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PT Symmetry Breaking and Nonlinear Optical Isolation in Coupled Microcavities

We perform a theoretical study of nonlinear optical isolator devices based on coupled microcavities with gain and loss. Using coupled-mode theory, we derive a correspondence between the boundary of asymptotic stability in the nonlinear regime, where gain saturation is present, and the PT-breaking transition in the underlying linear system. For zero detuning and weak input intensity, the onset of optical isolation can be rigorously derived, and corresponds precisely to the PT transition point. When the couplings to the external ports are unequal, the isolation ratio exhibits an abrupt jump at the transition point, determined by the ratio of the couplings. This could be exploited to realize an actively controlled nonlinear optical isolator, in which strong optical isolation can be switched on or off using tiny variations in the inter-resonator separation.