Fundamentals of optical non-reciprocity based on optomechanical coupling

Optical isolation, non-reciprocal phase transmission and topological phases for light based on synthetic gauge fields have been raising significant interest in the recent literature. Cavity-optomechanical systems that involve two optical modes coupled to a common mechanical mode form an ideal platform to realize these effects, providing the basis for various recent demonstrations of optomechanically induced non-reciprocal light transmission. Here, we establish a unifying theoretical framework to analyze optical non-reciprocity and breaking of time-reversal symmetry in multimode optomechanical systems. We highlight two general scenarios to achieve isolation, relying on either optical or mechanical losses. Depending on the loss mechanism, our theory defines the ultimate requirements for optimal isolation and the available operational bandwidth in these systems. We also analyze the effect of sideband resolution on the performance of optomechanical isolators, highlighting the fact that non-reciprocity can be preserved even in the unresolved sideband regime. Our results provide general insights into a broad class of parametrically modulated non-reciprocal devices, paving the way towards optimal non-reciprocal systems for low-noise integrated nanophotonics.