Optical nonreciprocity in a piezo-optomechanical system

We theoretically study the optical nonreciprocity in a piezo-optomechanical microdisk resonator, in which the cavity modes and the mechanical mode are optically pumped and piezoelectrically driven, respectively. For asymmetric optical pumping and different piezoelectrical drivings, our system shows some nonreciprocal optical responses. We find that our system can function as an optical isolator, a nonreciprocal amplifier, or a nonreciprocal phase shifter.