  The Fano line profiles, originally discovered in the context of
photoionization, have been found to occur in a large class of systems like
resonators, metamaterials, plasmonics. We demonstrate the existence of such
resonances in cavity optomechanics by identifying the interfering contributions
to the fields generated at antiStokes and Stokes frequencies. Unlike the atomic
systems, the optomechanical systems provide great flexibility as the width of
the resonance is controlled by the coupling field. We further show how the
double cavities coupled by a single optomechanical mirror can lead to the
splitting of the Fano resonance and how the second cavity can be used to tune
the Fano resonances. The Fano resonances are quite sensitive to the decay
parameters associated with cavities and the mechanical mirror. Such resonances
can be studied by both pump probe experiments as well as via the spectrum of
the quantum fluctuations in the output fields.
