Calculation of dispersion equations for uniaxial dielectric-magnetic mediums

TL;DR

This paper systematically analyzes electromagnetic wave dispersion in uniaxial dielectric-magnetic media, highlighting how dissipation affects the number and nature of dispersion cases, including elliptic and hyperbolic relations.

Contribution

It provides a comprehensive classification of dispersion relations for both dissipative and non-dissipative uniaxial media, revealing new allowed cases in dissipative conditions.

Findings

Dispersion relations follow elliptic/hyperbolic patterns in non-dissipative media.

Dissipative media exhibit fewer dispersion cases but include some not possible in non-dissipative media.

The sign change in permittivity or permeability significantly alters dispersion behavior.

Abstract

In this overview paper, we investigate the dispersion of electromagnetic waves for dissipative and non-dissipative dielectric-magnetic uniaxial mediums. Changing the sign of one component of dielectric permittivity ({\epsilon}) or magnetic permeability ({\mu}) from positive to negative will lead to sixteen different cases (real or imaginary) for a non-dissipative medium and eight different cases for dissipative one. In a non-dissipative medium, dispersion relations follow the elliptic/hyperbolic relations. This rule completely vanishes regarding the dissipative medium. While the number of dispersion cases in a dissipative medium is lower than a non-dissipative one, there are cases which are not allowed in non-dissipative mediums but allowed in dissipative mediums.