Tri-and tetrahyperbolic isofrequency topologies complete classification of bianisotropic materials

We describe novel topological phases of isofrequency k-space surfaces in bianisotropic optical materials-tri-and tetrahyperbolic materials-which are induced by the introduction of chirality. This completes the classification of isofrequency topologies for bianisotropic materials, as we showed that all optical materials belong to one of the following topological classes-tetra-, tri-, bi-, mono-, or nonhyperbolic. We showed that phase transitions between these classes occur in the k-space directions with zero group velocity at high k-vectors. This classification is based on the sets of high-k polaritons (HKPs), supported by materials. We obtained the equation describing these sets and characterized the longitudinal polarization-impedance of HKPs.