Higher-order effects and ultra-short solitons in left-handed metamaterials

TL;DR

This paper derives higher-order nonlinear Schrödinger equations from Maxwell's equations to describe ultra-short solitons in nonlinear left-handed metamaterials, providing exact solutions for electric and magnetic field envelopes.

Contribution

It introduces a second and third-order nonlinear Schrödinger framework for modeling ultra-short solitons in left-handed metamaterials, including exact solutions.

Findings

Exact bright and dark soliton solutions derived.

Necessary conditions for soliton existence established.

Higher-order effects significantly influence soliton dynamics.

Abstract

Starting from Maxwell's equations, we use the reductive perturbation method to derive a second-order and a third-order nonlinear Schroedinger equation, describing ultra-short solitons in nonlinear left-handed metamaterials. We find necessary conditions and derive exact bright and dark soliton solutions of these equations for the electric and magnetic field envelopes.