m. de rosa inoa, lens, infn f. marin university of florence, lens, infn f. marino infn o. arcizet,...
TRANSCRIPT
M. De RosaINOA, LENS, INFN
F. MarinUniversity of Florence, LENS, INFN
F. MarinoINFN
O. Arcizet, M. Pinard, A. Heidmann Laboratoire Kastler Brossel, Paris
Experimental investigation of dynamic Photothermal Effect
ILIAS STREGA T2 – 2005 Meeting Palma de Mallorca
Photothermal effect Photon absorption
Local heating
Thermal expansion
Depends on: •laser power impinging on the mirrors•absorption coefficient•material: - thermal expansion
- thermal conductivity and capacitance
•temperature (through the above parameters)•mirror size and shape/suspension•beam waist•detection frequency
Photothermal effect Photon absorption
Local heating
Thermal expansion
Depends on: •laser power impinging on the mirrors•absorption coefficient•material: - thermal expansion
- thermal conductivity and capacitance
•temperature (through the above parameters)•mirror size and shape/suspension•beam waist•detection frequency
Mirror half space approximationBraginsky et al., Phys. Lett. A 264, 1 (1999)Cerdonio et al., Phys. Rev. D 63, 082003 (2001)
L = L0 K(/c)
P abs0 κπ
α σ)(1L
w2
s
c κ2
c
02222
22
)π
1K
2
)(i)((
u
dvduvuvu
eu
-3 -2 -1 0 1 2 3-6
-5
-4
-3
-2
-1
0
1
log
( K
()
)
log()
1/
: thermal expansion coefficient: Poisson ratiok: thermal conductivitycs: volumetric thermal capacitancew: beam waist
-3 -2 -1 0 1 2 3
-6
-5
-4
-3
-2
-1
0
1
log
( K
()
)
log()
Mirror half space approximationBraginsky et al., Phys. Lett. A 264, 1 (1999)Cerdonio et al., Phys. Rev. D 63, 082003 (2001)
L = L0 K(/c)
P abs0 κπ
α σ)(1L
w2
s
c κ2
c
02222
22
)π
1K
2
)(i)((
u
dvduvuvu
eu
: thermal expansion coefficient: Poisson ratiok: thermal conductivitycs: volumetric thermal capacitancew: beam waist
Logarithmic divergence !Size effects?Coatings ?
Calculatedc (Hz)
Fused silica Sapphire
w/2 300K 1K 300K 1K
10mm 0.0015 4.8 0.02 19000
0.1mm15 48000 200 1.9·108
• Cut-off depending on the mirror shape and suspension (heat
dispersion
• Large timescale and size spread necessity of accurate and
verified model over a complete frequency range)
Frequencyservo loop
Laser EOM1O.I.BS
PD1 QW
PBS
13.3 MHz
PD2
QWPBS
PD4
Cavity servo loopAOM
EOM2
C1
C2
PD3
Oscilloscope+
PC
Reference
cavity
Probed Cavities
Spacer Zerodur Aluminum
L (mm) 200 7.1
Waist (mm) 0.370 0.073
c (Hz) 2.2 57
Finesse 38000 40000
Mirrors substrate: Fused SilicaCoatings: SiO2/Ta2O5
Long cavity
a) half-infinite mirrorb) finite size effectsc) coating effect
IMPROVED MODEL
Low frequency: finite size effectHigh frequency: coating effect
One-dimensional model
= FS + coat
Short cavity
Frequency scaling with
waist as predicted
Phase at high frequency: to
be improved (coating depth
comparable with waist)
Setup of high-finesse cavitiesSetup 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
Cavity finesse = 230 000, input power > 3 mW
Test at cryogenic temperatureTest at cryogenic temperature
Cavity assembled in copper rings for thermal conductivity
Cryogenic facility with mechanical isolation from the helium tank
Observation of first optical resonances at low temperature
Upgrade of a bar with optical readout for cryogenic
operation
Conclusions
•beam waist dependence of cut-off frequency is verified
•finite size effects at low frequency
•coating effects at high frequency
•improvement of the half-infinite mirror model including finite size and coating effect (material properties)
•low-temperature setups under construction
•mirrors based on a silicon wafer currently being coated at the Laboratoire des Matériaux Avancés in Lyon
Solving the windmills noise problem...