Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials

TL;DR

This paper derives short-pulse equations for nonlinear metamaterials in frequency band gaps, analyzing their solutions and connections to solitons, advancing understanding of wave propagation in these complex media.

Contribution

It introduces two novel short-pulse equations specific to nonlinear metamaterials in frequency band gaps, linking their solutions to known soliton structures.

Findings

Derived two short-pulse equations for high- and low-frequency band gaps.

Discussed solution structures and their relation to nonlinear Schrödinger solitons.

Provided insights into wave behavior in nonlinear metamaterials with negative permittivity.

Abstract

We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. In the frequency "band gaps" (where linear electromagnetic waves are evanescent) with linear effective permittivity \epsilon<0 and permeability \mu>0, we derive two short-pulse equations (SPEs) for the high- and low-frequency band gaps. The structure of the solutions of the SPEs is also briefly discussed, and connections with the soliton solutions of the nonlinear Schrodinger equation are presented.