Thermalized polarization dynamics of a discrete optical waveguide system with four-wave mixing

TL;DR

This paper investigates the statistical mechanics and equilibrium polarization dynamics of coupled optical waveguides with four-wave mixing, revealing phase transitions, analytical distributions, and complex intermediate states.

Contribution

It introduces a Gibbs measure framework for polarization states in coupled waveguides and derives analytical and numerical results on their equilibrium and intermediate behaviors.

Findings

Identification of a transition at infinite temperature leading to discrete vector solitons.

Analytical expression for Stokes parameter distribution depending on initial conditions.

Complex multimodal intermediate polarization distribution influenced by nonlinear coupling.

Abstract

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line $T=\infty$ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.