Ilia Kuk: Complex dispersion and surface-wave localization at the interface between a hyperbolic material and a topological insulator

We study electromagnetic surface waves at an interface between an anisotropic hyperbolic material and a topological insulator. The topological response couples TE and TM fields, leading to a complex dispersion relation when material loss is included. A dispersion root represents a localized wave only if its fields decay away from the interface and attenuate consistently along it. We examine how these conditions select branches of the complex square roots that define the transverse decay constants. This analysis explains gaps in the physically admissible spectrum and shows how optical-axis orientation changes localization and propagation loss.