Kerr nonlinearity effect on the stability of Wannier-Stark states in active optical systems

TL;DR

This paper explores how Kerr nonlinearity influences the stability of Wannier-Stark states in active optical systems, combining analytical and numerical methods to understand lasing mode stability.

Contribution

It introduces a perturbation theory to explain the destabilization of Wannier-Stark lasing states caused by nonlinear frequency shifts.

Findings

Resonant frequency dependence on light intensity affects state stability

Numerical simulations confirm destabilization effects

Perturbation theory aligns with simulation data

Abstract

The paper provides an analytical and numerical investigation of the dynamics of a one-dimensional chain of coupled optical resonators with conservative cubic nonlinearity and the gain saturated by nonlinear losses. The linear dependency of the resonator eigenfrequencies on their indexes makes it possible to use Wannier-Stark states as lasing modes. Numerical simulations have shown that the dependency of the resonant frequencies on the light intensity strongly affects the stability of Wannier-Stark states. To explain the observed destabilization of monochromatic lasing based on Wannier-Stark states a simple perturbation theory has been developed and compared with the data obtained in the numerical simulations.