Zero-refractive-index materials and topological photonics

Abstract

The refractive index is one of the most basic optical properties of a material and its interaction with light. Modern materials engineering—particularly the concept of metamaterials—has made it necessary to consider its subtleties, including anisotropy and complex values. Here we re-examine the refractive index and find a general way to calculate the direction-dependent refractive index and the condition for zero index in a given direction. By analogy with linear versus circular polarization, we show that when the zero-index direction is complex-valued, a material supports waves that can propagate in only one sense, for example, clockwise. We show that there is an infinite family of both time-reversible and time-irreversible homogeneous electromagnetic media that support unidirectional propagation for a particular polarization. As well as extending the concept of the refractive index, shedding new light on our understanding of topological photonics and providing new sets of material parameters, our simple picture also reproduces many of the findings derived using topology. A general approach to derive direction-dependent complex refractive indices close to zero produces infinite families of time-reversible and infinite families of time-irreversible electromagnetic materials, without invoking the concept of topology.