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Gravitational wave interferometer OPTICS. François BONDU CNRS UMR 6162 ARTEMIS, Observatoire de la Côte d’Azur, Nice, France EGO, Cascina, Italy May 2006. Fabry-Perot cavity in practice Rules for optical design Optical performances. Contents. I. Fabry-Perot cavity in practice

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Gravitational wave interferometer OPTICS

  • François BONDU

  • CNRS UMR 6162 ARTEMIS,

  • Observatoire de la Côte d’Azur, Nice, France

  • EGO, Cascina, Italy

  • May 2006

Fabry-Perot cavity in practice

Rules for optical design

Optical performances


Contents
Contents

  • I. Fabry-Perot cavity in practice

  • Scalar parameters – cavity reflectivity, mirror transmissions, losses

  • Matching: impedance, frequency/length tuning, wavefront

  • Length / Frequency measurement: cavity transfer function

  • II. Rules for gravitational wave interferometer optical design

  • Optimum values for mirror transmissions

  • “dark fringe”: contrast defect

  • “Mode Cleaner”

  • III. Optical performances

  • Actual performances:

  • Mirror metrology

    • Optical simulation

    • Accurate in-situ metrology


Virgo optical design

Input <<Mode Cleaner>> to filter out input beam jitter and select mode

Output Mode Cleaner to filter output mode

Michelson configuration at dark fringe + servo loop to cancel laser frequency noise

Recycling mirror to reduce shot noise

Long arms to divide mirror and suspension thermal noise

L=3 km

L=144m

Slave laser

Master

laser

VIRGO optical design

Fabry-Perot cavity to detect gravitational wave

Suspended mirrors to cancel seismic noise


1 fabry perot cavity a parameters
1. Fabry-Perot cavity: A. parameters select mode

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

REFLECTION

TRANSMISSION

Can we understand these shapes?


1 fabry perot cavity a parameters1
1. Fabry-Perot cavity: A. parameters select mode

Round Trip Losses

Free Spectral Range

Recycling gain

Cavity Pole

Finesse

Cavity reflectivity

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

Ein

Etrans

Esto

Eref

Mirror 1

Mirror 2

Ert = r1 P-1 r2 P Esto


1 fabry perot cavity a parameters2
1. Fabry-Perot cavity: A. parameters select mode

Round Trip Losses

Free Spectral Range

Recycling gain

Cavity Pole

Finesse

Cavity reflectivity

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

Ert = r1 P-1 r2 P Esto

Round trip “losses”


1 fabry perot cavity a parameters3
1. Fabry-Perot cavity: A. parameters select mode

Round Trip Losses

Free Spectral Range

Recycling gain

Cavity Pole

Finesse

Cavity reflectivity

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

Ert = r1 P-1 r2 P Esto

Period:

Free spectral range


1 fabry perot cavity a parameters4
1. Fabry-Perot cavity: A. parameters select mode

Round Trip Losses

Free Spectral Range

Recycling gain

Cavity Pole

Finesse

Cavity reflectivity

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

RESONANCE CONDITION

Recycling gain


1 fabry perot cavity a parameters5
1. Fabry-Perot cavity: A. parameters select mode

Round Trip Losses

Free Spectral Range

Recycling gain

Cavity Pole

Finesse

Cavity reflectivity

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

RESONANCE CONDITION

Suppose now

Cavity pole


1 fabry perot cavity a parameters6
1. Fabry-Perot cavity: A. parameters select mode

Round Trip Losses

Free Spectral Range

Recycling gain

Cavity Pole

Finesse

Cavity reflectivity

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

Finesse


1 fabry perot cavity a parameters7
1. Fabry-Perot cavity: A. parameters select mode

Round Trip Losses

Free Spectral Range

Recycling gain

Cavity Pole

Finesse

Cavity reflectivity

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

on resonance reflectivity



1 fabry perot cavity a parameters9
1. Fabry-Perot cavity: A. parameters select mode

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

T1 = 12%

T2 = 5%

L = 0

(finesse = 35)

REFLECTION

TRANSMISSION


1 fabry perot cavity b matching
1. Fabry-Perot cavity: B. Matching select mode

Impedance matching

Frequency/length tuning (“lock”)

Wavefront matching

alignment

beam size / position

surface defects - stability

The Fabry-Perot interferometer

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

Optimal coupling

Over-coupling

Under-coupling


1 fabry perot cavity b matching1
1. Fabry-Perot cavity: B. Matching select mode

Impedance matching

Frequency/length tuning (“lock”)

Wavefront matching

alignment

beam size / position

surface defects - stability

The Fabry-Perot interferometer

SCALAR MODEL:

“plane waves”

scalar transmissions, scalar losses of mirrors

Frequency/Length tuning


1 fabry perot cavity b matching2
1. Fabry-Perot cavity: B. Matching select mode

Impedance matching

Frequency/length tuning (“lock”)

