G040452-E

LIGO I simulation using FFTHiro Yamamoto / LIGO-Caltech

A few news from LIGO I commissioningthermal compensation systemphase camera

LIGO I mirror phase mapFFT toolsThermal lensingBeam splitter curvatureInterpretation of results using modal model

October 13-15, 2004, Virgo 2G040452-E

Phase camera andthermal compensation system

Phase camera» EIFO : Field from interferometer

– SB-, CR, SB+ with modulation frequency of 25MHz

» Elaser : Field from laser frequency shifted by 75MHz» Demodulate EIFO + Elaser by 50, 75 and 100Mhz to measure SB+, CR and

SB- separately

Thermal compensation system (TCS)» CO2 laser to heat ITMs

– Central heating : enhance NdYAG heating effect– Annular heating : suppress NdYAG heating effect

» Somehow, differential heating, inline ITM cooler than offline ITM, preferred» It seems SB imbalance is related

October 13-15, 2004, Virgo 3G040452-E

Phase camera image at dark port2W Input, TCS : AX600-CY75

SB+

SB-

I-demod

(SB+)

Gaussian fit

Signal-Gaussian fit

CR

Q-demod

DC

By L.Matone and K.Kawabe

October 13-15, 2004, Virgo 4G040452-E

FFT tools

Calculation of static fields in Core Optics system» Orsay -> MIT» Core optics phase map» Thermal lensing effect» Beam splitter curvature

Propagation with magnification» Virgo Physics Book, Volume 2 “OPTICS and related TOPICS”, 3.1.7» FFT pixel size can be scaled - 25 cm mirrors to mm detector» Fields can be propagated through telescopes to actual detectors

FFT lock vs LSC lock» FFT lock uses only CR, LSC lock uses CR and SBs» Lock FFT by itself -> Lock using ASQ,REFL,POB» Arm lengths change by 10^-12m, Michelson lengths by 10^-9m» Quantitative results affected, most of qualitative results OK

October 13-15, 2004, Virgo 5G040452-E

Effect of mirror aberration

2.5e-4+ Differential heating

2.3e-4+ Mirror phase maps

1.2e-4+ BS curvature

6.8e-5+ as-built arms

5.5e-7Mode matched,identical arms

Contrast defect

P(CR)=46W ->36 W P(CR)=3.3kW -> 2.6kW

P(C

R)=

3.2

kW

->

2.5

kW

Dark port CR

October 13-15, 2004, Virgo 6G040452-E

Thermal lensing in FFT- P. Willems calculated based on MIT model -

1

f=

n 1

Rm+

1

RoptPower

Ropt=1.7km

Op

tica

l th

ick

nes

s @

1w

Sid

eban

d r

ecy

clin

g g

ain

radius (m)

total heating (mW)

1

Rf (HR)=

1

Rf (AR)

1

f

Power = 58mW

Flat BS

Carrier gain is constant

October 13-15, 2004, Virgo 7G040452-E

Gaussian and Annular

Piston subtracted

Op

tica

l th

ick

nes

s (1

0-6

m)

October 13-15, 2004, Virgo 8G040452-E

Beam splitter phase map

WA4K BS

WA4K BS - curvature subtracted

x 10-8

nm

nm

concave ROC > 200km, convex ROC > 720km

October 13-15, 2004, Virgo 9G040452-E

Mode disturbance in PRM- BS and ITM curvature and BS lens -

cur =z

z0(1

Rf (z)

RITM

) : 0.23(cold) ~ 0(hot)

ref (x / y) =z2 + z0

2

z0 RBS 2±1 : 0.027

tra =n 1

2 ref : 0.005

TEM 00(out) =1

(1+ i x )(1+ i y )TEM00(in)

RBS = -200km

RITM = -14km

z0(Rayleigh range) = 3.6km

z(distance to waist) = -1km

Reflection and transmission change field curvature

October 13-15, 2004, Virgo 10G040452-E

ITM differential heatingand beam splitter curvature

hot

hotflat

hot

coldflat

hot

hotcurved

cold

hotflat

Power on Symmetric port

CR

lower

upper + +

xy

5cmx2,y2

P(x,0) vs x2, P(0,y) vs y2

• Linear line : gaussian

• Blue vs red : sideband imbalance

• --- vs + + + : astigmatism

P(x,y)

October 13-15, 2004, Virgo 11G040452-E

SB gain vs differential heatingR

ecy

clin

g g

ain

60mW

Gaussian

On both

Upper SB Lower SBFlat BS

200km BS

ITMy annular heatingITMx annular heating

200 mW-200 mW

October 13-15, 2004, Virgo 12G040452-E

Reflection by a locked arm- CR~00, SB~00+02/20 -

ESB =1

1+ iE00

i / 2

(1+ i )3(E02 + E20 ) +O(

2 )

ECR =1

1+ iE00

i / 2

(1+ i )3(E02 + E20 ) +O(

2 ) E4

21

1+ i / 2(

1

1+ i / 2E00

i / 2 / 2

(1+ i / 2)3(E02 + E20 ) +O(

2 )) E7

=1

1+ iE00 +O(

2 )

=z

z0(1

RFieldRITM

)z

z0(nsubstrate

RITM

RRM

RITM

Rthermal)

October 13-15, 2004, Virgo 13G040452-E

Fields in mode mismatched FP

R = R0 Exp[i CR,00 + i ], R0 = rRM rITM

CR,00 = 2kCRL + 2 arctan( )

mix =1

2cot(2 ) 2

= 2kSBL + mix

Ecav =tRM Ein

(1 R)(1+ C02 )(EPRM ,00 i C2 (EPRM ,02 + EPRM ,20 )) +O(

3)

C0 =(1 i cot(2 )) R

2(1 Exp(i4 )R)

C2 =Exp(i 2 )

2(1 Exp(i 4 )R)

SBPower(kSB ) =

F(kSBL + f1( ) + f2 ( ))

SBPower(kSB ) SBPower( kSB )

October 13-15, 2004, Virgo 14G040452-E

FFT vs LSC lock

lower SB upper SB

FFT lock LSC lock

-0.50i-0.48iSpob

5.111.8SB-

-1.24.9SB+

-80.2CR

-0.57i-0.57iSpob

5.17.2SB-

-2.3-0.6SB+

-1.90.3CR

LSCFFT

sym

met

ric

dif

fere

nti

al

0.96-0.96 1.10-0.96

n(ITMx)-n(ITMy)

SB becomes more

symmetric

October 13-15, 2004, Virgo 15G040452-E

Dark Port sideband profile by FFT- after LSC lock -

upper SB

lower SB

No phase map

Symmetric heating

With phase map

Symmetric heating

With phase map

Differential heating

200k BS

curvature