Geometrical analysis of wave propagation in left-handed metamaterials. Part II

Abstract

—Geometrical analysis of basic equations of electromagnetics waves propagation in anisotropic dielectric materials with magnetic isotropy are presented in two complementary papers (Part I and Part II). In this paper, analysis arises from local properties of dielectric permittivity tensor and M¨ohr’s plane graphical construction compatible with circumferences that represent general plane wave equation. This theoretical study allows to know how rays propagate in left-handed metamaterials (LHMs) exhibiting dielectric anisotropy and magnetic isotropy. Geometrical analysis yields plane graphical procedures for ray tracing, that are extremely easy. In particular, indefinite dielectric media, where dielectric permittivities are not all the same sign, has been investigated and a joint study of materials having the same eigenvalues of ˜ε, but with opposite values of µr is performed. The opposite sense of propagation of rays in “opposite media” (media with opposite values of εi and µr) has been also shown. It must be pointed out that the presented method always allows graphical plane constructions, even when dealing with biaxial media.