High-order rainbows of a spherical particle produced by near-grazing incident light.

This study is concerned with the formation of high-order rainbows by near-grazing light incident on a spherical particle. As the number of internal reflections involved increases, the incident Descartes ray strikes the sphere surface increasingly closer to its edge, where the predictions of ray theory and Airy theory become invalid. The deflection angle of the confluence of the stationary points of the phase of the partial wave scattering amplitudes is studied as a function of rainbow order and sphere radius. It is found that as the rainbow order increases, the angular interval over which the upper supernumerary ray stationary point occurs shrinks to zero. In addition, for deflection angles beyond the confluence of the upper supernumerary ray with the tunneling ray, intensity oscillations are due to interference of the field of the lower supernumerary ray with that of the edge region Fock transition, rather than interference between the upper and lower supernumerary rays.