Modeling photothermal effects in high power optical resonators used for coherent levitation

Radiation pressure can be used to enable optomechanical control and manipulation of the quantum state of a mechanical oscillator. Optomechanical interaction can also be mediated by photothermal effects which, although frequently overlooked, may compete with radiation pressure interaction. Understanding of how these phenomena affect the coherent exchange of information between optical and mechanical degrees of freedom is often underdeveloped, particularly in mesoscale high-power systems where photothermal effects can fully dominate the interaction. Here we report an effective theoretical model to predict and successfully reconstruct the dynamics of a unique optomechanical system: a cavity-enhanced setup for macroscopic optical levitation, where a free-standing mirror acts as the optomechanical oscillator. We decompose the photothermal interaction into two opposing light-induced effects, photothermal expansion, and thermo-optic effects. We then reconstruct a heuristic model that links the intracavity field to four types of cavity length changes caused by acoustic (x_ac), centre of mass (x_lev), photothermal (x_ex) and thermo-optic (x_re) displacements. This offers refined predictions with a higher degree of agreement with experimental results. Our work provides a means to precisely model the photothermal effect of high power optomechanical systems, as well as for developing more precise photothermal modeling of photonics systems for precision sensing and quantum measurements.