Interaction of orthogonal-polarized waves in 1D metamaterial with Kerr nonlinearity

TL;DR

This paper presents a theoretical analysis of wave interactions in 1D metamaterials with Kerr nonlinearity, deriving nonlinear equations for orthogonal polarizations and exploring their solutions in the gigahertz range.

Contribution

It introduces a generalized system of nonlinear equations for orthogonal-polarized wave interactions in 1D metamaterials with Kerr nonlinearity, extending previous models.

Findings

Derived nonlinear evolution equations for wave interactions

Found and analyzed solutions for slow-varying envelopes

Obtained traveling wave solutions and explicit dispersion relations

Abstract

A theoretical study of wave propagation in 1D metamaterial is presented. A system of nonlinear evolution equation for electromagnetic waves with both polarizations account is derived by means of projection operators method for general nonlinearity and dispersion. The system describes interaction of opposite directed waves with a given polarization. The particular case of Kerr nonlinearity and Drude dispersion is considered. In such approximation it results in the correspondent systems of nonlinear equations that generalizes the Sch\"{a}fer-Wayne one. Particular solutions in case of slow-varying envelopes are found, plotted and analyzed in gigahertz range. Travelling wave solution for the system of equation of interaction of orthogonal-polarized waves is also obtained and the correspondent nonlinear dispersion relations are written in explicit form.