Direction-dependent parity-time phase transition and nonreciprocal amplification with dynamic gain-loss modulation

Abstract

We show that a dynamic gain-loss modulation in an optical structure can lead to a direction-dependent parity-time ($\mathcal{PT}$) phase transition. The phase transition can be made thresholdless in the forward direction, and yet remains with a nonzero threshold in the backward direction. As a result, nonreciprocal directional amplification can be realized. Such a dynamic gain-loss modulation can be directly integrated with a semiconductor laser to provide optical isolation for the laser.