Transcript Nessun titolo diapositiva - ego

New Results on Photothermal Effect:
Size and Coating Effect
M. De Rosa
INOA, LENS, INFN
F. Marin
University of Florence, LENS, INFN
F. Marino
INFN
O. Arcizet, M. Pinard, A. Heidmann
Laboratoire Kastler Brossel, Paris
Cascina 9/06/05
Photothermal effect
Photon absorption

Local heating

Thermal expansion
In GW detectors:
Intensity noise
turns into
position fluctuations
A theoretical model:
beam waist
mirror size
materials (substrates and coatings)
Half-infinite mirror
Cerdonio et al., Phys. Rev. D 63, 082003 (2001)
S xx () 
K ( )  
1

Braginsky et al., Phys. Lett. A 264, 1 (1999)
2 (1   )
Sabs K  
2
(  )
2


0

 du  dv
2
2 u 2 / 2
2 2 (1   ) 2
1
S xx () 
S
abs
(  C ro2 ) 2
2
2
ue
(u 2  v 2 ) (u 2  v 2  i)
1
c 

0
Cr
2
o
Logarithmic divergence !
Size effects?
Coatings ?
log( K() )
-1
-2
-3
-4
-5
-6
-3
-2
-1
0
log()
1
2
3
First experimental test
Power modulation, P=Po + Pm sin ωmt
10
-12
10
-13
10
-14
10
-15
l (m)
Phase-sensitive detection
C2
C1
D3
BS
10
D2
Laser
OI
P
EOM1
10
-2
10
-1
10
0
10
1
10
2
10
3
m (Hz)
FM locking
HW
-3
P
D1
EOM2
BS
lock-in
De Rosa et al., Phys. Rev. Lett. 89, 237402 (2002)
Fitting curve: l = Lo K(/c)½
c = 2.8 ± 0.6 Hz
(calculated: 1.8 — 2.7 Hz)
absorption coefficient: ~ 5 • 10-7
Scheme of the measurements
•The laser frequency is locked to the reference cavity
•The intensity of the light impinging on the probed
cavity is modulated at a frequency Ωmod
•Phase sensitive detection of the induced mirror
displacements by measuring the frequency detuning of
the cavity resonance (Amplitude and phase
information)
Old setup (AURIGA laser system)
•Modulation on both cavities: differential effect
•Small modulation depth (1% of total power)
•No relative locking of the cavities: large errors on long time series,
drift...
•Small relative tuning range
C2
C1
D3
BS
D2
FM locking
P
HW
Laser
OI
EOM1
P
D1
EOM2
BS
lock-in
New setup
•Modulation on one cavity
•High modulation depth (> 20% of total power)
•AOM allows large and fast tunability of the cavities and relative locking of
the two cavities
C1
QW
PD1
Frequency
servo loop
Oscilloscope
+
PC
PBS
AOM
Cavity
servo loop
13.3 MHz
C2
PD2
Laser
O.I.
EOM2
EOM1
BS
PBS
PD3
QW
PD4
PD3: PowerFrequency
monitor (mod)
servo loop
PD2: error/correction
signal
Oscilloscope
+
PC
QW
PD1
PBS
AOM
Cavity
xc servo loop
Numerical lock-in: 13.3 MHz
amplitude and phase of
Laser
O.I.
syncronous detection
at modEOM1
xe
C2
PD2
PD4
EOM2
PBS
BS
QW
PD3
s
GPDH
xe
GAOM
Gloop
xc
1
s
(1  GP DHGloopGAOM) xc
GPDHGloop
s
1
GPDH
(1  GP DHGloopGAOM ) xe
Probed Cavities
Mirrors substrate: Fused Silica
Coatings: SiO2/Ta2O5
Spacer
Zerodur Aluminum
L (mm)
200
7.1
Waist (mm)
0.370
0.073
c (Hz)
2.2
57
Finesse
38000
40000
Long cavity
a) half-infinite mirror
b) finite size effects
c) coating effect
Short cavity
we cannot investigate very low
frequency (long time PT drift)
-12
coating effect
-13
10
-14
10
0.1
1
10
100
1000
10000
0
Frequency (Hz)
-10
-20
-30
Phase (°)
Displacement (m/W)
10
-40
-50
-60
-70
-80
-90
-100
0.1
1
10
100
Frequency (Hz)
1000
10000
Conclusions
•beam waist dependence of cut-off frequency
•finite size effects at low frequency
•coating effects
•improvement of the half-infinite mirror model including
finite size and coating effect (material properties)
Future
•behaviour at low temperature
•different substrates (Sapphire, Silicon,…)
FP transmission by sweeping L: hysteresis
-0.20
Pt
-0.15
-0.10
-0.05
0.00
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
(L-C)/g
Optical cavities showed bistability and
stochastic resonance due to photo-thermal
effect
Effects very important for ultra-sensitive
displacement detection
New questions:
Stochastic-driven nonlinear dynamics will
prevent from observing signals?
Stochastic Resonance can improve sensitivity?