Conical diffraction and the dispersion surface of hyperbolic metamaterials

TL;DR

This paper explores the unique optical properties of biaxial hyperbolic metamaterials, revealing conical singularities in their dispersion surfaces and demonstrating distinct refraction and diffraction phenomena compared to conventional materials.

Contribution

It provides a comprehensive analysis of conical diffraction and the dispersion surface in biaxial hyperbolic metamaterials, including topological and wave optics descriptions.

Findings

Conical singularities occur at intersecting index surface sheets.

Distinct topological and quantitative features of conical refraction are identified.

Diffraction patterns are asymmetric and differ from those in positive index materials.

Abstract

Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal dielectric constants $\epsilon_1<0$, $0<\epsilon_2\neq\epsilon_3$. In this general case the two sheets of the index surface intersect forming conical singularities. We derive the ray description of conical refraction in these materials, and show that it is topologically and quantitatively distinct from conical refraction in a conventional biaxial material. We also develop a wave optics description, which allows us to obtain the diffraction patterns formed from arbitrary beams incident close to the optic axis. The resulting patterns lack circular symmetry, and hence are qualitatively different from those obtained in conventional, positive index materials.