The diversity of isofrequency surface topologies in a hypercrystal composed of ferrite- and semiconductor-based metamaterials

Recent studies have centered on the potential for effectively controlling the topology state of iso-frequency surfaces in artificial photonic structures using external fields. This paper delves into the topological transitions and singularity states of the isofrequency surface of a highly anisotropic superlattice. This superlattice is composed of alternating layers of ferrite-dielectric and semiconductor-dielectric metamaterials. The superlattice is placed in an external magnetic field in the Voigt geometry that is parallel to the boundaries of the structure layers and perpendicular to the periodicity axis. Material properties of both constituent metamaterials are described in terms of effective components of permittivity and permeability in the long-wave approximation. An external magnetic field influences the properties of transverse electric (TE) waves in the ferrite-dielectric metamaterial, and the properties of transverse magnetic (TM) waves in the semiconductor-dielectric metamaterial. This results in the iso-frequency surface transition from a closed ellipsoid to an open hyperboloid for both TE and TM waves in various configurations. Furthermore, the superlattice can be identified as a hypercrystal under certain conditions, specifically when the constituent metamaterials possess a hyperbolic isofrequency surface state. This research demonstrates that the isofrequency surface properties of the studied hypercrystal can be effectively controlled by altering the external magnetic field, the fill factors of metamaterials, and frequency. Special attention is devoted to investigating the topological singularities that take place when iso-frequency surfaces of TE and TM polarized waves intersect. This intersection leads to the degeneracy of the hypercrystal’s isofrequency surface and the potential observation of unique phenomena such as conical refraction or the existence of surface states.