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/phase noise of all the relevant dynamical quantities from the quantum Langevin equations, and obtain a closed-form expressions 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/phase noise inter-transfers are ignored.