Tri- and Tetrahyperbolic Anisotropic and Bianisotropic Optical Metamaterials

Hyperbolic metamaterials have open iso-frequency Fresnel surfaces in momentum space and allow high-k electromagnetic waves. Recently, magnetic hyperbolic metamaterials were experimentally demonstrated [1] and bi-hyperbolic metamaterials were predicted [2]. In this work we introduce a complete taxonomy of optical metamaterials and show that all optical materials belong to one of the following topological classes: tetra-, tri-, bi-, mono- or non-hyperbolic, which includes 2 novel classes - the tetra- and trihyperbolic metamaterials [3]. The prefix in the name of each topological class indicates the number of the double cones in the high-k limit. We explain the formation of tri- and tetrahyperbolic phases in both anisotropic and bianistropic media with or without magnetoelectric coupling by hybridization of plasmonic and magnetic high-k Bloch waves [4]. We predict that tri- and tetrahyperbolic phases can appear in realistic metamaterial structures and will find applications in nanoresolution optics, emission rate and directivity control, and to achieve optical magnetism.
[1] Kruk et al, Nature Comm. 7, 1 (2016)
[2] Tuz, Fedorin, Fesenko, Opt. Lett, 42, 4561 (2017)
[3] Durach, Williamson, Laballe, Mulkey, Appl. Sci. 10, 763 (2020)
[4] Durach, Opt. Comm, 476, 126349 (2020)