The Geometric Optics Contribution to the Scattering from a Large Dense Dielectric Sphere

An analysis is presented for calculating the back-scattered fields of an electromagnetic plane wave by lossless dielectric spheres of arbitrary density. This method involves the Watson transformation which serves to split the exact Mie solution, given as an infinite series, into the geometrical optics fields and the diffracted fields. The former comes from the illuminated region of the sphere and may be obtained from the geometrical optics method. The latter comes from the shadow region and consists of two different types of surface waves. One is a “creeping wave” analogous to that of perfectly conducting spheres. The other is a wave which enters the sphere and emerges as a surface wave in the shadow region. This wave is unique to dielectric spheres and is the stronger of the two surface waves. In the widely used geometric optics methods it is assumed that the optics fields are the dominant contributors even though stationary rays which are not in the direction of backscatter must be added in to give a degree of agreement with the exact Mie series results. In this paper we derive the optics fields and show that they differ in some respects from those obtained by the geometric optics method. They are smaller than heretofore assumed and contribute negligibly to the backscatter in this particular range of ka (4–20). Using our rigorous approach we can show the diffracted fields to be the major contributors to the total backscatter. Numerical results for the backscattering cross sections using diffracted and optics fields, and optics fields alone will be presented for relative index of refraction of 1.6. The agreement between our results (diffracted and optics) and exact results from the Mie series is excellent. A subsequent paper will be concerned with the diffracted fields.