Ab initio self-consistent laser theory and random lasers

TL;DR

This paper introduces a novel time-independent method for solving the steady-state Maxwell-Bloch equations in complex and open laser systems, including random lasers, bridging non-linear laser physics and wave chaos.

Contribution

We developed a time-independent technique to find stationary solutions of laser equations applicable to complex and open systems, validated against numerical simulations and applied to random lasers.

Findings

Method accurately matches time-dependent solutions

Successfully finds lasing modes in random lasers

Links non-linear laser physics with wave chaos

Abstract

We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by fully time-dependent numerical simulations or by using major approximations which neglect non-linear modal interactions and/or the openness of the laser system. We have found a time-independent technique for determining these stationary solutions which can treat lasers of arbitrary complexity and degree of openness. Our method has been shown to agree with time-dependent numerical solutions to high accuracy and has been applied to find the electric field patterns (lasing modes) of random lasers, which lack a laser cavity and are so strongly damped that the linear system has no detectable resonances. Our work provides a link between an important non-linear wave system and the field of quantum/wave chaos in linear systems.