Hamiltonian and Phase-Space Representation of Spatial Solitons

TL;DR

This paper employs Hamiltonian ray tracing and phase-space methods to analyze the propagation and collision dynamics of spatial solitons in Kerr media, providing intuitive visualizations of energy exchange and wave effects.

Contribution

It introduces a novel application of Hamiltonian ray tracing combined with phase-space analysis to study spatial solitons and their interactions in nonlinear media.

Findings

Energy within a soliton is effectively tracked using ray trajectories.

Soliton collisions involve energy exchange visualized through phase-space shearing.

The method accounts for wave effects and Kerr nonlinearity simultaneously.

Abstract

We use Hamiltonian ray tracing and phase-space representation to describe the propagation of a single spatial soliton and soliton collisions in a Kerr nonlinear medium. Hamiltonian ray tracing is applied using the iterative nonlinear beam propagation method, which allows taking both wave effects and Kerr nonlinearity into consideration. Energy evolution within a single spatial soliton and the exchange of energy when two solitons collide are interpreted intuitively by ray trajectories and geometrical shearing of the Wigner distribution functions.