  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.
