhz
High Frequency
EOM
Optical fiber
PLL
SHG
AOM
Prometheus PD
Low Frequency
Arm length stabilization configuration(Y-arm).
PLL system is this. The frequency of Prometheus needs to be locked to the frequency of the PSL. Comparing PSL frequency and Prometheus frequency and beat signal is sent to PLL filters.
PDH system is this. The green is generated from an IR source laser by SHG in Prometheus. The green is injected into PR2 mirror by optical fiber. Low frequency of PDH signal is sent to ETM suspension and high frequency of PDH signal is sent to AOM. AOM is used for frequency actuator.
IMC
PR2 BS
ITMY
ETMY
Arm Cavity
PSL laser
PR3

7. ALS Configuration by Simulink Noise Budget
PDH signal ① ⑪ ⑥ ⑦ ⑧ ③
Beat signal ④ ②
Low ⑤
High
PZT actuator ⑨
This Simulation is based on Tatsumi-san’s study. He did not use Noise budget, So I reproduce the noise simulation by Noise Budget over. The left part is PLL system and the right part is PDH system. The beat signal between the Prometheus signal and PSL signal is feedbacked to PZT actuator in Prometheus. PDH system is this. Green laser is generated by SHG and sent to cavity via optical fiber. LOW PDH signal is sent to suspension and high frequency is sent to AOM.
Stabilized laser comparing PSL. ⑩
Green Block : Photo detector
Pink Block : Actuator
Blue Block : Filter
Orange Block : Noise
2016/8/27
F2F Meeting in University of Toyama

8. Open-loop Transfer Function
PLL Open Loop TF
Gain (dB)
Phase (deg)
Open-loop Transferfunction is this. The left graph is PLL system and the right one is PDH system.
Frequency (Hz)
2016/8/27
F2F Meeting in University of Toyama

9. Open-loop Transfer Function
PLL Open Loop TF
Gain (dB)
The same as Tatsumi-san’s study!!!
Phase (deg)
This result is the same as Tatsumisan’s study using Noise budget, so my simulation is good .
Frequency (Hz)
2016/8/27
F2F Meeting in University of Toyama

10. Amount of noise source estimation
①PROMETHEUS frequency noise
=10000/f Hz/√Hz **Prometheus catalog spec
②PSL frequency noise
=1.0654e-6×f-2/(1+(2/f)-8) Hz/√Hz **modeled
③Local Oscillator noise
=5e-5/f Hz/√Hz **Agilent E8663D-UNX catalogue spec
④Shot noise PLL
=2.5e-8 rad/√Hz **[5]
⑤PLL servo Erectronic noise
=100e-9 V/√Hz **[5]
⑥Fiber phase noise
=1 **[1]
⑦Shot noise GREEN PDH
=8e-6 Hz/√Hz **[5]
⑧Seismic motion noise
=1e-9/f2 m/√Hz **[5]
⑨VCO noise
=5e-5/f Hz/√Hz **E8663D-UNXcatalogue spec
⑩Shot noise IR PDH
=8e-7 Hz/√Hz **[5]
⑪SHG noise
=1e-5 Hz/√Hz **[5]
Amount of noise source estimation. These values are calculated by Tatumisan.
I checked not all noise source . I checked only Red values. So I need to check all values .
Red is checked value by myself
2016/8/27
F2F Meeting in University of Toyama

11. Result : Displacement noises at IR Error
Requirement ; 33 pm rms [4]
The reult of noise budget is this. This graf is Displacement noises at IR Error.
The blue curve is Sum of these noises and the orange curve is fiber noise. Fiber noise is main noise.
The noise level is under the requiment values.
2016/8/27
F2F Meeting in University of Toyama

12. F2F Meeting in University of Toyama
Conclusion
I can reproduce the ALS system noise simulation which was calculated by Tatsumi-san using a different method ; Noise Budget!!.
I need to check the all noise sources.
The main displacement noise is Fiber noise. In this simulation, the displacement noise level is under the requirement value. I simulated the noise using 4 km optical fiber, but practically we need only 50m fiber in KAGRA, so I think the noise level will decrease.
2016/8/27
F2F Meeting in University of Toyama

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Future Works
Table-top ALS experiment at University of Toyama
Calculation remaining noise values
PLL circuit will be designed by Doi-san
2016/8/27
F2F Meeting in University of Toyama