Light propagation characteristics for arbitrary wavevector directions in biaxial media by a coordinate-free approach

The general case of light propagation in lossless anisotropic media occurs in crystals that are biaxial, either naturally so or by induced means (e.g., by electrooptic effect). In these crystals the optical properties, such as the refractive indices, change with propagation direction and are conveniently described by the two-sheeted wavevector surface. Most published work treats light propagation only in the principal planes of the crystal, where the wavevector surface reduces to a circle and an ellipse and the mathematics is simplified. Commonly, however, a biaxial bulk or waveguide device, especially an active device, will be oriented so that the light propagation is not in a principal plane. A complete and concise coordinate-free approach is presented for isolating each sheet, thereby providing a convenient means for calculating the directional optical properties of the two decoupled waves for arbitrary wavevector directions and birefringence levels. The versatility of this approach coupled with available graphics software is demonstrated by displaying numerous cross sections of the wavevector surfaces.