Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops

Abstract

The characterization of short-wavelength scattering phenomena has been advanced by the study of diffraction catastrophes1,2. Examples include optical phenomena1–5 and molecular collisions6. The most familiar example of a diffraction catastrophe is the ordinary rainbow7–9. The angular variation of the scattering from a spherical drop locally corresponds to that of a fold-diffraction catastrophe1,2, a result most clearly seen with monochromatic illumination. We have studied the scattering from drops whose shape closely approximated that of an oblate spheroid with the short axis—the symmetry axis—vertical. The drops were illuminated by a horizontally propagating gaussian beam with a wavelength λ = 633 nm. These drops were observed to scatter in the horizontal rainbow region with patterns like those of hyperbolic–umbilic (classification D +4) diffraction catastrophes1,5,6. Visible D+4 diffraction patterns observed previously include light transmitted by frosted glass surfaces10 and by liquid lenses clinging to tilted glass plates1,4.