Noise coupling
due to scattered lightfrom output optics
Koji Arai
National Astronomical Observatoryof Japan(TAMA Collaboration)

Contents of the talkl Brief introduction of simulation activities
in TAMA/LCGT collaborations
l Scattered light noise
Motivation
Principle of the noise
Approach used in this study
Simulation and interpretation of the result
Michelson/Recycled MI/Recyceld FPMI
Discussion/Conclusion

Simulation activities in TAMA/LCGTl No comprehensive work to construct our own
simulation environment / tooll As users of the simulation softwares
E2E: (ICRR - Hayakawa, et al, with LIGO E2E team)Modeling of CLIO (100-m cryogenic prototype in Kamioka)
h(t) injection module
Finesse:(NAOJ - Kawamura, et alwith LIGO 40m team)
Lock acquisition study for Caltech 40m
Sensing design for an RSE interferometer (NAOJ - Kokeyama, et al)
Scattered light noise estimation (NAOJ - Arai, et al)

LISO:Linear circuit simulations (NAOJ, U-Tokyo. etc)

l Analysis related simulations
Software signal injection of galactic GW events
Crosstalk study of two co-located interferometer(Osaka City Univ - Kanda, et al)Scattered light ~ introductionl Demand of simulations from the site
Commissioning work
> Various kind of problems day by day> Always confused by the complicated real world

To grasp what is happening in the real detector> Even a simple model is often sufficient
if it reflects the physics we want.
> No need to be too exact--- actual values will be obtained from experiments

Feedback to experiments> Suggestions to the experiment> Suggestions of experimental methods

Scattered light ~ motivationl Scattered light noiseA) Scattered light in the beam tubeB) Scattered light at the optical portsA) Scattered light in the beam tube
> For the design of the long vacuum tubes and the buffles
seismic motion
scatterscatter& recombine> Experiment in TAMA
Excitation of a tube resonance: 5.6um@ 776.5Hz => 1x10-17 m in the sensitivity
i.e. Seismic motion dx = 1x10-7 / f 2 m/sqrtHz => ~ 2 x 10-19 / f 2 m/sqrtHz=> Negligible
PRD, Vol.70, 062003
R. Takahashi, K. Arai, S. Kawamura, and M. R. SmithScattered light ~ motivation
B) Scattered light at the optical ports
Fact: touching of the output optics=> mechanical peaks in the sensitivitye.g.
> Tapping of the dark port optics=> huge noise> Bright portnoise!
=> moderate noise

excitation

Expect some fraction of the noise is owing to the scattered light
Q. Which optical port is dangerous? How much?
> Tapping every optics> More systematic estimation?

Scattered light ~ principlel Coupling of scattered light to the output signal
GW detector
optical phase sensor
Electric field of the main beam E=E0 ei Ω tIm(E0)Im(E0)

main beam+
GW

main beam+
scatteredlightGW

main beamψ'ψ

scatteredlightφ

main beamRe(E0)

ψ'ψ

Scattered light recombined to the main beam
Motion of the scattering body=> perturbation of the optical phase=> Appear in the output signal

Re(E0)

Scattered light ~ back scatteringl Only back scattering is considered
In order to couple to the output signal=> The scattered light should be spatially matchedto the main beamInterferometermismatched
beam
Scatteringbody
matched beam=back scattering=> Only consideration of TEM00 is enoughScattered light ~ factorsl Factors to determine the amount of the noiseInterferometer
4
3

2
Scatteringbody

1
matched beam=back scattering
1. Amount of the light power arriveson the scattering body.
2. Efficiency of effective back scattering
3. Sensitivity of the signal to the scattering
4. Amount of the scattering body s motion

Pout
ηscat
α
δxscatScattered light ~ factorsl Factors to determine the amount of the noiseInterferometer
4
3

2
Scatteringbody

1
matched beam=back scattering

1. Amount of the light power arriveson the scattering body. => Easy to simulate2. Efficiency of effective back scattering=> Experiment
3. Sensitivity of the signal to the scattering => Easy to simulate
4. Amount of the scattering body s motion => ExperimentSimulation ~ Using Finessel Finesse" is selected for the tool
Reason: It looked the easiest tool for the purpose
Any kind of length sensing tool does fit

l Use Finesse at the most basic level
Modulation sideband: up to 1st order

Spatial mode:
Frequency range:

only TEM00
only at DCl Based on the TAMA300 parameters
Michelson (MI) / Recycled Michelson (RMI) model=> To understand nature of the scattered light noise

Recycled Fabry-Perot Michelson (RFPMI) model=> To acquire the applicable knowledge to TAMA300

Simulation ~ MI/RMI model
RMI:The carrier is resonant
The sidebands are not resonant

