Transcript Presentazione di PowerPoint - ego
Task T2 (WG 11)
AIM:
exact definition (theoretical and experimental) of
photo-thermal
noise
PARTICIPANTS
• INFN (AURIGA group; also LENS Florence, INOA Florence and Naple) • CNRS (LKB Paris) • IGR (expressed interest in the task)
ILIAS 5-6/11/2004 WG T2
Photo-thermal effect
Physical origin: noise heating of mirrors by absorbed laser light by thermal expansion: deformation/displacement due to shot noise in the absorbed radiation: displacement Depends on: • laser power impinging on the mirrors • absorption coefficient • material: • beam waist - thermal expansion - thermal conductivity and capacitance • temperature (through the above parameters) • mirror size and shape/suspension • detection frequency
ILIAS 5-6/11/2004 WG T2
Photo-thermal effect
Frequency dependence (theory): • Half-space approximation: - linear decay above w
c = 2k/c s w 2
k: thermal conductivity where c s : volumetric thermal capacitance w: beam waist - logarithmic below w
c
n
c (Hz)
w/ 2 10mm 0.1mm
Fused silica 300K 0.0015
15 1K 4.8
48000 Sapphire 300K 0.02
200 1K 19000 1.9·10 8 • Cut-off depending on the mirror shape and suspension (heat dispersion)
ILIAS 5-6/11/2004 WG T2
Mirror half space approximation Braginsky
et al
., Phys. Lett. A
264
, 1 (1999) Cerdonio
et al
., Phys. Rev. D
63
, 082003 (2001) d L = L 0 K( w / w c ) L 0 (1 σ) α π κ P abs c 2 κ
c
s w 2 K ( ) 1 π 0
dv ( u
2
v
2
u )(
2
e
u
2
u
2 2
v
2
i
)
1 0 -1 -2 -3 -4 -5 -6 -3
1/
-2 -1 0
log( )
1 2 3 ILIAS 5-6/11/2004 WG T2
Fitting curve: l L 0 P abs P abs P in K(υ
/
υ C ) L 0 /P abs = 1.5·10 -4 m m/mW M. De Rosa
et al
.: “Experimental measurement of photothermal effect in Fabry-Perot cavities ”, Phys. Rev. Lett.
89
, 237402 (2002)
Cryogenic operation, high Finesse cavity n c : 2.8 Hz 10 kHz (fused silica) 50 MHz (sapphire) L 0 /P abs : 1.5·10 -4 m m/mW 0.5·10 -5 m m/mW F : 40 000 1000 000
ILIAS 5-6/11/2004 WG T2
Work Plan
a) Years 1-2: Room temperature meas. of photo-th. noise; waist dependence b) Years 2-3: Different substrates and coatings.
c) Years 1-3: Test and setup of high Finesse cavities at low T d) Years 2-4: Measurements at low T
ILIAS 5-6/11/2004 WG T2
a) Years 1-2: Room temperature meas. of photo-th. noise; waist dependence Work performed: • Optimized the measurement apparatus: - AOM for wider and faster tuning on both cavities - EOM for amplitude modulation on one single cavity • Designed and built specific mounts for using short ( small waist) cavities on the present acoustically-isolated, thermally stabilized environment Next step: • Check of the previous measurements, with better accuracy (fall of half-space approximation??) • Independent measurement of absorption??
ILIAS 5-6/11/2004 WG T2
b) Years 2-3: Different substrates and coatings Depends on the availability of different mirrors (at present: fused-silica substrates and coatings by REO
ILIAS 5-6/11/2004 WG T2
Setup and test of high-finesse cavities
Mirrors made by J.M. Mackowski
Input mirror T = 20 ppm, total losses < 10 ppm
Compact cavity: L = 0.2 mm