Fig. 1

Hyperbolic materials. Metal nanowire (a) and planar multilayer (b) metamaterials are artificially structured materials engineered to exhibit metallic response in some directions and dielectric response in others. In the effective medium limit, this anisotropy leads to hyperbolic isofrequency surfaces, which in principle would result in a diverging photonic density of states. In reality, the hyperbolic dispersion is only realized for wave vectors up to k _max ~π/d, where d is the periodicity of the medium which is typically on the order of tens of nanometers. Natural hyperbolic materials (c) possess no artificial structuring and their hyperbolic dispersion extends much further in reciprocal space being limited only by the atomic periodicity of the crystal structure