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The photo-thermal transfer function from absorbed power incident on adielectric mirror to the effective mirror position is calculated using thecoating design as input. The effect is found to change in amplitude and signfor frequencies corresponding to diffusion length comparable to the coatingthickness. Transfer functions are calculated for the $Ti$-doped ${\rmTa_2O_5:SiO_2}$ coating used in Advanced LIGO and for a crystalline ${\rmAl_xGa_{1-x}As}$ coating. The shape of the transfer function at highfrequencies is shown to be a sensitive indicator of the effective absorptiondepth, providing a potentially powerful tool to distinguish coating-internalabsorption from surface contamination related absorption. The sign change ofthe photo-thermal effect could also be useful to stabilize radiationpressure-based opto-mechanical systems. High frequency corrections to thepreviously published thermo-optic noise estimates are also provided. Finally,estimating the quality of the thermo-optic noise cancellation occurring infine-tuned ${\rm Al_xGa_{1-x}As}$ coatings requires the detailed heat flowanalysis done in this paper.

Photo-Thermal Transfer Function of Dielectric Mirrors for Precision Measurements