Parity-time symmetry in monolithically integrated graphene-assisted microresonators.

Recently, optical systems with parity-time (PT) symmetry have attracted considerable attention due to its remarkable properties and promising applications. However, these systems usually require separate photonic devices or active semiconductor materials. Here, we investigate PT symmetry and exceptional points (EPs) in monolithically integrated graphene-assisted coupled microresonators. Raman effect and graphene cladding are utilized to introduce the balanced gain and loss. We show that PT-symmetry breaking and EPs can be achieved by changing the pump power and the chemical potential. In addition, the intracavity field intensities experience suppression and revival as the graphene-induced loss increases. Due to the unique distribution of optical field, tunable nonreciprocal light transmission is theoretically demonstrated when introducing the gain saturation nonlinearity. The maximum isolation ratio can reach 26 dB through optimizing the relevant parameters. Our proposed scheme is monolithically integrated, CMOS compatible, and exhibits remarkable properties for microscale light field manipulation. These superior features make our scheme has promising applications in optical communication, computing and sensing.