Dynamical stability of 2D topological lasers

TL;DR

This paper investigates the dynamical stability of a 2D topological laser using a Bogoliubov approach, revealing key instabilities and proposing a simplified 1D model to understand the laser's behavior.

Contribution

It introduces a novel analysis of the stability of 2D topological lasers, including a mapping to a 1D laser model and insights into instability mechanisms.

Findings

Identification of instabilities from chiral propagation and nonlinearities

Mapping of 2D topological laser to a 1D laser model

Analysis of the role of reservoir dynamics in stability

Abstract

In this internship report, I have considered the topological laser built by amplifying the edge of a 2D Harper-Hofstadter photonic lattice, with the reservoir of carriers being treated explicitly. The dynamical stability of the resulting chiral laser operation is investigated by means of the Bogoliubov approach on top of the lasing state. In particular, I propose a mapping to the 1D model of a standard laser which captures the main features of the slow decaying Goldstone mode. Also, instabilities arising from the interplay of chiral propagation with refractive index nonlinearities and the non-adiabatic reservoir of carriers are highlighted.