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Wan Wu, Volker Quetschke, Ira Thorpe, Rodrigo Delgadillo, Guido Mueller, David Reitze, and David Tanner

Noise associated with the EOM in Advanced LIGO

Physics DepartmentUniversity of Florida

Gainesville, FL

Supported by NSF PHY-0555453

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Laser noise coupling

• The coupling of laser noise to the readout signals arises through two mechanisms :

1. Loss difference of arm cavities (at high frequencies)2. Technical radiation pressure noise (at low frequencies)

Requirement on the laser amplitude and phase noise.

The coupling effect in the DC sensing scheme is highly dependent on the readout phase (K. Somiya, Y. Chen, S. Kawamura, and N. Mio, Phys. Rev. D, 2006)By choosing a proper readout quadrature, laser intensity noise (~ ) and laser phase noise (~ at 100 Hz)will not be a problem

Hz/102 9 Hz/10 10

• EOM produces additional amplitude and phase noises on the transmitted light

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EOM to be placed in Advanced LIGO

Signal recycling cavity

SRM

BS

ETMITM

ITM

Mode Cleaner

EOM PRM

ETM

Noise due to the Mach-Zehnder configuration not discussed here

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Noise generation mechanism I

])[(01

])[(0100

)]sin([0 )()()( titititmti eEmJeEmJeEmJeEE

• Variation of modulation index changes the amplitude of both the carrier and the sidebands

• RF modulation on the laser:

Carrier Sidebands

mmJ

mJ

A

A

C

C )(

)(

0

1

Carrier light circulates inside the arm cavities and the power imbalance leads to the technical radiation pressure noise.

d

Vnr

Lm z

z3

33

modulation index

(Guido Mueller, LIGO T020021-00 )

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Noise generation mechanism II

• Misalignment of the EOM imposes a phase retardation (Δ ) between the linear polarized light orthogonal components – along the e-axis and along the o-axis of the crystal.

( S. Kawamura, A. Abramovici and M.E. Zucker,Rev.Sci.Inst , 1997 )

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Fluctuation of Δin the gw band Phase noise on the light

Residual amplitude modulation

(laser amplitude noise)

Lnn xz )(2

phase retardation

Noise generation mechanism II

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Fabry-Perot cavity effect due to the reflectivity of the front and end surfaces of the crystal.

Noise generation mechanism III

cceTAeTATAeEE tiss

tisscc

ti .00

c

Lni

c

Lni

err

errT

2

21

22

21

1

11

0TTc

0TTs

Possible amplitude change due to the 0.2% reflectivity

0 5 10 15 20-2

-1

0

1

2x 10

-3

temperature(K)

rela

tive

ampl

itude

cha

nge

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Measurement of the intrinsic EOM noise

Nd:YAG

Nd:YAG

EOM

PLL

Phase meter

f 1

f 2

• Phase lock two lasers with a frequency offsetPhase lock two lasers with a frequency offset

• Measure the beat signals – Measure the beat signals – Carrier-CarrierCarrier-Carrier (C-C)(C-C), , Carrier-Sideband (C-S)Carrier-Sideband (C-S)

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Phase meter

• Phase meter is the DSP instrument to have the I/Q measurement on the RF signals - developed by UF LISA group

- 100 MHz sampling frequency

- time series measurement on the mixture of signals

- output amplitude and unwrapped phase

Advantage we gain: Avoid using diode mixers!

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Amplitude noise & phase noise

101

102

103

10-6

10-4

10-2

frequency (Hz)rela

tive

ampl

itude

noi

se (

/ H

z)

Carrier-Carrier

Carrier-Sideband

101

102

103

10-8

10-6

10-4

frequency (Hz)

Pha

se n

oise

(cy

cle/

Hz)

Carrier-Carrier

Carrier-Sideband

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Noise in the beat notes

• Beam jitter between two laser beams

• Laser intensity noise

Noise in two beat signals (C-C, C-S) in common mode

Noise in two beat signals in differential mode (amplitude & phase noise)

- produced by the EOM

Common mode noise

rejection analysis

CCofamplitude

SCofamplitudefft

CCSCfft

Amplitude

Phase

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Data analysis

101

102

103

10-6

10-4

10-2

frequency (Hz)rela

tive

ampl

itude

noi

se (

/ H

z)

Carrier-Carrier

Carrier-Sideband

101

102

103

10-6

10-4

10-2

frequency (Hz)rela

tive

ampl

itude

noi

se (

/ H

z)

Carrier-Carrier

Carrier-Sideband

C-S/C-C

101

102

103

10-6

10-4

10-2

frequency (Hz)rela

tive

ampl

itude

noi

se (

/ H

z)

Carrier-Carrier

Carrier-Sideband

C-S/C-C

Laser intensity noise

101

102

103

10-6

10-4

10-2

frequency (Hz)rela

tive

ampl

itude

noi

se (

/ H

z)

Carrier-CarrierCarrier-SidebandC-S/C-CEOM driverLaser intensity noise

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Data analysis

101

102

103

10-8

10-6

10-4

frequency (Hz)

Pha

se n

oise

(cy

cle/

Hz)

Carrier-Carrier

Carrier-Sideband

101

102

103

10-8

10-6

10-4

frequency (Hz)

Pha

se n

oise

(cy

cle/

Hz)

Carrier-Carrier

Carrier-Sideband

c-s

-c-c

101

102

103

10-8

10-6

10-4

frequency (Hz)

Pha

se n

oise

(cy

cle/

Hz)

Carrier-CarrierCarrier-Sideband

c-s-

c-c

EOM driver

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recommendation

• Two important factors: n and L

TdT

dnnn oe

oeoe ),(),(0),(

TLL 0

Acoustic vibration could also change the length of the crystal L.

Temperature effect:

Need temperature stabilization and possibly acoustic isolation

Test a modulator made of wedged crystal.