Overview
Optical thermodynamics, a theoretical framework for describing Rayleigh-Jeans (RJ) modal power distributions in multimoded nonlinear photonic circuits, traditionally operates within the constraint of weak nonlinear mode-mode interactions. This work addresses this limitation by developing an extended theoretical framework. It introduces a steady-state interacting RJ modal distribution, termed non-ideal RJ (NIRJ), which incorporates renormalized temperature and optical chemical potential. This development establishes a connection with existing grand-canonical statistical-mechanical formulations relevant to discrete nonlinear systems. A key outcome of this theory is the derivation of an optical analogue to the compressibility factor, which governs the transition between an ideal, non-interacting equation of state (EoS) and a van der Waals-like interacting EoS.
Research Context
The field of optical thermodynamics has recently focused on understanding the Rayleigh-Jeans (RJ) modal power distribution, which characterizes multimoded nonlinear photonic circuits. However, the applicability of this framework has been restricted to systems where nonlinear mode-mode interactions are weak. This constraint limits the scope of optical thermodynamics to specific interaction regimes. Earlier work has explored grand-canonical statistical-mechanical formulations in the context of discrete nonlinear systems.
Approach
The research employs a Transfer Integral Operator to extend the theoretical description of optical thermodynamics. This operator enables the formulation of a steady-state interacting RJ modal distribution, referred to as non-ideal RJ (NIRJ). The application of this operator facilitates the renormalization of critical thermodynamic parameters, specifically temperature and optical chemical potential. This methodology connects the new framework to previous investigations into grand-canonical statistical-mechanical formulations for discrete nonlinear systems. The theoretical development also includes the derivation of an optical analogue for the compressibility factor.
Findings
- The research establishes a steady-state interacting Rayleigh-Jeans (RJ) modal distribution, designated as non-ideal RJ (NIRJ), which operates beyond the weak nonlinearity limit in optical thermodynamics.
- The application of a Transfer Integral Operator facilitates the renormalization of both temperature and optical chemical potential within this extended framework.
- This framework builds a bridge with earlier work on grand-canonical statistical-mechanical formulations that address discrete nonlinear systems.
- The theory derives an optical analogue of the compressibility factor.
- This optical compressibility factor is identified as controlling the transition from an ideal, non-interacting equation of state (EoS) to a van der Waals-like interacting EoS.