1. Detection Of High Frequency Gravitational Waves At LIGO W. Butler , A
Detection Of High Frequency Gravitational Waves At LIGO W.Butler , A.C.Melissinos University of Rochester
Parametric Conversion “Picture”
Angle of Incidence of the G.W.
Results from H4K
Sensitivity
Possibilities with Advanced LIGO
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2. PARAMETRIC CONVERSION
THE LIGO IFO ADMITS A SPECTRUM OF DISCRETE FREQUENCIES n
THE FREQUENCIES ARE EQUALLY SPACED
Δ 0= 2L/c
0 IS THE FREE SPECTRAL RANGE (fsr)
0 = kHz
_____
_____ n+1
_____ n
_____ n-1
WHEN THE IFO IS LOCKED ONLY ONE MODE IS OCCUPIED n = n / 0  1010
THE WIDTH OF THE MODES IS
   / Q Q = F (2L / )  1012
IN THE PRESENCE OF A PERTURBATION AT FREQUENCY
    
THE (n+1) AND (n-1) MODES BECOME POPULATED
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LSC Presentation 3/17/03

3. En1 = En (x0 / 0) F /[1 + ( / )2] 1/2
2. EXPECTED SIGNAL
En FIELD IN MODE n
En1 FIELD IN MODE n1
 DIMENSIONLESS PERTURBATION
FOR En1 << En AND t >> Q / 
En1 = 0.5 En  Q
3. EXAMPLE: END MIRROR (ETM) MOTION
x = x0 cos  t  = x0 / L
En1 = En (x0 / 0) F /[1 + ( / )2] 1/2
 = 0 ( / F)
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4. EFFECT OF A GRAVITATIONAL WAVE
TRANSFER FUNCTION FOR “OPTIMAL INCIDENCE”,  = 0
H1() = sinc() e-i
 = 2L / c = 1 / 0 H1() = 0
TRANSFER FUNCTION FOR   
H1() = cos2 {sinc[ sin ]e-i + sinc[ +sin ] ei} e-i()(2+sin )
FOR F-P CAVITY
HFP() = H1() /[(1- r1)2 + 4r1 sin2(/2)]1/2
AVERAGE OVER ANGLES, POLARIZATION 1/5
SIDEBANDS AT     
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7. RESULTS FROM H4K (2002-W.BUTLER)
SHAKE ITMX (SINGLE ARM)
EXTRAPOLATE MIRROR MOTION FROM D.C. CALIBRATION. (FOR 1V DRIVE)
x0(0) = xDC / (1 + (0/p)2) = 8 x m (1)
OBSERVE AT A.S.PORT EA
CARRIER FIELD ON BS E2
SIDEBAND FIELD ON BS ERF
|EA / E2| = 4 (x0 / c) F (2)
PHOTODIODE VOLTAGE
VA = k |E2|2 |ERF / E2| |EA / E2|  30 |EA / E2| (V)
OBSERVE (FOR 1V DRIVE)
VA = 3 x 10-5 V  |EA / E2|  10-6
FIND USING (2)
x0  m
IN AGREEMENT WITH (1).
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9. SHAKE ITMX (FULLY RECYCLED IFO)
PARAMETRIC RESONANCE MUCH NARROWER GOVERNED BY “DOUBLE CAVITY POLE”
cc  0 (1 – rF*R)
rF*R REFLECTIVITY OF FRONT CAVITY MIRROR WHEN RECYCLING CAVITY ON RESONANCE
SENSITIVITY
FOR TINT = 100 s OBSERVE
VN = 2 x 10-7 V (S/N 150)
FOR TINT = 105 s (1 DAY) EXPECT
VN = 0.6 x 10-8 V
(S/N = 5) x0 = m
x0 / L = h = 2.5 x 10-22
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14. LIGO WITH SIGNAL RECYCLING
THE “RECYCLING” MIRROR NOW COUPLES THE TWO ARMS (CAVITIES)
LASER
THE CAVITY MODES SPLIT INTO
S = 0 + (c / 2L)(1/) tan{arctan [(1-r1)/(1+r1) cot z/4]}
A = 0 - (c / 2L)(1/) tan{arctan [(1-r1)/(1+r1) tan z/4]}
z = 2 (2a / ) 2a = distance between cavities
r1 = cavity input mirror reflectivity
LOCK LASER AT S
SIGNAL APPEARS AT A
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