Linearized theory of the fluctuation dynamics in 2D topological lasers

TL;DR

This paper provides a theoretical analysis of fluctuation dynamics in 2D topological lasers, identifying excitation modes, stability conditions, and strategies for stable single-mode operation in a photonic Harper-Hofstadter lattice.

Contribution

It introduces a comprehensive theoretical framework for understanding fluctuation modes and stability in 2D topological lasers with a detailed Bogoliubov analysis.

Findings

Dispersion relations of excitation modes are calculated and interpreted.

Various dynamical instabilities are identified and characterized.

Strategies for achieving stable single-mode operation are proposed.

Abstract

We theoretically study the collective excitation modes of a topological laser device operating in a single-mode steady-state with monochromatic emission. We consider a model device based on a two-dimensional photonic Harper-Hofstadter lattice including a broadband gain medium localized on the system edge. Different regimes are considered as a function of the value of the optical nonlinearity and of the gain relaxation time. The dispersion of the excitation modes is calculated via a full two-dimensional Bogoliubov approach and physically interpreted in terms of an effective one-dimensional theory. Depending on the system parameters, various possible physical processes leading to dynamical instabilities are identified and characterized. On this basis, strategies to enforce a stable single-mode topological laser operation are finally pointed out.