  We propose to create optical nonreciprocity in a three-mode optomechanical
system comprising one mechanical and two optical modes, where the mechanical
mode is coupled with only one of the optical modes. The optical nonreciprocal
response of the system is based on the nonlinearity induced by the
optomechanical interaction. However, nonlinearity is a necessary but not a
sufficient condition for observing nonreciprocity. Another necessary condition
for nonreciprocal response of the system to a classical driving field is
demonstrated analytically. The effects of the parameters on the nonreciprocal
response of the system are discussed numerically. The three-mode optomechanical
system provides a platform to realize nonreciprocity for strong optical signal
fields.
