Uniform asymptotic theory of the secondary rainbow: Regularization of polarization-dependent caustics
Phys. Rev. A 114, 033516 – Published 15 September, 2026
DOI: https://doi.org/10.1103/wjt3-8w4w
Abstract
The secondary rainbow, a classic fold caustic, presents a long-standing challenge in wave theory because standard semiclassical approximations predict unphysical intensity nulls near the Brewster angle. We resolve this Brewster-caustic confluence by developing a uniform asymptotic theory that integrates complex angular momentum theory with the Chester-Friedman-Ursell expansion. By incorporating first-order amplitude gradients, our framework regularizes these polarization-dependent caustics, effectively decoupling the macroscopic caustic envelope from high-frequency Mie diffraction. Validated for relative refractive indexes , this size-parameter-independent computational framework bridges classical meteorological optics with modern singular optics, providing a robust analytical foundation for polarimetric inverse scattering.
