An Alternative Model for Wave Propagation in Anisotropic Impedance-Matched Metamaterials

Abstract

Abstract-The propagation of light in an anisotropic impedancematched metamaterial is studied in the frame of geometrical optics. We prove that directions of fieldsD,B andv (ray velocity) are a triad of conjugate directions with respect to the inverse relative dielectric permittivity tensor and constitutes a local basis, whose reciprocal one is formed by directions ofĒ,H fields and wave-vectork. Consequently, both dual bases are intrinsically related to the physical properties of medium. We have identified these bases with direct and reciprocal bases of a curvilinear coordinates system, showing that physics defines geometry. This identification provides a powerful tool to solve two kinds of problems (direct and inverse ones) that currently arise: In direct problems, medium properties are given and it suffices to know ε =μ tensor at every point, to obtain the wave structure. In inverse problems, medium properties must be found for the rays to propagate along prescribed trajectories. The procedure is applied to an illustrating example.

On Inhomogeneous Metamaterials Media: A New Alternative Method for Analysis of Electromagnetic Fields Propagation

“…Throughout the paper it will be shown that from the knowledge of tensorε (relative permittivity/ permeability) at any pointr of the wave front (or the ray), the use of direct and reciprocal bases associated with vector fields [6,12] together with ray velocity or phase gradient (found in the first step) the remaining fields may be obtained immediately. In fact, for a given electromagnetic energy density, not all the fields are allowed: only those whose directions form reciprocal bases with respect to relativepermittivity/permeability tensor are possible.…”

“…Following the procedure given in [6], two conjugate vector bases can be introduced. We choose a direct local basis (P,ē i /{i = 1, 2, 3}) consisting of three unit vectors:…”

“…One of the most important objectives of this discipline is the achievement of macroscopic invisibility-cloaking structures [4][5][6]. Nevertheless, in Transformation Optics impedance matched to vacuum media are required, where the relative permittivity tensor is equal to the relative permeability one (ε =μ) at every point of space, when referred to the same vector basis (ε(r) =μ(r)).…”

Mesh Optimization for Maxwell's Equations With Respect to Anisotropic Materials Using Geometric Algebra

“…However, in our case the Hodge star depends on material distributions which may be inhomogeneous, making it a function of space. Several formalisms have been proposed in related settings, for example anisotropic materials have been theoretically studied in [8] using classical tensor calculus, while differential forms have been used to recast Maxwell's equations in [9]. However, here GA was chosen due to its clearer geometric interpretation compared to other formalisms.…”