Full utilization of semi-Dirac cones in photonics

Abstract

In this study, realization and applications of anisotropic zero-refractive-index materials are proposed by exposing the unit cells of photonic crystals that exhibit Dirac-like cone dispersion to rotational symmetry reduction. Accidental degeneracy of two Bloch modes in the Brillouin zone center of two-dimensional ${C}_{2}$-symmetric photonic crystals gives rise to the semi-Dirac cone dispersion. The proposed ${C}_{2}$-symmetric photonic crystals behave as epsilon-and-mu-near-zero materials (${\ensuremath{\varepsilon}}^{\mathrm{eff}}\ensuremath{\approx}0, {\ensuremath{\mu}}^{\mathrm{eff}}\ensuremath{\approx}0$) along one propagation direction, but behave as epsilon-near-zero material (${\ensuremath{\varepsilon}}^{\mathrm{eff}}\ensuremath{\approx}0, {\ensuremath{\mu}}^{\mathrm{eff}}\ensuremath{\ne}0$) for the perpendicular direction at semi-Dirac frequency. By extracting the effective medium parameters of the proposed ${C}_{4}$- and ${C}_{2}$-symmetric periodic media that exhibit Dirac-like and semi-Dirac cone dispersions, intrinsic differences between isotropic and anisotropic materials are investigated. Furthermore, advantages of utilizing semi-Dirac cone materials instead of Dirac-like cone materials in photonic applications are demonstrated in both frequency and time domains. By using anisotropic transmission behavior of the semi-Dirac materials, photonic application concepts such as beam deflectors, beam splitters, and light focusing are proposed. Furthermore, to the best of our knowledge, semi-Dirac cone dispersion is also experimentally demonstrated for the first time by including negative, zero, and positive refraction states of the given material.