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Modeling the 40m QND Workshop, Hannover Dec 15, 2005 Robert Ward Seiji Kawamura, Osamu Miyakawa, Hiro Yamamoto, Matthew Evans, Monica Varvella. Modeling tools used at the 40m. Twiddle Frequency domain, analytical, no radiation pressure Finesse Frequency domain, no radiation pressure - PowerPoint PPT Presentation
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40m Modeling and Experiment 1
Modeling the 40m
QND Workshop, HannoverDec 15, 2005
Robert Ward
Seiji Kawamura, Osamu Miyakawa, Hiro Yamamoto, Matthew Evans, Monica Varvella
40m Modeling and Experiment 2
Modeling tools used at the 40m
Twiddle» Frequency domain, analytical, no radiation pressure
Finesse » Frequency domain, no radiation pressure
E2E » Time domain, now with classical radiation pressure
TCST (Thomas Corbitt Simulation Tool)» Two-photon formalism, frequency-domain
Optickle» Frequency domain, Matlab, two-photon formalism
40m Modeling and Experiment 3
Finesse
0 50 100 150 200 250 300 3500
50
100
150
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300
350
Demodulation Phase of f1
Dem
odul
atio
n Pha
se o
f f2
Double Demodulation at SP- 0.4
- 0.4
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dc=0l+l-ls
Dem
odu
latio
n P
hase
of
f2
Lockingpoint
Finesse used extensively at the 40m lab 2004-2005
Seiji Kawamura modeled the DRMI very thoroughly using Finesse
Very useful for investigating quirks of double & differential demodulation
40m Modeling and Experiment 4
Differential Demodulation:offset vs gain
40m Modeling and Experiment 5
Finesse
100
101
102
103
104
105
-100
-80
-60
-40
-20
0
20
40
dB m
ag
CARM response
100
101
102
103
104
-150
-100
-50
0
50
100
150P
hase
f (Hz)
•Also used to investigate the coupled cavity response in our offset CARM state, and design compensation.
•Unfortunately has no radiation pressure effects
40m Modeling and Experiment 6
Straight from the ilog
Location of peak RSE response (in CARM) as a function of offset, modeled in Finesse, and then measured.
40m Modeling and Experiment 7
Dynamic compensation filterfor CARM servo
Optical gain of CARMOpen loop TF of CARM• Optical gain (normalized by transmitted power) shows moving peaks due to reducing CARM offset.
• We have a dynamic compensative filter having an nearly the same shape as optical gain except for upside down. Designed using FINESSE.
• Open loop transfer function has no phase delay in all CARM offset.
40m Modeling and Experiment 8
Error signal sweeps at 10-9 m/s for the 40m IFO obtained in
E2E framework and compared with TWIDDLE predictions
Example:DARM @ AP 166 MHz
TWIDDLE and E2E comparison
e2e SIMULATION:4Om/AdvLIGO package
TWIDDLE
E2E
40m Modeling and Experiment 9
e2e SIMULATION: 4Om/AdvLIGO package
Comparison between real data (black) and e2e simulated data (red) of the transmitted light for both the arms (full IFO): the mirror velocities used in
E2E simulation are the values obtained fitting the real data
Real data have been used to estimate relative mirror velocity for
both the arms:
Vxarm= (0.35 ± 0.13) μm/s
Vyarm= (0.26 ± 0.13) μm/s
E2E
E2E
real data
real data
Tr X
Tr Y
40m Modeling and Experiment 10
e2e SIMULATION: 4Om/AdvLIGO package
Comparison between real data , e2e simulated data and the
theoretical prediction V(t) of the SP error signal @ 166 MHz
The τ and the velocity v is the value obtained fitting real data
τ = 0.7 msv = 0.26 μm/s
V(t) ~ exp(t/τ) sin( a t2)
with a = (k v) / (2 T)
40m Modeling and Experiment 11
E2E: 40m Lock Acquisition
Simulation indicates that controlled reduction of CARM offset should work.
E2E simulation by Matthew Evans in June 2005
40m Modeling and Experiment 12
Optical spring in E2E
• Calculated by time domain simulation
• No length control• Lock lasts ~0.7sec, so
statistics at low frequency is not good.
• Simple length control required
• Calculation time ~5min using DRMI summation cavity
Hiro Yamomoto
40m Modeling and Experiment 13
E2E DARM TF to I and Q
•5W Input•Arms controlled with POX, POY (no DARM)•no MICH control
Hiro Yamomoto
40m Modeling and Experiment 14
E2E Optical Noise
40m Modeling and Experiment 15
Optical noise of 40m in E2E
• Simple length control (UGF~100Hz)
• Err2/(Err1/DARM) DARM: DARM excitation on mirrorsErr1: error signal with DARM
excitationErr2: error signal with optical noise
• How much further does E2E need to go? 2-photon?
• input vacuum?• Quantum control?• Or just classical physics +
shot noise + radiation pressure noise ?
Err2/(Err1/DARM)
40m Modeling and Experiment 16
TCST
102
103
80
90
100
110
120
130
140CARM optical springs at different CARM offsets
f (Hz)
CA
RM
opt
ical
res
pons
e (d
B)
Arm power = 6
Arm power = 8Arm power = 10•Solid lines are from TCST
•Stars are 40m data•Max Arm Power is ~80•Also saw CARM anti-springs, but don’t have that data
40m Modeling and Experiment 17
Optickle
101
102
103
104
-20
-10
0
10
20
30
40
50
60
70
80
f (Hz)
dB (
a.u.
)
DARM Response
40m DataOptickle
101
102
103
104
10
20
30
40
50
60
70
80
f (Hz)
dB (
a.u.
)
DARM Response
40m DataOptickle
40m Modeling and Experiment 18
CARM optical springs, with no offsets (TCST)