Abstract: The optical nonreciprocity has very important applications in optical signal processing and quantum networks. The optical nonreciprocity in a two-cavity optomechanical system with two mechanical resonators is investigated. In the system, there is a coulomb interaction between the two mechanical resonators and the two cavities are coupled together by optical fiber. Based on the time evolution equation of the system operator and the standard input-output relationship in frequency domain, the transmission amplitude equation is obtained. The results show that when the system are on the red-sideband, the quantum coherence between the two paths of the optomechanical interaction and the linearly-coupled interaction can make the system present the optical nonreciprocity. Furthermore, it is shown that the phase difference can not only determine whether optical nonreciprocity can occur in the system, but also determine the direction of optical nonreciprocity. It is also found that the optical nonreciprocity can be enhanced by increasing the strength of the effective optomechanical interactionor the linearly-coupled strength between the two cavities.

Key words: cavity optomechanical system, optical nonreciprocity, Hamilton, phase difference