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

Abstract

Abstract-The analysis of waves propagation in homogeneous anisotropic media constitutes a classical topic in every field of science and has been preferentially discussed using locally plane waves. Specific physical quantities and their behaviour laws are really what make the difference. Although the use of Fourier transform enables an approach formally analogous to that of plane waves in linear evolution equations, its application to constitutive equations of inhomogeneous media involves cumbersome convolution products that mask the solution. This paper proposes a polar representation (amplitude and phase) of electromagnetic fields, that appears to be more suitable and provides two sets of equations that can be easily decoupled, reducing the problem to the superposition of two simpler ones. The procedure is based upon the following steps: a) The identification of dispersion equation with Hamilton-Jacobi equation yields the evolution laws of rays and/or wave-fronts. b) From the knowledge of tensorε(r) at any pointr of the wave front (or the ray), the use of the intrinsic character (conjugation relations) of fields, introduced by the authors in a previous work, together with ray velocity or phase gradient (found in the first step) the remaining fields are immediately obtained.

The Eikonal Equation for Metamaterials Optics From a Moving Boundary Variational Principle

“…is the determinant of tensorε (product of its eigenvalues). From equations given in Equation (39) and using the expression (41), the eikonal equation for these media is immediately derived, as shown in [21]:…”