Nonlinear behaviors in a PDE model for parity-time-symmetric lasers

Abstract

We propose a phenomenological time-dependent partial differential equation model to investigate the dynamical behaviors of certain parity-time () symmetric lasers during the nonlinear stage of their operations. This model incorporates physical effects such as the refractive index distribution, dispersion, material loss, nonlinear gain saturation and self-phase modulation. We show that when the loss is weak, multiple stable steady states and time-periodic states of light exist above the lasing threshold, rendering the laser multi-mode. However, when the loss is strong, only a single stable steady state of broken symmetry exists for a wide range of the gain amplitude, rendering the laser single-mode. These theoretical results corroborate the previous experimental results, and reveal the important role the loss plays in maintaining the single-mode operation of lasers.