# Theory of chiral edge state lasing in a two-dimensional topological system

## TL;DR

This paper theoretically explores topological laser operation in a two-dimensional Harper-Hofstadter model, highlighting the effects of chirality on lasing thresholds, stability, and robustness against disorder.

## Contribution

It introduces a theoretical framework for topological lasers with saturable gain, emphasizing the role of chirality and geometrical effects on lasing behavior and stability.

## Key findings

- Lasing threshold depends sharply on the shape of the amplifying region.
- Ultraslow relaxation times and convective instabilities are possible.
- Topological laser operation remains robust against static disorder.

## Abstract

We theoretically study topological laser operation in a bosonic Harper-Hofstadter model featuring a saturable optical gain. Crucial consequences of the chirality of the lasing edge modes are highlighted, such as a sharp dependence of the lasing threshold on the geometrical shape of the amplifying region and the possibility of ultraslow relaxation times and of convectively unstable regimes. The different unstable regimes are characterized in terms of spatio-temporal structures sustained by noise and a strong amplification of a propagating probe beam is anticipated to occur in between the convective and the absolute (lasing) thresholds. The robustness of topological laser operation against static disorder is assessed.