Reflection from uniaxial crystals: symmetries, and formulae for near-normal incidence

Abstract

The following symmetries and interrelationships are established: the direct reflection amplitudes rss,rpp are independent of the signs of the direction cosines of the optic axis. For example, they are unchanged by ϕ→π−ϕ or ϕ→−ϕ, where ϕ is the azimuthal angle of the optic axis. The cross-polarization amplitudes rspandrps are both odd in ϕ; they also satisfy the general relations rsp(ϕ)=rps(π+ϕ) and rsp(ϕ)+rps(π−ϕ)=0. All of these symmetries apply equally to absorbing media with complex refractive indices, and thus complex reflection amplitudes. Analytic expressions are given for the amplitudes which characterize the reflection from a uniaxial crystal when the incidence is close to normal. The amplitudes for reflection in which the polarization is unchanged (rssandrpp) have corrections which are second order in the angle of incidence. The cross-reflection amplitudes rspandrps are equal at normal incidence and have corrections (equal and opposite) which are first order in the angle of incidence. Examples for normal incidence and small-angle (6°) and large-angle (60°) incidence reflection are given for non-absorbing calcite and absorbing selenium.