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 %