  Optical levitation of mechanical oscillators has been suggested as a
promising way to decouple the environmental noise and increase the mechanical
quality factor. Here, we investigate the dynamics of a free-standing mirror
acting as the top reflector of a vertical optical cavity, designed as a testbed
for a tripod cavity optical levitation setup. To reach the regime of levitation
for a milligram-scale mirror, the optical intensity of the intracavity optical
field approaches 3 MW cm$^{-2}$. We identify three distinct optomechanical
effects: excitation of acoustic vibrations, expansion due to photothermal
absorption, and partial lift-off of the mirror due to radiation pressure force.
These effects are intercoupled via the intracavity optical field and induce
complex system dynamics inclusive of high-order sideband generation, optical
bistability, parametric amplification, and the optical spring effect. We modify
the response of the mirror with active feedback control to improve the overall
stability of the system.
