E_6 diffraction catastrophe of the primary rainbow of oblate water drops: observations with white-light and laser illumination

Abstract

Oblate drops of water illuminated perpendicular to their symmetry axis exhibit catastrophe patterns near the primary-rainbow scattering angle. Previous patterns include the hyperbolic umbilic focal section and separate lips events [see, e.g., H. J. Simpson and P. L. Marston, Appl. Opt. 30, 3468 (1991)]. The present observations concern a much higher-order singularity analyzed by J. F. Nye [Proc. R. Soc. London Ser. A 438, 397 (1992)], the E(6) or symbolic umbilic, in the scattering by levitated drops with monochromatic and collimated white-light illumination. Photographs show the colors produced when the drop is illuminated by white light. The E(6) occurs when the Gaussian curvature of the scattered wave front vanishes in both principal directions, resulting in a high degree of directional focusing. This type of focusing, although only slightly explored, is applicable to the more general problem of scattering from penetrable spheroids.