Wave propagation in the anisotropic media with single-sheeted hyperboloid dispersion relation

We investigate the wave propagation in the anisotropic metamaterial with single-sheeted hyperboloid dispersion relation. Based on boundary conditions and dispersion relations, we find that the opposite amphoteric refraction, such that E- (or H-) polarized waves are positively refracted whereas H- (or E-) polarized waves are negatively refracted, can occur at the interface associated with the anisotropic metamaterial. Under a certain condition, both E- and H-polarized waves can exhibit the same single-sheeted hyperboloid or straight dispersion relation, while the two polarized waves exhibit different propagation characteristics. We expect some potential device applications can be derived based on based on the unique amphoteric refraction properties.