The diffracted field contribution to the scattering from a large dense dielectric sphere

In a previous paper we discussed the geometric optics contribution to the scattering from a large dense dielectric sphere. This is a sequel to this paper and treats the more important diffracted wave contribution. The problem of electromagnetic wave scattering by a lossless dielectric sphere is more involved than that for the perfectly conducting sphere, since waves existing within the sphere can contribute significantly. The geometrical optics method which is relatively straightforward has been widely used for solving the problems of large, with respect to wavelength, dielectric spheres. Approximate expressions based on this method have been derived and have indicated that the geometrical optics fields are the major contributor to the total backscattering. However, a rigorous approach [1] based on the Watson transformation which splits the Mie series into two terms, geometrical optics fields and diffracted fields, shows that the former contributes negligibly to the total backscattering in the range
ka = 5
to 20 for relative refractive index
m = 1.6
. In this paper we confine ourselves to the diffracted fields which give rise to surface waves. It is shown that the dominant contributions come from the surface waves rather than the geometrical optics fields in the particular range where the geometrical optics fields have been assumed to be the dominant contributor. Although a rigorous mathematical analysis associated with the Watson transformation for the scattering problems has been known fundamentally for many years, a complete numerical result based on this transformation has not been available, especially for a dielectric cylinder or sphere. Such results would serve to provide a sound basis for understanding the scattering mechanisms involved and also would serve to check the validity of approximate expressions obtained under a particular assumption. Complete numerical results are included and lead to several interesting conclusions.