Hyperbolic metamaterials: production, properties, applications, and prospects

Manmade media (MMMs) consisting of uniaxial photonic crystals with inserts of layers (films) or cylinders embedded in a periodic way into a dielectric substrate with dielectric permeability (DP) are considered. Approximate model-based and accurate electrodynamic methods for describing such MMMs, which are referred to in the case of metal (conductive) or ferrite (metaatom) inserts as a ‘hyperbolic metamaterial’ (HMM), are analyzed. Homogenization methods, the role of dissipation, spatial dispersion (SD), and slow plasmon-polaritons are reviewed. The feasibility of obtaining the hyperbolic dispersion law in a macroscopic description of DP of inserts using the Drude–Lorentz model is studied. In the general case with dissipation and SD, the surface of the Fresnel-equation isofrequencies is shown to differ from a rotation hyperboloid and to be bounded. The ambiguity of a description based on effective material parameters, the effect of dissipation and SD on hyperbolicity, currently observable and possible physical phenomena, and HMM applications are discussed.