P=2W m=0.35
Laser EOM

Recycling
Mirror

Front R=0.988
Mirror2

Front
Beamsplitter Mirror1

For RMI: R~0.5
For MI: R~0Dark port
Photodetector

Simulation ~ MI/RMI model
Placing scattering bodies
with effective reflectivity of 1ppm

BSAR-coating
R=150ppm

ArmTransmitted
T=0.012

Scattering body
R=1ppmSimulation ~ MI/RMI model
Pickoff mirrors (R=10-3) are inserted at several places~ avoiding to disturb the internal condition

Pickoff(R=10-3)

Bright port

Scattering body
R=1

Pickoff(R=10-3)
Dark port

Simulation ~ MI/RMI model
Sweep the position of each scattering body=> Look at the dark port signal

shake

Dark portnoiseSimulation ~ how to evaluate the result
Effect of the motion of the scattering source

displacement
noise [m]Example: noise by the motion of the mirror behind the arm
1.5x10-12
no effect
1.0x10-12
0.5x10-12worst effect
0A
0.5x10-12
1.0x10-12-1.5x10-12
0
λ/4
λ/2
3λ/4
displacement> Small amplitude motion

δxmax = (4 π A / λ) δxscat> Large amplitude motion

dx = Aλat f = 2 vscat / λ (fringe frequency)> Note: Noise amplitude A is proportional
to the amplitude of the scattered light
Rscat = 1ppm => ARscat = 100ppm => A = 10 A

Simulation ~ Carrier/sideband decomposition
Scattering source ~ three kinds of mirrors

SidebandsCarrier> Separating the contribution ofthe carrier and the modulation sidebands

shakeMirror:
CA reflected
SB reflected

shakekeeping
resonated

SB resonant FP:
CA reflected
SB absorbed

CA resonant FP:
CA absorbed
SB reflected(reflection 99.7%, absorption ~100%)

Simulation method summaryl Sweep the position of each scattering source
Scattering source at: Arm trans., BS AR coat, Dark, Bright
Detector output:
Sin wave (amplitude A)=> A = (Pout)ε α ηscat for ηscat = 1 ppml Decompose the contribution of CA/SB
Ordinary mirror:

Carrier + Sidebands

SB resonant FP:
CA resonant FP:

only Carrier
only Sidebands

l Inject imperfections of the interferometer
Michelson offset: dx = 10-12 m ~ 10-10 m
Reflectivity mismatch of the arm mirrors:dR = 100 ppm ~ 10000 ppm

Note:

Macro- and microscopic deviations of
the recycling cavity hardly effect the results

MI/RMI model ~ DC power
RMI case:

P0: carrier power
P1: sideband power

P0=2W
P1=0W

Power consumption:
94% is reflected to the bright port
60mWx2 (3%x2) transmitted from the arms

P0=1.88W P0=10.1W (G0=5.4)
P1=59mW P1=11mW (G1=0.19)

P0=61mW
P1=67uW

P0=1.76W
P1=58mW

P0=0.75mW
P1=0.83uW
P0~0
P1=0.81mW

MI case: Change RM with R=0-1110-1210

A: Scattering noise amplitude [m]A: Scattering noise amplitude [m]MI model ~ Result-13-14-1210

Arm Trans
BrightBS AR

10-1110Arm Trans
Dark
Bright-131010-1410-1510BS AR-1510Dark-1610For 1ppm scattering-17100-1210-1110Michelson Offset [m]-1610-1010For 1ppm scattering-17100102103dR [ppm]104Arm trans. / BS AR noise level: not affected by the deviations
Carrier added to only one of the arm => becomes the signal directly
A = 9.0 x 10-11 Pout [m](for 1ppm scattering)

Bright/Dark case: depends on how much the imperfection isIdeal case: no noise <= No carrier at dark, perfect common mode rejection

MI model ~ Result
A: Scattering noise amplitude [m]l Separate the contrib. of CA and SB-12

CA scat@dark
CA scat@brightSB scat@dark

10-13

10

SB scat@bright-14

10

Michelsonoffset

-15

10

R mismatch

-16

10

10

-10

-910-8-7-6101010
Contract Defect (1-C)-510No matter what the origin of the leakage carrier is~ Noise coupling is determined by sqrt of contrast defect(= by the leakage carrier field at the dark)MI model ~ Interpretationl Noise coupling is determinedby the leakage carrier at the dark
Leakage carrier field

Pca@dark

Carrier scattering at the dark port:
All of the injected carrier from the dark port becomes the noise=> Noise coupling is proportional to Pca@dark

Carrier scattering at the bright port:
How much the carrier does leak to the dark port=> proportional to Pca@dark

Sideband scattering at the dark port/the bright port:
Some amount of the scattered sidebands appears at the dark port=> Couples with the leakage carrier=> Proportional to Pca@dark

MI/RMI model ~ DC power
RMI case:

