Scattering of a plane electromagnetic wave by a generalized Luneburg sphere-Part 1: Ray scattering

•Computed scattering by a radially-inhomogeneous sphere in ray theory.•Determined the shape of the ray paths inside the sphere.•Found multiple rainbows per Debye series channel.•Found rainbows of radially-inhomogeneous bubbles.

We calculated scattering of an electromagnetic plane wave by both a radially-inhomogeneous particle and bubble, the square of whose refractive index profile is parabolic as a function of radius. Depending on the value of the two adjustable parameters of the parabola, the particle or bubble can have either a refractive index discontinuity at its surface, or the refractive index can smoothly merge into that of the exterior medium. Scattering was analyzed in ray theory, and various novel features of the scattering, including the details of the curved ray paths, transmission rainbows, and near-critical-angle scattering were apparent and were contrasted with their behavior for scattering by a homogeneous sphere.