BOUNDS AND ZEROS IN REFLECTION AND REFRACTION BY UNIAXIAL CRYSTALS

Bounds are given for the possible values of the following quantities: the reflection amplitudes r(ss), r(pp), r(sp), and r(ps); the transmission amplitudes t(so), t(se), t(po), t(pe); the Brewster angle given by the zero of r(pp); and the angle between the extraordinary my and the extraordinary wavevector. These bounds are for arbitrary orientation of the optic axis relative to the reflecting surface and for any angle of incidence. Index matching enhances the effects of anisotropy, particularly in the reflection properties. For example, the bounds on the Brewster angle approach 0-degrees and 90-degrees as the refractive index of the medium of incidence tends to the lower of the ordinary and extraordinary refractive indices. A formula is given for the Brewster angle in the case where the optic axis lies in the plane of incidence. The conditions under which the four transmission amplitudes can be zero are also discussed.