  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.
