Generalized conditions for the existence of optical axes

In this paper, exact analytical forms of the normal surface in anisotropic media are obtained. Both the permittivity and permeability tensors are supposed to be anisotropic, becoming simultaneously diagonal in the principal system of coordinates. Sufficient conditions for the existence of two, one or no optical axes are established. As a special case, the pseudo-isotropic medium is introduced, for which the birefringence completely vanishes while the crystal is still non-isotropic. Such a medium exhibits a zero-reflection coefficient for any polarization, incidence angle and wavelength, according to some constraints discussed here