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```Optical characterisation of VIRGO
E. Tournefier
ILIAS WG1 meeting, Cascina
January 25th ,2005
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Introduction
Beam matching
Measurements of Fabry-Perot parameters
Measurement of recycling gains
Lengths of the recycling cavity
Conclusion
Optical parameters of the ITF
losses
Finesses FN, FW
Recycling gains: Gcarrier, GSB
modulation: Fmod, m
Input beam matching
to the ITF
l1
l0
l2
Rrec
losses
Contrast defect, CMRR
And the lengthes:
- Recycling length:
lrec = l0+(l1 + l2)/2
- Asymmetry of the small Michelson: l = l1 - l2
Why are we interested in these measurements ?
The mirrors parameters (reflectivity, losses, radius of curvature) have been
measured in Lyon and are within the specifications.
=> are the ITF optical parameters as expected ?
=> also important for the tuning of the simulations
•
Finesse:
– expected value from Rinput=88%: F=50
– the rejection of the common mode depends on the finesse asymmetry
between the 2 FP cavities
•
Radius of curvature (ROC) of the end mirrors
– Important for the ‘automatic alignment’: it uses the Anderson technique
=> the first HG mode of the sideband must resonate in the cavity
=> the modulation frequency depends on the ROC
Why are we interested in these measurements ?
•
Losses (reflectivity) of the FP cavities:
– expected to be ~ 100ppm
– the recycling gain depends strongly on them through Rcav
– are they small enough ?
2
 trec 

Grec 1rrecrcav 
•
Recycling gains:
– with Rrec = 92.2% we expect Grec= 50
– does the recycling gain fit with the expected losses?
– we will soon change the recycling mirror
 Need to understand the actual gain in order to define the
reflectivity of the next mirror
•
Recycling length:
– The sidebands must resonate in the recycling cavity
 Recycling length has to be tuned to the modulation frequency
•
Contrast defect, CMRR: are they small enough?
Matching of the input beam to the ITF
tuning of the telescope length
Beam size and power
The matching of the input beam parameters is done by tuning
the length of the input telescope length:
 The best matching maximizes the power stored in the FP cavity
Note that the beam is astigmatic due to the spherical mirrors of the telescope:
 a perfect matching cannot be reached
Matching of the input beam to the ITF
The monitoring of the beam shape at 3km vs the telescope length allows to
determine the input beam parameters: wx, wy,Rx,Ry
 94% of the beam power is
coupled to the FP cavities
Stored power
x beam size
y beam size
Telescope length
Measurement of the Fabry-Perot parameters:
Finesse (F) and radius of curvature (ROC)
Use a single Fabry-Perot cavity with mirrors freely swinging
=> use the transmitted power
Transmitted DC power
FSR
FWHM
Shape of the Airy peaks (FWHM) +
distance between 2 peaks (FSR)
Finesse
F 
FSR
FWHM
d02
ROC 
Lcavity
2
1cos  d01
d00
 
Position of the first and second order modes => Radius of curvature of the end mirrors
Measurement of the Fabry-Perot parameters
Problem with real data: the speed of the mirrors is not constant
=> need to correct for the non-constant speed
We know that between 2 peaks the cavity length has changed by /2
=> deduce the cavity length l(t) versus time
Cavity length (/2)
/2
Time (s)
The cavity length is modeled with l(t) = A cos(wt+p) (true on ~1 period)
=> the speed and the length of the cavity are known
Measurement of the Fabry-Perot parameters:
Finesse (F)
Another difficulty for the finesse: the Airy peak is distorted by dynamical effects
=> the FWHM is not well defined and is ‘speed dependent’
Solution 1:
- Use the value of the speed measured
- Simulate the Airy peaks for different
values of F
- Find the F value for which the simulation
fits the best to the data
Simulation
------ static
------ dynamic
v=25um/s
Solution 2: use the ringing effect
- the amplitude and position of the peaks
depend on the speed and on F
=> Determine v and F by comparing data
and simulation
Finesse measurements
• From the data taken with free FP cavities:
The finesse is extracted from a comparison of the shape of the Airy peak between the
data and Siesta simulations:
– ringing effect, high speed cavity (method 2)
(RNI =87.5%)
– low speed cavity (method 1)
(RNI =88.0% RWI =88.4%)
•
North
47
49±0.5
West
51 ±1
To be compared to Lyon measurements of mirror reflectivities:
- RNI =88.2% RWI =88.3%
50
51
 Good agreement with the coating measurements
Note that the finesse can vary by ~+/-2%: effect induced by thickness variation of
the flat-flat input mirror with temperature variation (not observed yet)
d
Fabry-Perot effect in input mirror: d => F
r0
R=88%
Measurement of the Fabry-Perot parameters:
Radius of curvature of the end mirrors (ROC)
Radius of curvature of the end mirrors
• Principle of the measurement on the data:
– extract the ROC from the distance between the first and second HG
mode and the 00 mode (free cavity)
– difficulty: the speed of the cavity is not constant
Method
use the position of the TEM00 modes to
determine the length l(t) assuming
l(t) = A cos(wt+p)
1/ Measure the time of the HG modes TEM00,
TEM01, TEM02: t0, t1, t2 and deduce the
distance between modes: d0i=l(ti)-l(t0)
2/ extract ROC from d02 and d01 :
Lcavity
ROC 
2
1cos  d01
d00
 
