Resonance component of backscattering by large dielectric spheres

TLDR: In this paper, the Ricatti-Bessel functions were used to obtain expressions for the location and width of each spike in the backscattering from large dielectric spheres, where each spike can be allocated to two patterns, which are described in terms of sequences of two integers and whose repetition period is a function only of the refractive index m.

Abstract: Each spike that is observed in the backscattering from large dielectric spheres arises from just one term in the Mie series. By approximating the Ricatti–Bessel functions involved, one obtains expressions for the location and width of each spike. Every single spike can be allocated to just two patterns, which are described in terms of sequences of two integers and whose repetition period is a function only of the refractive index m. The physical process involved is shown to be a resonance inside the sphere of the electric or magnetic field, in which the appropriate field increases rapidly to a large value at a radial distance r/a ~ 1/m, whereas the other field remains small. As the sphere surface is approached, they combine to form a simple, spherical electromagnetic standing-wave pattern of large amplitude.