Uniaxial dielectric mediums with hyperbolic dispersion relations

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.