  Nonreciprocal devices are indispensable for building quantum networks and
ubiquitous in modern communication technology. Here, we use optomechanical
interaction and linearly-coupled interaction to realize optical nonreciprocal
transmission in a double-cavity optomechanical system. The scheme relies on the
interference between the two interactions. We derive the essential conditions
to realize perfect optical nonreciprocity in the system, and analyse the
properties of optical nonreciprocal transmission and the output fields from
mechanical mode. These results can be used to control optical transmission in
quantum information processing.
