Coherent coupling completes an unambiguous optomechanical classification framework*

Cavity optomechanics studies the dynamics of systems in which optical and mechanical degrees of freedom are coupled, e.g., optical resonators with movable/deformable boundaries and/or shapes. A system's behavior depends crucially on the nature of optomechanical coupling. In addition to the previously well-known dispersive (when real parts of optical eigenfrequencies depend on mechanical displacement) and dissipative coupling (when imaginary parts of optical eigenfrequencies depend on mechanical displacement), we identify coherent coupling as a new type of coupling (when neither depend on mechanical displacement) and show that the three together fit into a general, unambiguous classification framework. We discuss in detail a ring cavity with a movable mirror inside, a system that has pure coherent coupling without any dispersive or dissipative coupling.