Propagation of ultra-short solitons in stochastic Maxwell's equations

TL;DR

This paper derives stochastic generalizations of the short pulse equation to model ultra-short soliton propagation in media with random variations, demonstrating stable propagation and good approximation of solutions in stochastic Maxwell's equations.

Contribution

It introduces a modified multi-scale expansion for stochastic systems and derives new stochastic short pulse equations for the first time.

Findings

Stochastic short pulse equations accurately approximate stochastic Maxwell's equations.

Solitons propagate stably in stochastic media.

The approach works for different types of media variations.

Abstract

We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.