Indefinite by Nature: From Ultraviolet to Terahertz

Abstract

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.

Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons

“…Additionally, this inversion of the sign of the permittivity was also reported for SiO 2 /SiC/SiO 2 SPhP-based metamaterial designs [81]. Further investigations into other polar dielectric van der Waals crystals [76] and polar dielectric crystals [77] should experimentally demonstrate a wealth of such low-loss, naturally hyperbolic materials as well as potentially uncover other unanticipated optical properties. Furthermore, these van der Waals crystals offer the exciting potential for realizing the fundamental limit in photon confinement of SPhP modes, with recent results demonstrating that SPhP modes can be supported within three monolayer thick hBN flakes [54] and in nanostructures 86× smaller than the free-space wavelength [53].…”

“…The potential for hyperbolic media has been extensively discussed in the literature [80,177,178], however it has focused primarily on plasmonic/dielectric stacked systems, which typically exhibit high plasmonic losses and only support negative Re(ε) along one principal axis. In contrast, van der Waals crystals such as MoS 2 , WS 2 , etc [76], and other polar dielectrics [77] could potentially offer additional materials with naturally reciprocal hyperbolic response [53]. Such optical behavior, coupled with the low-loss nature of the SPhP modes, could enable the realization of sub-diffraction and/or flat optics such as mid-IR polarizers, wave plates, etc.…”

“…Such two-dimensional materials offer the potential for unanticipated optical properties. For instance, it was recently demonstrated [53,54] that hBN is a naturally hyperbolic material [77], whereby a material exhibits metallic (negative) and dielectric (positive real permittivity) optical response along orthogonal principal axes [78][79][80]. Unlike plasmonic/dielectric hyperbolic metamaterials, hBN was shown to offer the potential to invert the sign of the permittivity along a given axis, while maintaining low optical losses and offer a one atom thick unit cell.…”

Hyperbolic metamaterials: From dispersion manipulation to applications

“…65,67]. Many natural hyperbolic materials belong to the class of van der Waals (vdW) crystals (consist of individual atomic planes bonded by weak vdW forces), and the polaritons in natural hyperbolic materials possess the unprecedented control for the light-matter interaction[177,178].…”

Free-space components for microwave transmission

“…The phenomenon of filamentation has attracted great interest in both its fundamental science and applications, which include spectroscopy [4], remote sensing [5][6][7], triggering of lightning discharges and water condensation in the atmosphere [8], and attosecond physics [11,12]. Moreover, various kinds of "photonic lattices" formed out of filaments have been proposed for energy projection in orthogonal directions have different signs [19][20][21][22][23][24][25][26][27][28][29][30][31]. These structures have gained attention because of their unique physical properties, the most important of which being that their iso-frequency dispersion surfaces are hyperboloids.…”