  Despite the apparent simplicity, the problem of refraction of electromagnetic
waves at the planar interface between two media has an incredibly rich spectrum
of unusual phenomena. An example is the paradox that occurs when an
electromagnetic wave is incident on the interface between a hyperbolic medium
and an isotropic dielectric. At certain orientations of the optical axis of the
hyperbolic medium relative to the interface, the reflected and transmitted
waves are completely absent. In this paper, we formulate the aforementioned
paradox and present its resolution by introduction of infinitesimal losses in a
hyperbolic medium. We show that the reflected wave exists, but became extremely
decaying as the loss parameter tends to zero. As a consequence, all the energy
scattered into the reflected channel is absorbed at the interface. We support
our reasoning with analytical calculations, numerical simulations, and an
experiment with self-complementary metasurfaces in the microwave region. In
addition to the great fundamental interest, this paradox resolution discovers a
plethora of applications for the reflectors, refractors, absorbers, lenses,
antennas, camouflage and holography applications.
