Wedge refraction of electromagnetic waves in absorbing crystals

Abstract

Topological features of the self-intersection of wave surfaces near singular optical axes of an absorbing crystal are investigated. Distributions of complex polarization fields in the neighborhood of singular directions are obtained. It is shown that, when the wave normal m circumvents an optical axis, the corresponding rotation of polarization ellipses is characterized by the PoincarÉ index n=1/4. Using the example of an orthorhombic crystal, a wedge refraction of electromagnetic waves on the intersection line of the sheets of the surface of refractive indices is predicted and theoretically investigated. It is shown that the directions of the mean energy fluxes P̄ _± are close to the direction of normals n _± to the refraction surface only in the central region of a wedge, i.e., only in the domain where the polarization is almost linear and the group velocity of waves is well defined. When m moves to singular axes, the ellipticity of the polarization increases at the ends of the edge of the wedge and the orientations of the vectors P̄ _± and n _± gradually diverge, yet remain in the same plane that is orthogonal to the edge. The angle between P̄ ₊ and P ̄ − monotonically decreases, and P̄ ₊ || P̄ ₋ for the propagation along singular axes; in this case, the angle between n ₊ and n ₋ increases, and they have a plane-fan-type orientational singularity along the optical axes. When m is scanned along the edge of the wedge, the unaveraged vectors P _± describe per period the same conical surface that coincides with the refraction cone of a transparent crystal, while the endpoints of the vectors P _± run over elliptic orbits whose shape and slope depend on m. The possibilities of observing a wedge refraction are analyzed.