Rainbow Scattering by a Coated Sphere

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 alpha12 and the thickness of the coating delta are varied. As the ratio delta/alpha12 increases from 10(-4) to 0.33, we find three classes of rainbow phenomena that cannot occur for a homogeneous-sphere rainbow. For delta/alpha12 less than or similar to 10(-3), the rainbow intensity is an oscillatory function of the coating thickness, for delta/alpha12 almost-equal-to 10(-2), the first-order rainbow breaks into a pair of twin rainbows, and for delta/alpha12 almost-equal-to 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.