We experimentally and theoretically investigate mechanical nanooscillators coupled to the light in an optical ring resonator made of dielectric mirrors. We identify an optomechanical damping mechanism that is fundamentally different to the well known cooling in standing wave cavities. While, in a standing wave cavity the mechanical oscillation shifts the resonance frequency of the cavity in a ring resonator the frequency does not change. Instead the position of the nodes is shifted with the mechanical excursion. We derive the damping rates and test the results experimentally with a silicon-nitride nanomembrane. It turns out that scattering from small imperfections of the dielectric mirror coatings has to be taken into account to explain the value of the measured damping rate. We extend our theoretical model and regard a second reflector in the cavity that captures the effects of mirror back scattering. This model can be used to also describe the situation of two membranes that both interact with the cavity fields. This may be interesting for future work on synchronization of distant oscillators that are coupled by intracavity light fields.
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