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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