Cavity length (/2)
•
Transmitted DC power
00
d02
01
t0
t1
02
t2
Time (s)
Measurement of the radius of curvature
Results using this method:
ROC(North)
– From the data
• using 2nd mode
• using 1rst mode
ROC(West)
3550 ± 20 m
3540 ± 20 m
3600 ± 40 m
3570 ± 80 m
 The ROC can be determined within ~1-2%
– From the map of the mirrors measured at Lyon
-> simulation of the cavity with the real mirror maps, same method as on the data:
• using 2nd mode:
• using 1rst mode:
3558 ± 10 m
3566 ± 20 m
3614 ± 10 m
3643 ± 20 m
Differences are expected: the different modes do not see the same radius of
curvature
 Data and simulation results differ by at most 70 m
Do the ROCs fit with the modulation frequency ?
The modulation frequency has been tuned so that it resonates in the input mode cleaner
(see Raffaele’s talk)
One sideband should also resonate in the FP cavities for the 01 mode (Anderson technique)
 the modulation frequency should correspond to the Anderson frequency within 500Hz
The Anderson frequency is defined by the radius of curvature of the end mirror:
with the extreme values obtained from the measurement or the simulation with real
maps:
- R=3530m => fAnderson = 6264540 Hz
- R=3640m => fAnderson = 6263930 Hz

OK with fmod = 6264150 Hz :
fmod is different from the Anderson frequency by at most 400Hz
Measurement of the Fabry-Perot parameters:
losses (or cavity reflectivity)
rcav
rin
losses (L)
The cavity reflectivity decreases with losses:
rcav  rin 1L  1  L 1rin
2 1rin
1rin 1L
Losses on the cavity mirrors due to absorption + scattering :
~ 10 ppm measured in Lyon
But a simulation with real mirror maps gives: Rcav~ 98%
 Expect non negligible losses:
Rcav~ 98%  L = 600 ppm
with L = round trip losses
These losses might be due to mirror surface defects.
Tentative measurement of the cavity reflectivity (losses)
Use a freely swinging FP cavity:
- When the cavity goes through a resonance
the reflected power is
Pmin = P0 x Rcav
- Out off resonance the reflected power is
Pmax = P0
=> Rcav = (Pmax-Pmin)/Pmax
Transmitted power
Reflected power
Pmax
Pmin
Problems:
- large dynamical effects
=> need a very slow cavity
- the measurements seem very dependent on the alignement
=> Some hints for Rcav = 96-98% but no clear measurement
=> indicates round trip losses of the order of 500-1000ppm
=> Try to extract Rcav
2


from the recycling gain measurement: G  trec 

rec 
1r recrcav 
Measurement of the recycling gains: Gcarrier , GSB
2
 trec 

Gcarrier 1rrecrcar 
Recycling gain of the carrier:
Recycling gain of the sidebands:
Expected values (with Rcar, RSB=1) :
Gcarrier = 50 and GSB = 36


trec
GSB
l
1cos
c

2




rrecrSB 

 
l = l1 - l2
 = 2fmod
Measurement of the recycling gains:
• Compare the power stored in the cavity
with/ without recycling
• Can also use the reflected power
to extract rcar
2
 rrecrcar 

