Hyperbolic umbilic diffraction catastrophe in the scattering from a penetrable spheroid at short wavelengths

Abstract

There has been recent progress in understanding the scattering patterns from spheroids at long wavelengths. At short wavelengths, however, partial wave sums are difficult to evaluate, while geometric optics is not applicable near angular foci where the scattering is enhanced. Consequently, the discovery and classification of angular foci is important to the understanding of short wavelength scattering. A novel focus or “diffraction catastrophe” was recently observed in the light scattered from oblate spheroidal drops of water in air [P. L. Marston and E. H. Trinh, Nature 312, 529–531 (1984)]. Hyperbolic umbilic focal sections were characteristic of drops having D/H≃1.31, where the drop's diameter is D in the equatorial plane and is H along the axis of rotational symmetry. This critical axis ratio was subsequently calculated [J. F. Nye, Nature 312, 531–532 (1984)] to be related to the refractive index μ by (D/H)2 = 3μ2/4μ2 − 1). This expression is in agreement with the observed D/H≃1.31 for water drops having μ = 1.332. In the present research, this expression was confirmed using a general ray‐tracing formalism. Nontrivial diffraction catastrophes should also be present in the farfield acoustical scattering from nonspherical penetrable objects. [Work supported by ONR.]