Supernumerary Spacing of Rainbows Produced by an Elliptical-Cross-Section Cylinder. I. Theory

A sequence of rainbows is produced in light scattering by a particle of high symmetry in the short-wavelength Limit, and a supernumerary interference pattern occurs to one side of each rainbow. Using both a ray-tracing procedure and the Debye-series decomposition of first-order perturbation wave theory, I examine the spacing of the supernumerary maxima and minima as a function of the cylinder rotation angle when an elliptical-cross-section cylinder is normally illuminated by a plane wave. I find that the supernumerary spacing depends sensitively on the cylinder-cross-section shape, and the spacing varies sinusoidally as a function of the cylinder rotation angle for small cylinder ellipticity. I also find that relatively large uncertainties in the supernumerary spacing affect the rainbow angle only minimally. (C) 2000 Optical Society of America OCIS codes: 290.0290, 290.4020, 080.1510.