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 a₁₂ and the thickness of the coating δ are varied. As the ratio δ/a₁₂ increases from 10⁻⁴ to 0.33, we find three classes of rainbow phenomena that cannot occur for a homogeneous-sphere rainbow. For δ/a₁₂ ≲ 10⁻³, the rainbow intensity is an oscillatory function of the coating thickness, for δ/a₁₂ ≈ 10⁻², the first-order rainbow breaks into a pair of twin rainbows, and for δ/a₁₂ ≈ 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.

© 1994 Optical Society of America

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