Self-consistent multi-mode lasing theory for complex or random lasing media

TL;DR

This paper develops a self-consistent multi-mode lasing theory for complex and random media, introducing a new basis for describing lasing modes and emission patterns, applicable to open and chaotic cavities.

Contribution

It introduces a self-consistent linear response framework with a discrete basis for open complex media, extending lasing theory beyond closed cavity approximations.

Findings

The new basis accurately describes emission patterns outside the cavity.

Near threshold approximations are shown to be unreliable in these systems.

Applications demonstrate the theory's relevance to random and wave-chaotic lasers.

Abstract

A semiclassical theory of single and multi-mode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing modes, we introduce an appropriate discrete basis of functions which describe also the intensity and angular emission pattern outside the cavity. This constant flux (CF) basis is dictated by the Green function which arises when formulating the steady state Maxwell-Bloch equations as a self-consistent linear response problem. This basis is similar to the quasi-bound state basis which is familiar in resonator theory and it obeys biorthogonality relations with a set of dual functions. Within a single-pole approximation for the Green function the lasing modes are proportional to these CF states and their intensities and lasing frequencies are determined by a set of non-linear equations. When a near threshold approximation is made to these equations a generalized version of the Haken-Sauermann equations for multi-mode lasing is obtained, appropriate for open cavities. Illustrative results from these equations are given for single and few mode lasing states, for the case of dielectric cavity lasers. The standard near threshold approximation is found to be unreliable. Applications to wave-chaotic cavities and random lasers are discussed.