  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 ($x_\textrm{ac}$), centre of mass
($x_\textrm{lev}$), photothermal ($x_\textrm{ex}$) and thermo-optic
($x_\textrm{re}$) displacements. This offers refined predictions with a higher
degree of agreement with experimental results. Our work provides a mean to
precisely model the photothermal effect of high power optomechanical systems,
as well as for developing more precise photothermal modelling of photonics
systems for precision sensing and quantum measurements.
