Transcript Laser system and optical performances of the Virgo GW detector

Gravitational wave interferometer OPTICS
François BONDU
Fabry-Perot cavity in practice
Rules for optical design
Optical performances
CNRS UMR 6162 ARTEMIS,
Observatoire de la Côte d’Azur, Nice,
France
EGO, Cascina, Italy
May 2006
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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
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VIRGO optical design
Fabry-Perot cavity to detect gravitational wave h  2
L
~ 3.10  23 / Hz
L
Output
Mode
Cleaner
to filter
output
mode
Input
Michelson
Suspended
<<Mode
configuration
mirrors
Cleaner>>
cancel
attoshot
dark
filter
seismic
fringe
outnoise
input
+ servo
beam
loop
jitter
to cancel
and select
lasermode
frequency noise
Long
Recycling
arms
mirror
to
divide
totoreduce
mirror
and
suspension
noise
thermal
noise
L=3 km
L=144m
Slave laser
Master
laser
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1. Fabry-Perot cavity: A. parameters
SCALAR MODEL:
“plane waves”
scalar transmissions, scalar losses of mirrors
REFLECTION
TRANSMISSION
Can we understand these shapes?
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1. Fabry-Perot cavity: A. parameters
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
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1. Fabry-Perot cavity: A. parameters
SCALAR MODEL:
“plane waves”
scalar transmissions, scalar losses of mirrors
Ert = r1
P-1
r2 P Esto
r1  1  T1  L1  1 
Round Trip Losses
Free Spectral Range
Recycling gain
Cavity Pole
Finesse
Cavity reflectivity
T1  L1
2
Prt  Psto (1  LRT )
with LRT 
T1  T2  L1  L2
2
Round trip “losses”
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1. Fabry-Perot cavity: A. parameters
SCALAR MODEL:
“plane waves”
scalar transmissions, scalar losses of mirrors
Ert = r1 P-1 r2 P Esto
Round Trip Losses
Free Spectral Range
Recycling gain
Cavity Pole
Finesse
Cavity reflectivity
P  propagation  delay  exp(i 2L / c)
steady statesolution: Esto  t1 Ein  ERT
 Esto
t1

Ein
 i
1  r1r2e
L  L  
Period:
4L
with  
c
2
    FSR , FSR 
c
2L
Free spectral range
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1. Fabry-Perot cavity: A. parameters
SCALAR MODEL:
“plane waves”
scalar transmissions, scalar losses of mirrors
Esto 
RESONANCE CONDITION
Round Trip Losses
Free Spectral Range
Recycling gain
Cavity Pole
Finesse
Cavity reflectivity
t1
Ein
i
1  r1r2 e
 t1 

  0 [2 ]  Psto  Pin 
 1  r1r2 
 t1 

G  
 1  r1r1 
2
2
Recycling gain
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1. Fabry-Perot cavity: A. parameters
SCALAR MODEL:
“plane waves”
scalar transmissions, scalar losses of mirrors
RESONANCE CONDITION
   0   
Round Trip Losses
Free Spectral Range
Recycling gain
Cavity Pole
Finesse
Cavity reflectivity
4 ( 0  f ) L0
c
  1
4 0 L0
Suppose now ( 0 , L0 ) so that  0 
 k 2
c
G
Esto  Ein
1  if / f P
with
f P  Half Linewidth Half Maximum FSR
1  r1r2
2r1r2
Cavity pole
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1. Fabry-Perot cavity: A. parameters
SCALAR MODEL:
“plane waves”
scalar transmissions, scalar losses of mirrors
FSR
Finesse 
2 fP
Round Trip Losses
Free Spectral Range
Recycling gain
Cavity Pole
Finesse
Cavity reflectivity
Finesse
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1. Fabry-Perot cavity: A. parameters
SCALAR MODEL:
“plane waves”
scalar transmissions, scalar losses of mirrors
r( f ) 
Eref
Ein
Round Trip Losses
Free Spectral Range
Recycling gain
Cavity Pole
Finesse
Cavity reflectivity
r1  r2 (1  L1 )ei ( f )

1  r1r2ei ( f )
r1  r2 (1  L1 )
r (0) 

1  r1r2
R(0)   2
on resonance reflectivity
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1. Fabry-Perot cavity: A. parameters
2nd order
In T+P
1st order
in T+P
2
T p
 r1r2
Finesse
1r1r2
On resonance
reflection
transmission
r1r2(1 p1) 

