Laser-rate-equation description of optomechanical oscillators

We develop a set of laser rate equations that accurately describes mechanical amplification in optomechanical oscillators driven by photothermal or radiation pressure forces. In the process we introduce a set of parameters describing gain, stored energy, slope efficiency, and saturation power of the mechanical laser. We identify the three-phonon parametric interactions as a microscopic mechanism enabling self-oscillation. Our theory shows remarkable agreement with our experimental data, demonstrating that optomechanical self-oscillation is essentially a "phonon lasing" process in which an optical pump generates coherent acoustic phonons.