Phase diagram and complexity of mode-locked lasers: from order to disorder

TL;DR

This paper explores how disorder affects mode-locking in lasers, revealing a phase diagram with paramagnetic, ferromagnetic, and spin-glass phases, and quantifies the impact of disorder on mode-locking thresholds.

Contribution

It introduces a mean-field spin-glass theoretical framework to analyze the phase diagram of mode-locked lasers with varying disorder levels, connecting laser physics with complex systems theory.

Findings

Identifies three distinct phases: paramagnetic, ferromagnetic, and spin-glass.

Quantifies how disorder influences the mode-locking threshold.

Establishes relevance to other disordered physical systems like Bose-Einstein condensates.

Abstract

We investigate mode-locking processes in lasers displaying a variable degree of structural randomness, from standard optical cavities to multiple-scattering media. By employing methods mutuated from spin-glass theory, we analyze the mean-field Hamiltonian and derive a phase-diagram in terms of the pumping rate and the degree of disorder. Three phases are found: i) paramagnetic, corresponding to a noisy continuous wave emission, ii) ferromagnetic, that describes the standard passive mode-locking, and iii) the spin-glass in which the phases of the electromagnetic field are frozen in a exponentially large number of configurations. The way the mode-locking threshold is affected by the amount of disorder is quantified. The results are also relevant for other physical systems displaying a random Hamiltonian, like Bose-Einstein condensates and nonlinear optical beams.