High symmetry versus optical isotropy of a negative index metamaterial

TL;DR

This paper investigates the optical isotropy of a negative index metamaterial, revealing that high symmetry does not guarantee isotropy in the negative refraction spectral domain, and introduces a new analysis tool.

Contribution

It challenges the assumption that cubic symmetry ensures optical isotropy in metamaterials by analyzing the dispersion relation of a specific negative index MM.

Findings

The metamaterial is optically isotropic outside the negative refraction domain.

Optical isotropy is not guaranteed in the spectral domain of negative refraction.

A new tool for probing optical isotropy in metamaterials is introduced.

Abstract

Optically isotropic metamaterials (MMs) are required for the implementation of subwavelength imaging systems. At first glance one would expect that their design should be based on unit cells exhibiting a cubic symmetry being the highest crystal symmetry. It is anticipated that this is a sufficient condition since it is usually assumed that light does not resolve the spatial details of MM but experiences the properties of an effective medium, which is then optically isotropic. In this work we challenge this assumption by analyzing the isofrequency surfaces of the dispersion relation of the split-cube in carcass (SCiC) negative index MM. We show that this MM is basically optically isotropic, but not in the spectral domain where it exhibits negative refraction. The primary goal of this contribution is to introduce a tool that allows to probe a MM against optical isotropy.