RITF 1rrecrcar 
rrec
l1
rSB, rcar
l2
rITF
Preflected
rSB, rcar
Pstored
Recycling gain of the carrier
1/ Comparing the power stored in the cavity with and without recycling:
Gcarrier= (PVirgo/ Precombined )x TPR  30
Equivalent to Rcav= 97-98 %
Stored power (Watt)
Virgo
2/ And with the reflected power the ITF reflectivity:
RITF = PVirgo / Precombined  0.6
Recombined / TPR
Equivalent to Rcav = 99%
Effect of higher order modes: they are not recycled
=> With 1/ the recycling gain for TEM00 is underestimated => Rcav also
=> With 2/ the ITF reflectivity is overestimated => Rcav also
 Probably we have: 97% < Rcav < 99% and therefore losses around L=300-600ppm
We should have better estimations when the automatic alignment is implemented
Recycling gain of the sidebands
The stored power is demodulated at twice the modulation frequency
 A comparison of this power with and without the recycling gives an estimation of
the sidebands gain:
2f mod
P
G 2T
P
SB
rec
Virgo
2f mod
Stored power at 2xfmod (Watt)
recombined
 Gives GSB  20 equivalent to RSB  97%
Another method using the stored powered in
Michelson, CITF and Virgo configurations
gives ~ the same result
Virgo
Recombined / TPR
A simulation with real mirrors gives GSB  25
Again we will have a better estimation when the automatic alignment is implemented
and with the full input power
Measurement of the recycling mirror reflectivity
The reflectivity of the recycling mirror rrec is extracted from the measurement of the
gain of the central ITF (g0):
g0 = 1 / ( 1-rrec rin)
rin
g0 is obtained from the power stored in the
central recycled interferometer:
rin
rrec
g0 =  (PCITF / Pmich)
Pmich
CITF
rin is known precisely enough from the finesses measurement: rin =88.0+/-0.5 %
From g0 : Rrec = (92.0 +/- 1.6) %
<- limited by power fluctuations due to alignment
Which agrees with the coating measurement made in Lyon: Rrec = 92.2 %
New PR mirror
PR mirror will soon be changed:
- monolitic mirror (resonances of the actual mirror disturb the locking)
- flat-flat mirror instead of curved-flat
=> Change also the reflectivity ?
The actual PR mirror has a reflectivity RPR = 92.2%
The reflectivity can be increased in order to increase the recycling gains:
•
It should not be too close to the cavities reflectivity in order to avoid phases
rotations which will complicate the lock acquisition
=> keep RPR < Rcav for the carrier and the sidebands
•
FP effect in flat-flat mirror => need to be carefull with the AR side coating:
the ‘real’ PR reflectivity has to be defined including this effect
=> We decided to increase the PR reflectivity from 92% to ~95%
Measurement of the lengths lrec , l
Why do we need to know these lengths?
• The recycling length lrec should be tuned to the modulation frequency ( the SB
should resonate)
• The length asymmetry l gives the transmission of the sidebands
These lengths are known from the tower positions at +/- few cm.
Can we measure them using demodulation phase tuning of the dark fringe signal ?
- if lrec is wrong:
the optimum demodulation phase used for the recombined and the recycled ITF
will be different
- l: the optimum demodulation phase for the West cavity and for the North
cavity should be different by  =  l/c
A precision on  of 0.1o will give 1.3 cm on l
=> Still to be investigated
Contrast defect
In the recombined configuration, the power on the dark fringe is given by:
Pdf = P0 ( J02(m) (1-C)/2 + 2J12 (m) T )
Where T is the sidebands transmission: T = sin2( l/c) = 0.013
Minimum power observed on dark fringe: Pdf = 6.5 W
=> Pdf / P0 = 3 10-4
Power on the bright fringe:
P0 = 45 mW
But the contribution from the sidebands is not negligible:
2 P0 J12 (m) T = (6.5 2 ) W
 P0 J02(m) (1-C)/2 < 2 W
( m is not precisely known)
and 1 – C < 10-4
The same exercise on the full Virgo configuration gives the same result
=> The contrast defect seems quite good: 1 – C < 10-4
Commom mode rejection ratio (CMRR)
The common mode noise (for example frequency noise) is not completely canceled by
the interference on the dark fringe: the remaining contribution reflects the
asymmetry of the 2 arms ( finesse, losses,..) => CMRR
Some measurements have been in the recombined configuration (no recycling) during C4
run (june 2004):
- The photodiode used for the frequency
stabilisation had high electronic noise (n).
- The frequency stabilisation introduced this
noise in the ITF as frequency noise ().
- This noise was seen on the dark fringe as a L:
L =  x (/ L) x CMRR
=Gxn
n
L =  x (/ L) x CMRR
Commom mode rejection ratio (CMRR)
Propagation of the electronic noise introduced by the frequency stabilisation to the
sensitivity:
C4 sensitivity (m/Hz)
 x (/ L) x CMRR
 The CMRR is estimated at high frequency (> few kHz) : CMRR  0.5%
More studies are going on with some frequency noise lines injected during the C5 run
Conclusion
•
The measurement of the mirrors reflectivities (recycling, input mirrors)
with the ITF data fits with the expectations
•
The losses in the FP aren’t precisely known but seem not negligible:
L ~ 500 ppm
•
The recycling gains will be better known when the automatic alignment is
implemented and the measurement easier with the full input power
Gcarrier ~ 30 (expected 50)
GSB
~ 20 (expected 36)
•
The contrast and the CMRR are quite good: 1 – C < 10-4 and CMRR < 0.5 %
```
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