Manmade media (MMM) 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 MMM, which are referred to in case of metal (conductive) or ferrite (metaatoms) 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 the 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 the 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.

Keywords: hyperbolic metamaterial, photonic crystal, plasmon, dielectric permeability, dispersion, band structure, homogenization, volume integral equations PACS: 42.70.Qs, 78.67.Pt, 81.05.Xj (all) DOI: 10.3367/UFNe.2019.08.038643 URL: https://ufn.ru/en/articles/2019/12/a/ 000518758100001 2-s2.0-85082014296 Citation: Davidovich M V "Hyperbolic metamaterials: production, properties, applications, and prospects" Phys. Usp. 62 1173–1207 (2019) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 19th, April 2018, revised: 20th, December 2018, accepted: 13th, August 2019 Оригинал: Давидович М В «Гиперболические метаматериалы: получение, свойства, применения, перспективы» УФН 189 1249–1284 (2019); DOI: 10.3367/UFNr.2019.08.038643