Dispersion relation for anisotropic media

TL;DR

This paper derives a general tensorial dispersion relation for electromagnetic waves in anisotropic media with arbitrary permittivity and permeability matrices, applicable to classical and metamaterial media.

Contribution

It presents a compact, tensorial dispersion relation for anisotropic media with non-symmetric, non-positive definite matrices, extending previous models.

Findings

Derived a general dispersion relation tensor for anisotropic media.

Applicable to media with non-symmetric and non-invertible permittivity and permeability matrices.

Useful for studying wave propagation in classical and metamaterial media.

Abstract

The electromagnetic wave propagation in an anisotropic dielectric media with two generic matrices $\epsilon^{ij}$ and $\mu^{ij}$ of permittivity and permeability is studied. These matrices are not required to be symmetric, positive definite, and even invertible. In the framework of a metric-free electrodynamics approach, compact tensorial dispersion relation is derived. The resulted formula are useful for a theoretical study of electromagnetic wave propagation in a classical media and in a modern type of media with a generic linear constitutive relation including metamaterials.