We study the nonreciprocal transmission and the fast-slow light effects in a cavity optomechanical system, in which the cavity supports a clockwise and a counter-clockwise circulating optical modes, both the two modes are driven simultaneously by a strong pump field and a weak signal field. We find that when the intrinsic photon loss of the cavity is equal to the external coupling loss of the cavity, the system reveals a nonreciprocal transmission of the signal fields. However, when the intrinsic photon loss is much less than the external coupling loss, the nonreciprocity about the transmission properties almost disappears, and the nonreciprocity is shown in the group delay properties of the signal fields, and the system exhibits a nonreciprocal fast-slow light propagation phenomenon.
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