Abstract

The following symmetries and interrelationships are established: the direct reflection amplitudes ${r_{\textit{ss}}},{r_{\textit{pp}}}$ are independent of the signs of the direction cosines of the optic axis. For example, they are unchanged by $\phi \to \pi - \phi$ or $\phi \to - \phi$, where $\phi$ is the azimuthal angle of the optic axis. The cross-polarization amplitudes ${r_{\textit{sp}}}{\rm{\;and}}\;{r_{\textit{ps}}}$ are both odd in $\phi$; they also satisfy the general relations ${r_{\textit{sp}}}(\phi) = {r_{\textit{ps}}}({\pi + \phi})$ and ${r_{\textit{sp}}}(\phi) + {r_{\textit{ps}}}({\pi - \phi}) = 0.$ 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 (${r_{\textit{ss}}}{\rm{\;and}}\;{r_{\textit{pp}}}$) have corrections which are second order in the angle of incidence. The cross-reflection amplitudes ${r_{\textit{sp}}}{\rm{\;and}}\;{r_{\textit{ps}}}$ 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.

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