Figure 1. Subwavelength band structure engineering in resonant metamaterials.

(a) A subwavelength resonator and its scattering cross-section. (b) A dense two-dimensional ensemble of subwavelength resonators with arbitrary structure makes a metamaterial with negative permittivity (orange band) after the individual resonance of the resonators. Here the resonators are quarter wavelength copper rods sitting on a ground plane. (c) By adding a periodic subwavelength structure, in the form of a triangular array, such a metamaterial can acquire crystalline properties, involving a Bloch band structure with typical polaritonic dispersion corresponding to subwavelength bound modes localized to the array of rods. (d) More complex crystalline properties can be obtained, including point Dirac degeneracy at ϰ point, by considering the polaritons supported by a honeycomb metamaterial. (e) Same lattice as c but viewed in the extended unit cell picture, allowing for mathematical folding of two time-reversed Dirac cones at the Γ point. These two time-reversed degenerate states are exploited here as the equivalent of Kramers pairs to induce topological properties at the subwavelength scale.