Evolution equation for interaction of opposite directed waves with arbitrary polarization in 1D-metamaterial

Abstract

In this paper, a theoretical study of wave propagation in 1D metamaterial is presented. A system of evolution equations for electromagnetic waves with both polarizations account is derived by means of projection operators method for general nonlinearity and dispersion. It 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 corresponding system of nonlinear equations that generalizes the Schäfer–Wayne one. Traveling wave solution for the system of equation of interaction of orthogonal-polarized waves is also obtained. Dependence of wavelength on amplitude is written and plotted.