Cherenkov ray cones in crystalline media

Abstract

The rings of light on the photographic plate in Cherenkov emission in crystalline media are shown to come from sections of the Cherenkov ‘ray cones’ rather than the ‘wave-normal cones’. Equations are derived for the ordinary and extraordinary ray cones emitted by a charge moving in an arbitrary direction in a uniaxial crystal. It is shown that, for a range of angles between the direction of motion of the charge and the optic axis, the ray cones intersect one another, whereas the wave-normal cones do not do so. A method is given to obtain sections of the ray cones on the photographic plate from corresponding sections of the wave-normal cones emitted by a charge moving along a principal axis of a biaxial crystal. It is applied to study the Cherenkov analogue of internal conical refraction that occurs for a critical velocity of the charge such that a Cherenkov-wave normal coincides with a binormal of the crystal.