Percolation with coupled lasers: effect of non-linearities on the phase transition

TL;DR

This study experimentally explores percolation phenomena using coupled lasers, revealing how nonlinearities and system parameters influence phase transitions and cluster formation.

Contribution

It introduces a novel experimental platform with coupled lasers to investigate percolation, including effects of nonlinearities on the transition.

Findings

Percolation transition occurs at a threshold consistent with classical predictions.

Nonlinear regime alters the effective behavior of lasing sites.

Percolation probability exhibits a second-order transition.

Abstract

Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a platform of coupled lasers, where connectivity, interaction strength, and system size can be controlled. Using a square array of 100 lasers with astronomical number of possible cluster configurations, we show that the emergence of a percolating cluster corresponds to the onset of phase locking among the lasers. We also show that the percolation probability undergoes a second-order alike transition as a function of the site-occupation probability, with a threshold consistent with classical theoretical predictions. Surprisingly, we find that at low pump level, amplified mode competition (nonlinear regime) alters the effective behavior of the lasing sites and modify the nature of the percolation transition. The experimental results are interpreted by the means of a theoretical toy model with connectivity rules to the classical percolation.