The Mathematical Physics of Rainbows and Glories
The mathematical physics of rainbows and glories(2001) [pdf]
This comprehensive review explores the physics and mathematics of rainbows and glories, from geometrical optics and Airy theory to Mie scattering and complex angular momentum (CAM) methods. It covers backward, forward, and rainbow glories, their counterparts in atomic and nuclear scattering, and the role of diffraction catastrophes. The CAM method, based on a modified Watson transform, provides accurate approximations to Mie series. The review highlights how these phenomena connect diverse areas of physics.
The rainbow is one of the most beautiful phenomena in nature. It has inspired art and mythology in all people, and it has been a pleasure and challenge to the mathematical physicists of four centuries.