Metamaterials with index ellipsoids at arbitrary k-points

Ordinary materials have their index ellipsoids centered at k = 0. We propose a new type of metamaterial possessing multiple index ellipsoids centered at arbitrary nonzero k-points. Their locations in momentum space are determined by the connectivity of a set of interpenetrating metallic scaffolds that constitute the metamaterial, independent of the detailed geometry of the scaffold, which determines the group velocity of the modes. The existence of the quasi-static modes at non-zero k-points can be understood by solving Poisson’s equation and can be viewed as a real-space structure induced synthetic gauge potential that shifts the light cone in momentum space. Such metamaterials have broadband functionality as the long wavelength properties arise from global network connectivity rather than local resonance. For example, when interfaced with ordinary materials, they have an orientation-dependent coupling effect that can be used to design broadband directional antennae. We performed microwave experiments to confirm our findings.