Statistical mechanics models for multimode lasers and random lasers

TL;DR

This paper reviews statistical mechanical models for multimode and random lasers, highlighting theoretical approaches, recent developments, and the potential for glassy behavior in disordered photonic systems.

Contribution

It provides a comprehensive overview of statistical models for multimode lasers, including mean field, Monte Carlo, and replica methods, and discusses the emergence of glassy phases in disordered media.

Findings

Mean field theory effectively describes standard lasers.

Replica method reveals glassy behavior at lasing threshold.

Potential for experimental detection of replica symmetry breaking.

Abstract

We review recent statistical mechanical approaches to multimode laser theory. The theory has proved very effective to describe standard lasers. We refer of the mean field theory for passive mode locking and developments based on Monte Carlo simulations and cavity method to study the role of the frequency matching condition. The status for a complete theory of multimode lasing in open and disordered cavities is discussed and the derivation of the general statistical models in this framework is presented. When light is propagating in a disordered medium, the system can be analyzed via the replica method. For high degrees of disorder and nonlinearity, a glassy behavior is expected at the lasing threshold, providing a suggestive link between glasses and photonics. We describe in details the results for the general Hamiltonian model in mean field approximation and mention an available test for replica symmetry breaking from intensity spectra measurements. Finally, we summary some perspectives still opened for such approaches.