Nonlinear laser dynamics of a non-orthogonal chiral pair

Abstract

We extend the semiclassical Lamb theory to study the laser dynamics of a chiral pair of non-orthogonal resonance modes subject to the Maxwell–Bloch (MB) equations. The resulting reduced dynamics is described by three-variable ordinary differential equations. We analytically show that the reduced system has two stable fixed points corresponding to clockwise and counterclockwise chiral lasing modes, and that the basin boundary of the two stable fixed points coincides with the condition that the solution of the reduced system corresponds to a standing wave. We also show that the basin volume depends on the chirality, where the volume of one of the basins goes to zero when the system approaches the exceptional point. Some of these theoretical results are verified by numerical finite-difference time-domain simulations of the MB equations applied to an asymmetric optical billiard laser.