Electromagnetic scattering of a plane wave by a radially inhomogeneous sphere in the short wavelength limit

- Obtained the exact equations for electromagnetic scattering of a plane wave by a radially inhomogeneous sphere.
- Derived ray theory for scattering by a radially inhomogeneous sphere.
- Derived Airy theory for scattering by a radially inhomogeneous sphere.
- Obtained the connection between scattering by a radially inhomogeneous sphere and the Pearcey function that describes the longitudinal cusp caustic.

The formulas of ray theory and Airy theory for scattering of an electromagnetic plane wave by a radially inhomogeneous sphere are obtained from the generalization of exact Lorenz-Mie wave scattering theory using the WKB approximation to determine the radial portion of the partial wave scalar radiation potential, carrying out a Debye series expansion of it, approximating the sum over partial waves by an integral over an associated impact parameter, and approximately evaluating the integral using either the method of stationary phase or mapping it into one of the phase integrals that describe optical caustics. Various features of the results are commented on, and the procedure is extended to the merging of two rainbows in a given Debye series channel in the context of the longitudinal cusp caustic.