Rainbow scattering by a coated sphere

Abstract

We examine the behavior of the first-order rainbow for a coated sphere by using both ray theory and Aden-Kerker wave theory as the radius of the core a 1 2 and the thickness of the coating b are varied. As the ratio b/a 12 increases from 10-4 to 0.33, we find three classes of rainbow phenomena that cannot occur for a homogeneous-sphere rainbow. For b/a12 < 10-3, the rainbow intensity is an oscillatory function of the coating thickness, for 8/a 1 2 10-2, the first-order rainbow breaks into a pair of twin rainbows, and for 8/a,2 0.33, various rainbow-extinction transitions occur. Each of these effects is analyzed, and their physical interpretations are given. A Debye series decomposition of coated-sphere partial-wave scattering amplitudes is also performed and aids in the analysis.

Debye series analysis of scattering of a plane wave by a spherical Bragg grating

“…As was found in Ref. 22, the first-order rainbow for a coated sphere breaks into two components. The stronger ␤ component in Fig.…”

“…The connection between wave scattering and ray scattering in the large sphere or short-wavelength limit is made through the Debye series expansion in which each partial-wave scattering amplitude is written as a sum of diffraction of the partial wave, its external reflection from the sphere surface, and transmission through the sphere following all numbers of internal reflections from the surface. The Debye series was initially formulated for scattering of a normally incident plane wave by a cylinder 17 and has been subsequently extended to scattering by a sphere, 18 -20 the internal fields, 21 scattering by a coated sphere, 22 and scattering of a plane wave diagonally incident on a cylinder. 23 Perhaps the most important use of the Debye series has been to obtain a physical understanding of the various wave-scattering processes that interleaf to form the scattered intensity.…”

Debye-series analysis of the first-order rainbow produced in scattering of a diagonally incident plane wave by a circular cylinder

“…It has been derived for electromagnetic scattering by a cylinder at normal incidence, 16 for scattering by a homogeneous sphere, 8,17,18 and for scattering by a coated sphere. [19][20][21] Since scattering for those three geometries is polarization preserving, the Debye series simplifies substantially. For scattering by a cylinder at normal incidence or by a sphere, there are eight partial-wave Fresnel coefficients that couple together in two groups of 4 (i.e., the TE coefficients couple together, and the TM coefficients couple together) to form the partial-wave scattering and interior amplitudes.…”

Scattering of an electromagnetic plane wave by a Luneburg lens II Wave theory

“…(26), the well is very shallow, and its center is approximately halfway between the two classical turning points of Eq. (27). When the partial wave is at the low end of the edge region, X is slightly greater than 1 in Eq.…”