Nonparaxial description of reflection and transmission at the interface between an isotropic medium and a uniaxial crystal

Angular spectra of reflected and transmitted fields, induced by an arbitrary electromagnetic beam passing through the planar interface between a homogeneous medium and a uniaxially anisotropic medium, are derived and related to the incident medium. By using these formulas, we obtain the expressions for paraxial and slightly nonparaxial fields. The reflected paraxial field is related to the incident one by means of Fresnel relations; the transmitted paraxial field is the superposition of an ordinary and an extraordinary beam, multiplied by the Fresnel coefficient. We find that the nonparaxial corrections, owing to the medium discontinuity, are larger than their free-propagation counterparts and that they are very simply related to the paraxial solutions of the incident beam. The case of two homogeneous media with different refractive indices is also discussed. The general expressions obtained are applied to the case of a nonparaxial Gaussian beam.