P0: carrier power
P1: sideband power

P0=2W
P1=0W

Power consumption:
94% is reflected to the bright port
60mWx2 (3%x2) transmitted from the arms

P0=1.88W P0=10.1W (G0=5.4)
P1=59mW P1=11mW (G1=0.19)

P0=61mW
P1=67uW

P0=1.76W
P1=58mWP0=0.75mW
P1=0.83uW
P0~0
P1=0.81mW

MI case: Change RM with R=0

MI/RMI model ~ RMI Resultl Power recycling does not change the situation
Power recycling increases
the scattered light and the signal at the same rate
Arm Trans
BS AR

MI(unit: m)
1.02x10-12
1.26x10-14

RMI(unit: m)
1.02x10-12
1.26x10-14

CA scat @ dark
SB scat @ dark

1.16x10-10
1.07x10-10

(1-C)
(1-C)

1.20x10-10
1.14x10-10

(1-C)
(1-C)

CA scat @ brightSB scat @ bright

1.16x10-10
2.98x10-11

(1-C)
(1-C)

1.16x10-10
3.39x10-11

(1-C)
(1-C)

MI/RMI model ~ Result Summaryl Asymmetric scattered light
Constant noise coupling~ Independent from the interferometer conditionA = 9.0 x 10-11 Pout [m](for 1ppm scattering)l Scattering at the dark port and the bright port
Dependent on the contrast defectA ~ 1 x 10-10

c.f. Bright port
Dark port(1-C) [m](for 1ppm scattering)~ Carrier of 2W=> Same order contribution~ Carrier of ~0W

l Power recycling does not change
the scattered light noise level

RFPMI model ~ DC light level
50ppm loss

Power consumption:
50~60% is reflectedmost of the otherconsumed in the arms

P0=2W P0=1.88W
P1=0W P1=59mW

Bright port

50ppm loss

P0=8.69W(G0=4.6)
P1=261mW(G1=4.4)

P0=1.39kW(F0=506)
P1=386uW
0.5% loss

P0~0
P1=19mW
P0=1.18W(V0=62.9%)
P1=32mW(G1=54.2%)

50ppm loss

Arm PO

P0=27.2mW
P1=852uW

Dark port

ArmTransmitted
50ppm loss

P0=69mW
P1=19nWRFPMI model ~ Resultl Even with the FP arms the noise coupling isunderstood as the Michelson caseby including the signal enhancement by the FP arm(factor of NFP=322)
MI(unit: m)

RFPMI(unit: m)
4.23x10-15
9.0x10-11 Pout / G0 / NFPFP Arm Trans
BS AR (Arm PO)

9.0x10-11 Pout

CA scat @ dark
SB scat @ dark

1.16x10-10
1.07x10-10

(1-C)
(1-C)

1.11x10-100.89x10-10

(1-C)
(1-C)

CA scat @ brightSB scat @ bright

1.16x10-10
2.98x10-11

(1-C)
(1-C)

0.91x10-10
2.78x10-11

(1-C)
(1-C)

This means:
Scattered light noise level with MI or RMI will appear
in the RFPMI sensitivity by a factor of 1/NFP

Discussionl Calculation shows:
Noise from the dark port vs Noise from the bright port=> Comparable
Presence of higher order modes=> Higher order modes increase the scattered light
couples to the main beam
The noise from bright port is not affectedby the higher order modes=> It may be possible to estimate the imperfection levelof the interferometer using the bright port

Conclusionl Single mode simulation for scattered light noise
MI/RMI/RFPMI cases are essentially the same=> Considering:
Recycling gain & Signal enhancement by the FP armAsymmetric scattered light has the constant contrib.
=> Independent from the interferometer condition=> Dependent how much power appear at the optical port
Dark port and bright port=> Dependent on the contrast defectPresence of higher order modes=> Increase the noise from the scattering at the dark port

Experimental investigationl Factors to determine the amount of the noise
1. Amount of the light power arriveson the scattering body.

=> included in the calculation
2. Efficiency of effective back scattering
3. Sensitivity of the signal to the scattering=> included in the calculation
4. Amount of the scattering body s motion=> vibration measurement with an accelerometer
Actuation of the opticsa) with a small amplitudeb) with a large amplitude

Displacement [m]10-1310-14

10-15

10-16

10-17

1.2x10-8 m -> 2.2x10-14 m

2960

2980
3000
3020
Frequency [Hz]3040

RMI displacement (2004/2/18)-7

10-810

MC End mirror excited (5mVpk 1Hz)
Front/End targets open
End targets closed
Front targets closed
2004/2/16 (Ref.)

-9

1/2

Displacement noise [m/Hz ]10-1010-1110-1210-1310-1410-1510-1610-17100

101102

1010

Frequency [Hz]3104105