Anomalous propagation of electromagnetic waves in anisotropic media with a unique dispersion relation

We investigate the propagation of electromagnetic waves at the interface between an isotropic medium with a unique dispersion relation. We show that the refraction behaviour of E-polarized wave is opposite to that of H-polarized waves, through the dispersion relations for E- and H-polarized waves are the same. It is found that waves exhibit different propagation properties in anisotropic media with different sign combinations of the permittivity and permeability tensors. Some interesting properties of propagation are also found in the special anisotropic media, leading to potential applications.