Indefinite permittivity and negative refraction in natural material: Graphite

Abstract

In this work, we report a nature indefinite permittivity in crystalline graphite that exhibits negative group refraction at ultraviolet region. A hyperbolic equifrequency contour was obtained from ellipsometry data at 254 nm and an all angle negative refraction was verified experimentally. The indefinite permittivity is attributed to extremely strong anisotropy in the crystal structure and the hybrid electronic transitions. This result not only explores a route toward natural negative-index materials, but also holds a promise for ultraviolet hyperlens, which may lead to a breakthrough in nanolithography for the next generation of electronics.

Microscopic model of Purcell enhancement in hyperbolic metamaterials

“…Depending on the polarizability, dispersion curves are either elliptic or hyperbolic, in agreement with Eq. (12). The curves are generally well described by the effective medium approximation (11).…”

“…Such isofrequency curves can not be described by the Maxwell-Garnett theory Eqs. (11), (12), which predicts only one TM mode for given frequency. They were analyzed in Ref.…”

“…In particular, the so-called hyperbolic metamaterials described by an uniaxial medium where the main components of dielectric and magnetic tensor have different signs, have attracted significant attention [8][9][10]. Realizations of the regime of the hyperbolic medium with negative components of the dielectric tensor have been reported for magnetized plasma [11], graphite [12], for metamaterials based on nanorod assemblies [13][14][15] and for layered metal-dielectric structures [2,16,17]. In this regime, light wavevectors at a given frequency fill a surface of a hyperbolic shape, so that the area of hyperbolic isofrequency surface, giving the photonic density of states, is infinite.…”

Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption

“…Moreover, based upon periodic patterning of graphene, bi-periodic and/or multilayered graphene structures were extensively studied for enhanced transmission [32], optical absorption [33], and tunable metasurfaces in [34], as well as isolators and polarizers in the microwave regime [35][36][37]. It was shown that crystalline Graphite (the 3D parent of graphene) possess indefinite permittivity at UV frequencies [38].…”

Hyperbolic metamaterial feasible for fabrication with direct laser writing processes

“…Among the natural materials, triglycine sulfate and sapphire exhibit hyperbolic dispersion at far-infrared frequencies, bismuth at THz frequencies, and graphite at UV frequencies [38,39]. To date, most optical metamaterial structures have been fabricated by well-established two-dimensional (2D) fabrication technologies, such as e-beam lithography and evaporation of metal films.…”