1

r
1
r
2


 
2
 t1t2 
 1r1r2 


T p
T1
(1)
2
4T1T2
2
T  p
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1. Fabry-Perot cavity: A. parameters
SCALAR MODEL:
“plane waves”
scalar transmissions, scalar losses of mirrors
REFLECTION
T1 = 12%
T2 = 5%
L =0
(finesse = 35)
TRANSMISSION
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1. Fabry-Perot cavity: B. Matching
SCALAR MODEL:
“plane waves”
scalar transmissions, scalar losses of mirrors
r (0) 
r1  r2 (1  L1 )
  0
1  r1r2
Impedance matching
Frequency/length tuning (“lock”)
Wavefront matching
alignment
beam size / position
surface defects - stability
The Fabry-Perot interferometer
Optimal coupling
 0
Over-coupling
 0
Under-coupling
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1. Fabry-Perot cavity: B. Matching
SCALAR MODEL:
“plane waves”
scalar transmissions, scalar losses of mirrors
4 0 L0
0 
c
Impedance matching
Frequency/length tuning (“lock”)
Wavefront matching
alignment
beam size / position
surface defects - stability
The Fabry-Perot interferometer
Frequency/Length tuning
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1. Fabry-Perot cavity: B. Matching
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
Ert = r1 P-1 r2 P Esto
Mirror 2
Ein(x,y) ; Esto(x,y) ;
r1, P, r2 are operators
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1. Fabry-Perot cavity: B. Matching
NON-SCALAR MODEL:
Wavefront matching:
Esto(x,y) = k Ein(x,y)
(k complex number)
Ein
Esto
Impedance matching
Frequency/length tuning (“lock”)
Wavefront matching
alignment
beam size / position
surface defects - stability
The Fabry-Perot interferometer
Superpose angles and lateral drifts
of incoming and resonating beam
<<ALIGNMENT ACTIVITY>>
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1. Fabry-Perot cavity: B. Matching
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>>
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1. Fabry-Perot cavity: B. Matching
NON-SCALAR MODEL:
Definition of beam coupling:
C ( 1 , 2 ) 
 1 , 2
 1 , 1
2
Impedance matching
Frequency/length tuning (“lock”)
Wavefront matching
alignment
beam size / position
surface defects - stability
The Fabry-Perot interferometer
 2 , 2
Round trip coupling losses:
Lrt  1  C( Ert , Esto )
 Too small mirror diameters “clipping”
 imperfect surface: local defects, random figures
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1. Fabry-Perot cavity: B. Matching
NON-SCALAR MODEL:
Definition of stability:
Lrt  T1  T1  L1  L2
Impedance matching
Frequency/length tuning (“lock”)
Wavefront matching
alignment
beam size / position
surface defects - stability
The Fabry-Perot interferometer
Definition of stability in case of perfect surface figures:
0  (1 
L
L
)(1  )  1
R1
R2
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1. Fabry-Perot cavity: B. Matching
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
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1. Fabry-Perot cavity: B. Matching
Impedance matching
Frequency/length tuning (“lock”)
Wavefront matching
alignment
beam size / position
surface defects - stability
The Fabry-Perot interferometer
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1. Fabry-Perot cavity: C. measurement
Phase modulated laser:
 in   0 e
i 2f C
m
fm
m i 2f m
m i 2f m 

e

e
1 

2
2


C
SB+
phase modulation index
modulation frequency


 ref   0ei 2f t  R(fC )  R(fC  f m )
C
SB-
m i 2f mt
m

e
 R(f C  f m ) ei 2f mt 
2
2

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1. Fabry-Perot cavity: C. measurement
error signal:
sP  P0

