Theory of the spatial structure of non-linear lasing modes

TL;DR

This paper develops a self-consistent integral equation approach to determine steady-state lasing modes in open multi-mode lasers, revealing complex spatial structures and interactions, applicable to various media including chaotic and random lasers.

Contribution

It introduces a novel formalism that describes lasing modes through biorthogonal modes of a linear wave equation, surpassing traditional resonance-based methods.

Findings

Lasing modes exhibit non-trivial spatial structures even in single-mode operation.

The formalism accurately accounts for spatial hole-burning and mode competition.

Applicable to complex, chaotic, and random laser media.

Abstract

A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multi-mode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a linear wave equation and not in terms of resonances of the cold cavity. A one-dimensional cavity laser is analyzed and the lasing mode is found to have non-trivial spatial structure even in the single-mode limit. In the multi-mode regime spatial hole-burning and mode competition is treated exactly. The formalism generalizes to complex, chaotic and random laser media.