Uniaxial dielectric mediums with hyperbolic dispersion relations

TL;DR

This paper explores the unique hyperbolic dispersion relations in uniaxial dielectric media, revealing their propagation characteristics and conceptualizing them as homogenized composites, expanding understanding beyond traditional elliptical models.

Contribution

It introduces the analysis of hyperbolic dispersion in uniaxial dielectrics and presents a homogenized composite medium model for such hyperbolic-like materials.

Findings

Phase velocity remains positive for evanescent and nonevanescent waves.

Hyperbolic dispersion relations differ from conventional elliptical ones.

A conceptual model as a homogenized composite medium is proposed.

Abstract

The dispersion relations for conventional uniaxial dielectric mediums may be characterized as elliptical or elliptical-like, according to whether the medium is nondissipative or dissipative, respectively. However, under certain constitutive parameter regimes, the dispersion relations may be hyperbolic or hyperbolic-like. We investigate planewave propagation in a hyperbolic/hyperbolic-like uniaxial dielectric medium. For both evanescent and nonevanescent propagation, the phase velocity is found to be positive with respect to the time-averaged Poynting vector. A conceptualization of a hyperbolic--like uniaxial medium as a homogenized composite medium is presented.