Optical Thermodynamics Beyond the Weak Nonlinearity Limit

TL;DR

This paper extends optical thermodynamics beyond weak nonlinear interactions by developing a new theoretical framework that accounts for strong interactions, leading to a non-ideal Rayleigh-Jeans distribution with renormalized parameters.

Contribution

It introduces a Transfer Integral Operator approach to describe steady-state interacting RJ distributions, bridging optical thermodynamics with statistical mechanics of nonlinear systems.

Findings

Established a non-ideal RJ distribution with renormalized temperature and chemical potential.

Derived an optical analogue of the compressibility factor controlling phase transition.

Connected optical thermodynamics with grand-canonical statistical mechanics.

Abstract

Optical thermodynamics has recently emerged as a theoretical framework describing a Rayleigh-Jeans (RJ) modal power distribution of multimoded nonlinear photonic circuits. However, its applicability is constrained to systems exhibiting weak nonlinear mode-mode interactions. Here, by employing a Transfer Integral Operator, we circumvent this limitation and establish a steady-state interacting RJ modal distribution -- referred to as non-ideal RJ (NIRJ) -- with renormalized temperature and optical chemical potential. This also builds a natural bridge with earlier work on grand-canonical statistical-mechanical formulations of discrete nonlinear systems. The theory derives the optical analogue of the compressibility factor, which controls the transition from an ideal, non-interacting equation of state (EoS) to a van der Waals-like interacting EoS.