Influence of thermal effects on the optomechanical coupling rate in acousto-optic cavities

Optomechanical (OM) cavities simultaneously localize photons and phonons, thus enhancing their mutual interaction through radiation-pressure force. This acousto-optic interaction can be quantified by means of the optical-frequency shift per mechanical displacement G. The aforesaid frequency shift can also be related to the vacuum OM coupling rate g0, where only photoelastic and moving-boundary effects are commonly taken into account. However, the thermo-optic and thermal-expansion effects may also play a role since the material forming the OM cavity could be heated by the presence of photons, which should naturally affect the mechanical properties of the cavity. In this work, we introduce a theoretical approach to determine how thermal effects change the canonical OM coupling rate. To test the model, a complete set of optical-thermal-mechanical simulations was performed in two OM crystal cavities fabricated from two different materials: silicon and diamond. Our results lead us to conclude that there is a non-negligible thermal correction that is always present as a negative shift to the OM coupling rate that should be considered in order to predict more accurately the strength of the OM interaction.