Light propagation characteristics in biaxial crystals by a simple coordinate-free approach

Abstract

Many crystals are optically biaxial, either naturally or by induced effects (e.g., electrooptic effect). The optical characteristics of these crystals may be conveniently described by the two-sheeted wavevector surface. However, most published work explores light propagation only in a principal plane of the crystal, where the wavevector surface reduces to a circle and an ellipse. Even this situation can be misleading since, in the x-z principal plane, there is a circle intersecting with an ellipse, but for evaluating optical characteristics, there are, in fact, a distinct outer surface and a distinct inner surface to consider. Each sheet of the wavevector surface represents the dispersive nature of a semiaxis length of the crosssectional ellipse of the biaxial index ellipsoid as the direction of propagation changes. Quantifying the propagation properties (phase velocity index, group velocity index, Poynting vector, etc.) for each of the two allowed orthogonally polarized waves requires the mathematical separation of the two sheets. Thus, a more complete and enlightening coordinate-free approach is presented here to calculate the directional propagation characteristics of each allowed polarization for an arbitrary wavevector direction and arbitrary level of birefringence. With this approach, any cross-sectional view of the two-sheeted surface can be directly calculated.