Is single-mode lasing possible in an infinite periodic system?

TL;DR

This paper introduces a rigorous method to analyze the stability of periodic lasing systems, demonstrating that nonlinear effects can enable stable single-mode lasing in infinite systems under certain conditions.

Contribution

It provides a novel stability criterion based on nonlinear Maxwell-Bloch equations for infinite periodic lasing systems, addressing the challenge of single-mode stability.

Findings

Nonlinear effects can stabilize single-mode lasing near threshold.

Stability depends on the sign of laser detuning relative to band curvature.

Results validated through time-domain simulations.

Abstract

In this Letter, we present a rigorous method to study the stability of periodic lasing systems. In a linear model, the presence of a continuum of modes (with arbitrarily close lasing thresholds) gives the impression that stable single-mode lasing cannot be maintained in the limit of an infinite system. However, we show that nonlinear effects of the Maxwell-Bloch equations can lead to stable systems near threshold given a simple stability condition on the sign of the laser detuning compared to the band curvature. We examine band-edge (1d) and bound-in-continuum (2d) lasing modes and validate our stability results against time-domain simulations.