Unusual 1/r-dependent radiation intensity in any biaxial crystal

Lighthill’s prediction of an unusual 1/r-dependent radiation intensity from a small monochromatic source is found to exist in any homogeneous and lossless biaxial crystal along the two optical ray axes, where r is the radial distance from the source. This is a consequence of the special shape of the wave-vector surface on which there is, around each singular point of self-intersection (or “dimple”), a circular locus of points all having the same surface normal direction and thus sharing a common tangent plane. A heuristic derivation of the result is given and a simple optical experiment is proposed to detect such an unusual distance dependence.