Abstract

Cavity optomechanical oscillations (OMOs) have been extensively studied for their rich physics and various practical applications. However, due to the highly nonlinear nature of the dynamical process, the exact sideband structure of an optomechanically oscillating optical cavity field remains unknown, although it is essential to a comprehensive understanding and accurate manipulation of such systems. Here, we establish a correspondence between the Bloch-band structure and the coupled sideband dynamics of OMOs, thus providing a theoretical framework for unveiling the detailed structure of cavity optical modes in terms of their resemblance to the well-known Wannier-Stark states and ladders. Surprisingly, the locations of these ladders are irrelevant to pump frequency or power but only depend on the resonant frequency of the optical mode and mechanical-mode frequency. By an energy transfer picture, we build up a connection between the highly nonlinear OMOs and a Bloch-band structure that can be solved linearly. Quantitatively, this picture uncovers the underlying mechanism of the optimization of the pump detuning and optical decay rate, as well as the determination of the minimum input pump power, for sustaining a cavity OMO.