Bounds and zeros in reflection and refraction by uniaxial crystals

Abstract

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 ray 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. 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.