Indefinite by Nature: From Ultraviolet to Terahertz

A class of strongly anisotropic materials having their principal elements of dielectric permittivity or magnetic permeability tensors of opposite signs, so-called indefinite or hyperbolic materials, has recently attracted significant attention. These materials enabled such novel properties and potential applications as all-angle negative refraction, high density of states, and imaging beyond the diffraction limit using a so-called hyperlens. While several studies identified a few examples of negative refractions in birefringent crystals existing in nature, the majority of optical materials with hyperbolic dispersion relations known to date are engineered composite materials, metamaterials, such as metal-dielectric subwavelength multilayered structures or metal nanowires in a dielectric matrix. In this paper, we investigate naturally existing hyperbolic materials with indefinite permittivity for a range of frequencies from terahertz to ultraviolet. These include graphite, MgB2, cuprate, and ruthenate. Spectroscopic ellipsometry is used to characterize the dielectric properties of graphite and MgB2, and a fitting method based on reflectance spectra is used to determine the indefinite permittivity of the cuprate and ruthenate. Lastly, we discuss the mechanisms behind indefinite properties of these materials.