m
Im R(f c ) R* (f c  f m )  R(f c ) R* (f c  f m )
2

f  f m
fc
sP  P0 m ImR(f c )  P0 m(1   )
fp
f 
1  c 
 fp 
2
Does not provide information about frequency behavior once locked
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1. Fabry-Perot cavity: C. measurement
Modulated laser + measurement line:
n
fn
SB-
C
SB+
phase modulation index
modulation frequency
f << FSR, f ≠ fm
This pole
TF( frequency noise ) 
P0 m(1   )
1 i f
fp
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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
26
2. Optical design: A. mirror transmissions
Fabry-Perot cavity with Rmax transmissions as end mirrors
RFP 1  LRT  Gcavity
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)
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2. Optical design: B. dark fringe
• Michelson simple :
C PmaxPmin
PmaxPmin
laser
Pin
BS
Pout
Pmax, Pmin = Pout
On black and white fringes
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2. Optical design: C. Mode Cleaners
Input <<Mode Cleaner>> to filter out input beam jitter and select mode
L=3 km
L=144m
Slave laser
Master
laser
Output Mode Cleaner to filter output mode
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Detection
Photodiodes
on Detection Bench
Output Mode Cleaner
on Suspended Bench
Output Mode-Cleaner
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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
31
Measured optical parameters
Losses in input Mode Cleaner?
Arm finesses?
F = 51 ±1
Slave laser
Recycling gain?
16.7 W
1W
7.1 W
T=10%
Master
laser
F = 49±0.5
Gcarrier = 30-35 (exp. 50)
GSB ~ 20 (exp. 36)
1 – C = 3.10-3 (mean)
1 – C < 10-4
III. Optical performances
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Absorption
Photothermal Deflection System
Scatterometer CASI 400x400mm
Mirror metrology
Micromap 400x400 mm
(local defects)
Before and/or after the coating process, maps are measured:
- Mirror surface map (modified profilometer)
reproducibility 0.4 nm; step 0.35 mm
- bulk and coating absorption map (“mirage” bench)
resolution 30 ppb/cm // 20 ppb
- scatter
map (commercial instrument)
Phase
shift interferometer
resolution of a few ppm
- transmission map (commercial instrument)
transmission map
- local defects measurements
- birefringency
Instruments: ESPCI, Paris
Coating, 140 m2 room class 1: LMA, Lyon
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The VIRGO large mirrors: a challenge for low loss coatings, CQG 2004, 21
Surface maps
Ex: a large flat mirror
-Good quality silica
- Good polishing
- Control of coating deposition
(DIBS) with no pollutants
- Surface correction
Diam
Rms
p-p
III. Optical performances
35 cm
2.3 nm
11.5 nm
34
Optical simulation
- Check out cavity visibility
(total losses)
TWO optical programs:
- One that propagates wavefront
with FFT
- Check out expected recycling gain,
for varying radii of curvature
- Check out expected contrast defect
- One that decomposes beams
on TEM HG(m,n) base
- Check out modulation frequency
- Improve interferometer
parameters…
III. Optical performances
35
Optical program: typical results (Modal simulation)
Scalar defects
Maps
Maps+thermal
Opt mod index
0.068
0.172±0.001
0.215 ±0.001
Opt demod phase
0
2 ±0
17 ±1
Finesse N
49.26
49.1 ±0.2
49.3 ±0.2
Finesse W
49.79
49.6 ±0.2
49.7 ±0.2
dF/F [%]
0.27
0.23 ±0.12
0.24 ±0.12
Asymmetry [%]
1.05
1.00 ±0.3
2.78 ±0.5
Stored power N [kW]
15.38
10.82 ±0
11.15 ±0
Lost power N [W]
0.23
4.11 ±1
3.70 ±1
Surtension N
31.37
31.18 ±0.02
31.15 ±0.02
Stored power W [kW]
15.55
10.91 ±0
11.27 ±0.3
Lost power W [W]
0.19
6.05 ±0.02
5.85 ±0.04
Surtension W
31.70
31.42 ±0.01
31.48 ±0.1
Carrier power on BS [W]
978.5
684.5 ±0.5
725.1 ±2
Sideband power on BS [W]
1.70
8.56 ±0.1
10.9 ±0.2
Reflected carrier [W]
17.84
8.42 ±0.01
9.82 ±0.08
Reflected sb [W]
0.027
0.24 ±0
0.26 ±0.01
CITF surtension Carrier
49.04
34.74 ±0.03
37.10 ±0.08
CITF surtension SB
36.49
29.01 ±0.02
24.0 ±0.1
Transmitted (detected) carrier [mW]
0.064 (0.064)
359 ±6 (1.6 ±0)
324 ±40 (3.5 ±0.1)
Transmitted (detected) sb [mW]
18.7 (17.9)
93.0 ±0.8 (70.0 ±1)
125 ±2 (100 ±2)
Sensitivity [*1E-23]
2.48
2.87 ±0.01
2.96 ±0.02
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Example:
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
37
Fabry-Perot cavity transfer function measurements
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
38
Input Mode Cleaner Losses
T = 5.7 ppm
Roud-trip losses:
Computed from mirror maps: 115 ppm
From measurements: 846 +/- 5 ppm
Mirror transmission measurements
+ transfer function details measurements
=> Mode mismatching 17%
=> Cavity transmissitivity for TEM00 83%
(september 2005)
T=2457 ppm
III. Optical performances
T=2427 ppm
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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
40