Ab-initio multimode linewidth theory for arbitrary inhomogeneous laser cavities

TL;DR

This paper develops a comprehensive multimode laser linewidth theory applicable to arbitrary inhomogeneous cavities, incorporating known effects and novel nonlinear corrections, resulting in a precise, parameter-free linewidth formula based on steady-state modes.

Contribution

It introduces a new multimode linewidth theory that accounts for complex cavity geometries and nonlinear effects, extending previous models with a fully spatially resolved, parameter-free formula.

Findings

Includes a bad-cavity correction to the Henry α factor

Derives a multimode Schawlow--Townes relation

Provides a quantitatively accurate linewidth formula without free parameters

Abstract

We present a multimode laser-linewidth theory for arbitrary cavity structures and geometries that contains nearly all previously known effects and also finds new nonlinear and multimode corrections, e.g. a bad-cavity correction to the Henry $\alpha$ factor and a multimode Schawlow--Townes relation (each linewidth is proportional to a sum of inverse powers of all lasing modes). Our theory produces a quantitatively accurate formula for the linewidth, with no free parameters, including the full spatial degrees of freedom of the system. Starting with the Maxwell--Bloch equations, we handle quantum and thermal noise by introducing random currents whose correlations are given by the fluctuation--dissipation theorem. We derive coupled-mode equations for the lasing-mode amplitudes and obtain a formula for the linewidths in terms of simple integrals over the steady-state lasing modes.