Wavefront matching

alignment

beam size / position

surface defects - stability

The Fabry-Perot interferometer

NON-SCALAR MODEL:

Ein

Etrans

Esto

Eref

z axis

Mirror 1

Mirror 2

Ert = r1 P-1 r2 P Esto

Ein(x,y) ; Esto(x,y) ;

r1, P, r2 are operators


1 fabry perot cavity b matching3
1. Fabry-Perot cavity: B. Matching select mode

Impedance matching

Frequency/length tuning (“lock”)

Wavefront matching

alignment

beam size / position

surface defects - stability

The Fabry-Perot interferometer

NON-SCALAR MODEL:

Wavefront matching:

Esto(x,y) = k Ein(x,y)

(k complex number)

Esto

Ein

Superpose angles and lateral drifts

of incoming and resonating beam

<<ALIGNMENT ACTIVITY>>


1 fabry perot cavity b matching4
1. Fabry-Perot cavity: B. Matching select mode

Impedance matching

Frequency/length tuning (“lock”)

Wavefront matching

alignment

beam size / position

surface defects - stability

The Fabry-Perot interferometer

NON-SCALAR MODEL:

Wavefront matching:

Esto(x,y) = k Ein(x,y)

(k complex number)

Ein

Esto

Superpose beam positions and beam widths <<MATCHING ACTIVITY>>


1 fabry perot cavity b matching5
1. Fabry-Perot cavity: B. Matching select mode

Impedance matching

Frequency/length tuning (“lock”)

Wavefront matching

alignment

beam size / position

surface defects - stability

The Fabry-Perot interferometer

NON-SCALAR MODEL:

Definition of beam coupling:

Round trip coupling losses:

  • Too small mirror diameters “clipping”

  • imperfect surface: local defects, random figures


1 fabry perot cavity b matching6
1. Fabry-Perot cavity: B. Matching select mode

Impedance matching

Frequency/length tuning (“lock”)

Wavefront matching

alignment

beam size / position

surface defects - stability

The Fabry-Perot interferometer

NON-SCALAR MODEL:

Definition of stability:

Definition of stability in case of perfect surface figures:


1 fabry perot cavity b matching7
1. Fabry-Perot cavity: B. Matching select mode

Impedance matching

Frequency/length tuning (“lock”)

Wavefront matching

alignment

beam size / position

surface defects - stability

The Fabry-Perot interferometer

Charles Fabry (1867-1945)

Alfred Perot (1863-1925)

Amédée Jobin (mirror manufacturer) (1861-1945)

Gustave Yvon (>1911)

Marseille – beginning of 20th century

“Les franges des lames minces argentées”,

Annales de Chimie et de Physique, 7e série, t12, 12 décembre 1897

“A taste of Fabry and Perot’s Discoveries, Physica Scripta, T86,

76-82, 2000


1 fabry perot cavity b matching8
1. Fabry-Perot cavity: B. Matching select mode

Impedance matching

Frequency/length tuning (“lock”)

Wavefront matching

alignment

beam size / position

surface defects - stability

The Fabry-Perot interferometer


1 fabry perot cavity c measurement

SB- C SB+ select mode

1. Fabry-Perot cavity:C. measurement

Phase modulated laser:

m phase modulation index

fm modulation frequency


1 fabry perot cavity c measurement1
1. Fabry-Perot cavity: select modeC. measurement

error signal:

Does not provide information about frequency behavior once locked


1 fabry perot cavity c measurement2

SB- C SB+ select mode

This pole

1. Fabry-Perot cavity:C. measurement

Modulated laser + measurement line:

n phase modulation index

fn modulation frequency

f << FSR, f ≠ fm


Contents1
Contents select mode

  • I. Fabry-Perot cavity in practice

  • Scalar parameters – cavity reflectivity, mirror transmissions, losses

  • Matching: impedance, frequency/length tuning, wavefront

  • Length / Frequency measurement: cavity transfer function

  • II. Rules for gravitational wave interferometer optical design

  • Optimum values for mirror transmissions

  • “dark fringe”: contrast defect

  • “Mode Cleaner”

  • III. Optical performances

  • Actual performances:

  • Mirror metrology

    • Optical simulation

    • Accurate in-situ metrology


2 optical design a mirror transmissions
2. Optical design: A. mirror transmissions select mode

Fabry-Perot cavity with Rmax transmissions as end mirrors

Virgo mirrors: LRT ~500 ppm, Gcavity ~ 32  reflectivity defect 1.5%

Was estimated 1-5 % at design

Have as much as possible power on beamsplitter

  • Match “losses” of cavities with recycling mirror

    Was estimated 8 % at design (5.5 % recent refit)


