  We describe a new approach for on-chip optical non-reciprocity which makes
use of strong optomechanical interaction in microring resonators. By optically
pumping the ring resonator in one direction, the optomechanical coupling is
only enhanced in that direction, and consequently, the system exhibits a
non-reciprocal response. For different configurations, this system can function
either as an optical isolator or a coherent non-reciprocal phase shifter. We
show that the operation of such a device on the level of single-photon could be
achieved with existing technology.
