In most optomechanical systems, a movable mirror is a part of an optical cavity, and its oscillation modulates either the resonance frequency of the cavity or its coupling to the environment. There exists the third option—which we call a “coherent coupling”—when the mechanical oscillation couples several nondegenerate optical modes supported by the cavity. Identifying the nature of the coupling can be an important step in designing the setup for a specific application. In order to unambiguously distinguish between different optomechanical couplings, we develop a general framework based on the Hamiltonian of the system. Using this framework, we give examples of different couplings and discuss in details one particular case of a purely coherent coupling in a ring cavity with a movable mirror inside. We demonstrate that in certain cases coherent coupling can be beneficial for cooling the motion of the mechanical oscillator. Our general framework allows us to approach the design of optomechanical experiments in a methodological way, for precise exploitation of the strengths of particular optomechanical couplings
