Dynamics and stability of an optically levitated mirror

We analyze the dynamics of a one-dimensional vertical Fabry-Pérot cavity, where the upper mirror levitates due to intracavity radiation pressure force. A perturbative approach is used based around separation of timescales, which allows us to calculate the physical quantities of interest. Due to the dynamics of the cavity field, we find that the upper mirror's motion will always be unstable for levitation performed using only a single laser. Stability can be achieved for two lasers, where one provides the trapping potential and the other a damping effect, and we locate and characterize all parameter regimes where this can occur. Finally we analyze photothermal effects due to heating of the mirror substrate. We show that this can stabilize the system, even with only a single input laser, if it acts to increase the optical path length of the cavity. This work serves as a foundation for understanding how levitated optical cavity schemes can be used as stable metrological platforms.