Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

TL;DR

This paper develops a stochastic framework based on the nonlinear Schrödinger equation to analyze polarization and optical rotation in nonlinear birefringent media, incorporating randomness and dissipation effects.

Contribution

It introduces a novel stochastic approach linking the NLSE to Langevin and Fokker-Planck equations for polarization analysis in nonlinear birefringent media.

Findings

Derived Langevin equation for Stokes parameters.

Analyzed Fokker-Planck equation in strong coupling limit.

Provided statistical insights into optical rotation phenomena.

Abstract

A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two--component nonlinear Schr{"o}dinger equation (NLSE). On the basis of the ansatz of "soliton" solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker--Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincar{'e} sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.