2 optical design b dark fringe
2. Optical design: B. dark fringe select mode

  • Michelson simple :

laser

Pin

BS

Pmax, Pmin = Pout

On black and white fringes

Pout


2 optical design c mode cleaners

L=3 km select mode

Master

laser

2. Optical design: C. Mode Cleaners

Input <<Mode Cleaner>> to filter out input beam jitter and select mode

L=144m

Slave laser

Output Mode Cleaner to filter output mode


Detection
Detection select mode

Photodiodes

on Detection Bench

Output Mode Cleaner

on Suspended Bench

Output Mode-Cleaner

Beam


Contents2
Contents select mode

  • I. Fabry-Perot cavity in practice

  • Scalar parameters – cavity reflectivity, mirror transmissions, losses

  • Matching: impedance, frequency/length tuning, wavefront

  • Length / Frequency measurement: cavity transfer function

  • II. Rules for gravitational wave interferometer optical design

  • Optimum values for mirror transmissions

  • “dark fringe”: contrast defect

  • “Mode Cleaner”

  • III. Optical performances

  • Actual performances:

  • Mirror metrology

    • Optical simulation

    • Accurate in-situ metrology


Measured optical parameters

F = 51 ±1 select mode

Slave laser

16.7 W

7.1 W

F = 49±0.5

1 W

1 – C = 3.10-3 (mean)

Master

laser

1 – C < 10-4

Measured optical parameters

Losses in input Mode Cleaner?

Arm finesses?

Recycling gain?

Gcarrier = 30-35 (exp. 50)

GSB ~ 20 (exp. 36)

T=10%

III. Optical performances


Mirror metrology

Absorption select mode

Photothermal Deflection System

Scatterometer CASI 400x400mm

Micromap 400x400 mm

(local defects)

Phase shift interferometer

Mirror metrology

  • Before and/or after the coating process, maps are measured:

  • Mirror surface map (modified profilometer)

  • bulk and coating absorption map (“mirage” bench)

  • scatter map (commercial instrument)

  • transmission map (commercial instrument)

  • local defects measurements

  • birefringency

reproducibility 0.4 nm; step 0.35 mm

resolution 30 ppb/cm // 20 ppb

resolution of a few ppm

transmission map

Instruments: ESPCI, Paris

Coating, 140 m2 room class 1: LMA, Lyon

The VIRGO large mirrors: a challenge for low loss coatings, CQG 2004, 21


Surface maps select mode

Ex: a large flat mirror

  • Good qualitysilica

  • Good polishing

  • Control of coating deposition

  • (DIBS) with no pollutants

  • - Surface correction

Diam 35 cm

Rms 2.3 nm

p-p 11.5 nm

III. Optical performances


Optical simulation
Optical simulation select mode

  • Check out cavity visibility

  • (total losses)

  • Check out expected recycling gain,

  • for varying radii of curvature

  • Check out expected contrast defect

  • Check out modulation frequency

  • Improve interferometer

  • parameters…

  • TWO optical programs:

  • One that propagates wavefront

  • with FFT

  • One that decomposes beams

  • on TEM HG(m,n) base

III. Optical performances



Example: select mode

Virgo simulation with surface maps and with an incoming field of 20W

Contrast defect= 0.94%

North arm amplification = 31.65

West arm amplification = 32.06

Recycling gain = 34.56

III. Optical performances


Fabry-Perot cavity transfer function measurements select mode

Details at FFSR

Fit values with 95% confidence interval:

fp = 479 +/- 3.3 Hz

fz = -177 +/- 2.2 Hz

FSR = 1044039 +/- 2.2 Hz

L = 143.573326 +/- 30 mm

Error bars: from measurement errors,

Not for constant biases.

(fit both real and imaginary parts simultaneously)

III. Optical performances


Input mode cleaner losses

Roud-trip losses: select mode

Computed from mirror maps: 115 ppm

From measurements: 846 +/- 5 ppm

Input Mode Cleaner Losses

T = 5.7 ppm

Mirror transmission measurements

+ transfer function details measurements

=> Mode mismatching 17%

=> Cavity transmissitivity for TEM00 83%

(september 2005)

T=2457 ppm

T=2427 ppm

III. Optical performances


Contents3
Contents select mode

  • I. Fabry-Perot cavity in practice

  • Scalar parameters – cavity reflectivity, mirror transmissions, losses

  • Matching: impedance, frequency/length tuning, wavefront

  • Length / Frequency measurement: cavity transfer function

  • II. Rules for gravitational wave interferometer optical design

  • Optimum values for mirror transmissions

  • “dark fringe”: contrast defect

  • “Mode Cleaner”

  • III. Optical performances

  • Actual performances:

  • Mirror metrology

    • Optical simulation

    • Accurate in-situ metrology


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