Breather solitons in highly nonlocal media

TL;DR

This paper studies the breathing behavior of optical solitons in highly nonlocal media, deriving a differential equation for oscillations and showing limitations of previous models through theoretical and numerical analysis.

Contribution

It generalizes the Ehrenfest theorem to describe soliton breathing and demonstrates the inadequacy of the Snyder-Mitchell model for certain oscillation dynamics.

Findings

Oscillations in beam width follow a fourth-order differential equation.

The original accessible soliton model does not accurately predict oscillation periods.

Numerical simulations confirm the theoretical predictions.

Abstract

We investigate the breathing of optical spatial solitons in highly nonlocal media. Generalizing the Ehrenfest theorem, we demonstrate that oscillations in beam width obey a fourth-order ordinary differential equation. Moreover, in actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell [Science \textbf{276}, 1538 (1997)] cannot accurately describe the dynamics of self-confined beams as the transverse size oscillations have a period which not only depends on power but also on the initial width. Modeling the nonlinear response by a Poisson equation driven by the beam intensity we verify the theoretical results against numerical simulations.