Ray and wave tracing in uniaxial crystals perturbed by an external field.

Uniaxial crystals may become biaxial in an external field. The general and exact law of double refraction on the boundary of an isotropic medium and a biaxial crystal lead to an unwieldy set of involved formulas. Rotations of the principal axes of the optical permittivity tensor in the crystal subjected to the field lead to further difficulties in ray and wave tracing. Therefore, we propose a calculus in which the directions of refracted rays and waves in an unperturbed uniaxial crystal are taken as the first approximation, and then small perturbations of rays and waves due to the applied field are considered. Our approach is based on Huygens's principle and a generalized form of Fresnel's ray equation. As an example, the method is applied to the electro-optic modulation of ray and wave directions in a BaTiO(3) crystal of 4mm symmetry.