Optomechanical cooling with generalized interferometers

The fields in multiple-pass interferometers, such as the Fabry--P\'erot cavity, exhibit great sensitivity not only to the presence but also to the motion of any scattering object within the optical path. We consider the general case of an interferometer comprising an arbitrary configuration of generic `beam splitters' and calculate the velocity-dependent radiation field and the light force exerted on a moving scatterer. We find that a simple configuration, in which the scatterer interacts with an optical resonator from which it is spatially separated, can also significantly enhance the optomechanical friction.