The Complex Spherical 2+4 Spin Glass: a Model for Nonlinear Optics in Random Media

TL;DR

This paper introduces a mean field model for multimode lasers in disordered media, revealing complex phase transitions including a novel spontaneous phase locking and glassy behavior with multiple metastable states.

Contribution

It develops a comprehensive replica analysis of a disordered laser model, identifying new optical regimes and phase transition phenomena not previously characterized.

Findings

Identification of four distinct optical regimes including a novel spontaneous phase locking.

Prediction of a replica symmetry breaking phase transition at the random lasing threshold.

Discovery of glassy behavior with multiple metastable states in disordered laser systems.

Abstract

A disordered mean field model for multimode laser in open and irregular cavities is proposed and discussed within the replica analysis. The model includes the dynamics of the mode intensity and accounts also for the possible presence of a linear coupling between the modes, due, e.g., to the leakages from an open cavity. The complete phase diagram, in terms of disorder strength, source pumping and non-linearity, consists of four different optical regimes: incoherent fluorescence, standard mode locking, random lasing and the novel spontaneous phase locking. A replica symmetry breaking phase transition is predicted at the random lasing threshold. For a high enough strength of non-linearity, a whole region with nonvanishing complexity anticipates the transition, and the light modes in the disordered medium display typical discontinuous glassy behavior, i.e., the photonic glass has a multitude of metastable states that corresponds to different mode-locking processes in random lasers. The lasing regime is still present for very open cavities, though the transition becomes continuous at the lasing threshold.