Anomalous reflection from hyperbolic media

Despite the apparent simplicity, the problem of refraction of electromagnetic waves at the planar interface between two media has a vibrant spectrum of unusual phenomena. An example is the paradox when an electromagnetic wave impinges on the interface between a hyperbolic medium and an isotropic dielectric. At specific orientations of the optical axis of the hyperbolic medium relative to the interface, the reflected and transmitted waves can disappear entirely, which contradicts reciprocity. In this paper, we analyze the above-mentioned paradox and present its resolution by introducing infinitesimal losses in the hyperbolic medium. We show that the reflected wave exists in the form of a ghost wave, which becomes infinitely localized at the interface of the hyperbolic medium when the losses vanish. Consequently, all the reflected waves are perfectly absorbed near the interface. We support our reasoning with analytical calculations, numerical simulations, and an experiment with self-complementary metasurfaces in the microwave range.