Zero index electromagnetic materials

TL;DR

This paper develops a formalism to calculate the direction-dependent refractive index in bi-anisotropic materials, introduces the concept of complex axis nihility media supporting unidirectional waves, and explores their unique scattering and interface properties.

Contribution

It provides a new general condition for zero refractive index in arbitrary directions and introduces complex axis nihility media supporting unidirectional propagation.

Findings

Infinite family of media supporting unidirectional waves

Complete exclusion of certain angular momentum partial waves

Interfaces supporting one-way interface states

Abstract

Here we re-examine one of the most basic quantities in optics: the refractive index. Considering propagation in a plane, we first develop a general formalism for calculating the direction dependent refractive index in a general bi-anisotropic material. From this we derive the general condition for achieving zero refractive index in a given direction. We show that when the zero-index direction is complex valued the material supports waves that can propagate in only one sense, e.g. in only a clockwise direction. We dub such materials complex axis nihility (CAN) media. Our condition shows that there are an infinite family of both time reversible and time irreversible homogeneous electromagnetic media that support unidirectional propagation for a particular polarization. We give examples showing that scattering from such media results in the complete exclusion of partial waves with one sign of the angular momentum, and that interfaces between such media generally support one-way interface states. As well as giving new sets of material parameters, our simple condition reproduces many of the findings derived using topology, such as unidirectional propagation in gyrotropic media, and spin-momentum locking of evanescent waves.