Mode-locking transitions in nano-structured weakly disordered lasers

TL;DR

This paper presents a statistical model for mode-locking transitions in nano-structured lasers, revealing a phase transition linked to mode coherence, with differences arising from mode localization and a predicted jump in relaxation time.

Contribution

It introduces a novel statistical approach mapping laser mode interactions onto a thermodynamic model, highlighting the role of mode localization and phase transitions in laser dynamics.

Findings

Mode-locking transition is a first order thermodynamic transition.

Localized modes lead to short-range interactions affecting the transition.

A jump in relaxation time occurs at the transition point.

Abstract

We report on a statistical approach to mode-locking transitions of nano-structured laser cavities characterized by an enhanced density of states. We show that the equations for the interacting modes can be mapped onto a statistical model exhibiting a first order thermodynamic transition, with the average mode-energy playing the role of inverse temperature. The transition corresponds to a phase-locking of modes. Extended modes lead to a mean-field like model, while in presence of localized modes, as due to a small disorder, the model has short range interactions. We show that simple scaling arguments lead to observable differences between transitions involving extended modes and those involving localized modes. We also show that the dynamics of the light modes can be exactly solved, predicting a jump in the relaxation time of the coherence functions at the transition. Finally, we link the thermodynamic transition to a topological singularity of the phase space, as previously reported for similar models.