optical characterisation of virgo e. tournefier ilias wg1 meeting, cascina january 25 th ,2005
DESCRIPTION
Optical characterisation of VIRGO E. Tournefier ILIAS WG1 meeting, Cascina January 25 th ,2005. Introduction Beam matching Measurements of Fabry-Perot parameters Measurement of recycling gains Lengths of the recycling cavity Conclusion. Radius of curvature. losses. Finesses F N , F W. - PowerPoint PPT PresentationTRANSCRIPT
Optical characterisation of VIRGO
E. Tournefier
ILIAS WG1 meeting, CascinaJanuary 25th ,2005
• Introduction• Beam matching• Measurements of Fabry-Perot parameters • Measurement of recycling gains• Lengths of the recycling cavity• Conclusion
Optical parameters of the ITF
And the lengthes: - Recycling length: lrec = l0+(l1 + l2)/2 - Asymmetry of the small Michelson: l = l1 - l2
Finesses FN, FW
losses
Radius of curvature
Recycling gains: Gcarrier, GSB
Input beam matching to the ITF lossesRrec
l1
l2l0
modulation: Fmod, m
Contrast defect, CMRR
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
• Losses (reflectivity) of the FP cavities:– expected to be ~ 100ppm– the recycling gain depends strongly on them through Rcav
– are they small enough ?
• 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?
Why are we interested in these measurements ?
2
cavrec
recrec rr1
tG
Matching of the input beam to the ITF
tuning of the telescope length
The matching of the input beam parameters is done by tuningthe 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
Beam size and power
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
Telescope length
Stored power
x beam size
y beam size
Matching of the input beam to the ITF
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
Shape of the Airy peaks (FWHM) + distance between 2 peaks (FSR)Finesse
FSR
FWHM
Position of the first and second order modes => Radius of curvature of the end mirrors
FWHMFSRF
d02
00
012
cavity
ddcos1
LROC
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
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
Cav
ity
len
gth
(/
2)
Time (s)
/2
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
Measurement of the Fabry-Perot parameters:Finesse (F)
------ static
------ dynamic v=25um/s
Simulation
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:
North West– ringing effect, high speed cavity (method 2) 47 (RNI =87.5%)
– low speed cavity (method 1) 49±0.5 51 ±1
(RNI =88.0% RWI =88.4%)
• 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
r0
R=88%
Fabry-Perot effect in input mirror: d => F
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 :C
avit
y le
ng
th (/
2)
Time (s)
00
012
cavity
ddcos1
LROC
t0 t1 t2
00
01 02
Transmitted DC power
d02
Results using this method: ROC(North)
ROC(West)– From the data
• using 2nd mode 3550 ± 20 m 3540 ± 20 m
• using 1rst mode 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: 3558 ± 10 m 3614 ± 10 m• using 1rst mode: 3566 ± 20 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
Measurement of the radius of curvature
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 realmaps: - 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)
The cavity reflectivity decreases with losses:
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.
in
in
in
incav
r1r1
2L1
L1r1L1rr
rcavrin
losses (L)
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
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 from the recycling gain measurement:
Pmax
Pmin
Transmitted power
Reflected power
2
cavrec
recrec rr1
tG
Measurement of the recycling gains: Gcarrier , GSB
Recycling gain of the carrier:
Recycling gain of the sidebands:
Expected values (with Rcar, RSB=1) :
Gcarrier = 50 and GSB = 36
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
carrec
reccarrier rr1
tG
2
SBrec
recSB
rrclcos1
tG
rrec
rSB, rcar
rSB, rcarrITF
2
carrec
carrecITF rr1
rrR
PstoredPreflected
l = l1 - l2
= 2fmod
l1l2
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 %
2/ And with the reflected power the ITF reflectivity:
RITF = PVirgo / Precombined 0.6
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
Stored power (Watt)
Virgo
Recombined / TPR
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:
Gives GSB 20 equivalent to RSB 97%
Another method using the stored powered in Michelson, CITF and Virgo configurations gives ~ the same result
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
PPT2G modf2
recombined
modf2
VirgorecSB
Virgo
Recombined / TPR
Stored power at 2xfmod (Watt)
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)
g0 is obtained from the power stored in the
central recycled interferometer:
g0 = (PCITF / Pmich)
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 %
PCITF
rin
rinrrec
Pmich
rin
rinrrec
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 + 2J1
2 (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 ( m is not precisely known)
P0 J02(m) (1-C)/2 < 2 W 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
nL = x (/ L) x CMRR
Propagation of the electronic noise introduced by the frequency stabilisation to the sensitivity:
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
x (/ L) x CMRR
C4 sensitivity (m/Hz)
Commom mode rejection ratio (CMRR)
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 %