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
Original Manuscript: September 8, 1993
Revised Manuscript: November 12, 1993
Published: July 20, 1994
James A. Lock, J. Michael Jamison, and Chih-Yang Lin, "Rainbow scattering by a coated sphere," Appl. Opt. 33, 4677-4690 (1994)