Gap soliton dynamics in an optical lattice as a parametrically driven pendulum

TL;DR

This paper demonstrates that the dynamics of a short wavelength gap soliton in an optical lattice can be modeled by a parametrically driven pendulum, revealing complex and potentially chaotic behavior through theoretical and numerical analysis.

Contribution

It introduces a novel analogy between gap soliton dynamics in optical lattices and the Newton equation of a parametrically driven pendulum, supported by numerical simulations.

Findings

Soliton dynamics follow the equations of a driven pendulum.

The system exhibits rich and chaotic behavior.

Numerical simulations validate the theoretical model.

Abstract

A long wavelength optical lattice is generated in a two-level medium by low-frequency contrapropagating beams. Then a short wave length gap soliton generated by evanescent boundary instability (supratransmission) undergoes a dynamics shown to obey the Newton equation of the parametrically driven pendulum, hence presenting extremely rich, possibly chaotic, dynamical behavior. The theory is sustained by numerical simulations and provides an efficient tool to study soliton trajectories.