1. Experimental investigation of dynamic Photothermal 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
ILIAS STREGA T2 – 2005 Meeting Palma de Mallorca

2. 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

3. 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

4. Mirror  half space approximation
Braginsky et al., Phys. Lett. A 264, 1 (1999)
Cerdonio et al., Phys. Rev. D 63, (2001)
dL = L0 K(w/wc)
 1/W
a: thermal expansion coefficient
s: Poisson ratio
k: thermal conductivity
cs: volumetric thermal capacitance
w: beam waist

5. Mirror  half space approximation
Braginsky et al., Phys. Lett. A 264, 1 (1999)
Cerdonio et al., Phys. Rev. D 63, (2001)
dL = L0 K(w/wc)
Logarithmic divergence !
Size effects?
Coatings ?
a: thermal expansion coefficient
s: Poisson ratio
k: thermal conductivity
cs: volumetric thermal capacitance
w: beam waist

6. Calculated nc (Hz) Fused silica Sapphire w/2 300K 1K 300K 1K
10mm
0.1mm ·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)

7. Reference cavity

8. Probed Cavities
Mirrors substrate: Fused Silica
Coatings: SiO2/Ta2O5

9. Long cavity a) half-infinite mirror b) finite size effects
c) coating effect

10. High frequency: coating effect
IMPROVED MODEL
High frequency: coating effect
One-dimensional model
K = KFS + Kcoat
Low frequency: finite size effect

11. Short cavity Frequency scaling with waist as predicted
Phase at high frequency: to be improved (coating depth comparable with waist)

12. Setup 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 = , input power > 3 mW

13. Test 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

14. Upgrade of a bar with optical readout for cryogenic operation

15. 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

16. Solving the windmills noise problem...