Critical-point phenomena and finite-size scaling in mean-field equal-coupling photonic networks

TL;DR

This paper investigates the mean-field optical phase transition in multimode photonic networks, using finite-size scaling and statistical mechanics analogies to identify critical points and exponents, confirming the transition's mean-field nature.

Contribution

It introduces a comprehensive finite-size scaling analysis of the optical phase transition in photonic networks, establishing the critical line and upper critical dimension, and connects equilibrium properties to thermodynamic quantities.

Findings

Confirmed mean-field nature of the transition

Established the critical line in the phase diagram

Identified the upper critical dimension as 4

Abstract

The mean-field optical phase transition in multimode equal-coupling photonic networks is studied by temporal evolution of the nonlinear equations of motion of the coupled modes. Analogies to statistical mechanics models of interacting classical spins, built upon the correspondence between complex-valued modes and two-component spins, are employed to define two-component and single-component order parameters. A comprehensive finite-size scaling analysis is performed to estimate critical points and exponents of a second-order phase transition, driven by the optical energy per mode. Equilibrium properties of the system are compared to exact results whenever applicable. Considering various parameter settings, our results confirm the mean-field nature of the transition and establish the critical line in the nonlinearity--energy-density phase diagram. Critical scaling leads to infer the upper critical dimension $d_c=4$. Connection to thermodynamic quantities is established by means of a kinetic temperature with appropriate zero-temperature limit. In the low temperature phase (low energy per mode), spins align. In the high temperature phase (large energy per mode), spins rotate independent of one another.