Phase noise of self-sustained optomechanical oscillators

In this paper we present a theory that predicts the phase noise characteristics of self-sustained optomechanical oscillators. By treating the cavity optomechanical system as a feedback loop consisting of an optical cavity and a mechanical resonator, we analytically derive the transfer functions relating the amplitude and phase noise of all the relevant dynamical quantities from the quantum Langevin equations, and obtain a closed-form expression for the phase noise spectral densities contributed from thermomechanical noise, photon shot noise, and low-frequency technical laser noise. We numerically calculate the phase noise for various situations and perform a sample calculation for an experimentally demonstrated system. We also show that the presented model reduces to the well-known Leeson's phase noise model when the amplitude noise and the amplitude to phase noise intertransfers are ignored. This paper not only addresses the practical questions about oscillator phase noise characteristics but also presents a theoretical framework for studying cavity optomechanical systems with large oscillation amplitude.