Аннотация:The refraction and reflection phenomena occurring at the boundaries of dielectric waveguides manufactured from the unusual materials have been discussed. Such materials are topological insulators and hyperbolic metamaterials with the electromagnetic properties being different from those for the ordinary dialectics. For example, the polarization of the refracted and reflected waves can be changed; the total internal reflection occurs at small angles of the incident wave that is less than a certain critical angle. As a result, the waveguides acquire new characteristics that distinguish them from the standard dielectric waveguides.