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

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 approximation Braginsky et al., Phys. Lett. A 264, 1 (1999) Cerdonio et al., Phys. Rev. D 63, 082003 (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

Mirror  half space approximation Braginsky et al., Phys. Lett. A 264, 1 (1999) Cerdonio et al., Phys. Rev. D 63, 082003 (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

Calculated nc (Hz) Fused silica Sapphire w/2 300K 1K 300K 1K 10mm 0.0015 4.8 0.02 19000 0.1mm 15 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)

Reference cavity

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

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

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

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

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 = 230 000, input power > 3 mW

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

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...