GENERAL EQUATION FOR DIRECTED ELECTROMAGNETIC WAVE PROPAGATION IN 1D METAMATERIAL: PROJECTING OPERATOR METHOD

Abstract

We consider a boundary regime problem for 1D wave propagation in a metamaterial medium with simultaneously negative dielectric permittivity and magnetic permeability. We apply a projecting operator method to the Maxwell system in the time domain that allows the space of the linear propagation problem to be split into subspaces of directed waves for the relations of a given material with general dispersion. After projection, the equations for directed waves have a maximally simplified form, which is most convenient for numerical and analytical integration. Matrix elements of the projectors act as integral operators. For a given nonlinearity and dispersion we derive a general system of interacting right/left waves with combined (hybrid) amplitudes. The result is specified for the Drude metamaterial model for both permittivity and permeability coefficients and the Kerr nonlinearity. We also discuss and investigate singular solitary wave solutions of the system as a limit stationary elliptic system related to some boundary regimes.