Multiple scattering of EM waves by spheres part I--Multipole expansion and ray-optical solutions

Author(s): J. Bruning ; Yuen Lo
Sponsor(s): IEEE Antennas and Propagation Society
Publisher: IEEE - Institute of Electrical and Electronics Engineers, Inc.
Publication Date: 1 May 1971
Volume: 19
Page(s): 378 - 390
ISSN (Paper): 0018-926X
ISSN (Online): 1558-2221
DOI: 10.1109/TAP.1971.1139944



Solution to the multiple scattering of electromagnetic (EM) waves by two arbitrary spheres has been pursued first by the multipole expansion method. Previous attempts at numerical solution have been thwarted by the complexity of the translational addition theorem. A new recursion relation is derived which reduces the computation effort by several orders of magnitude so that a quantitative analysis for spheres as large as10\lambdain radius at a spacing as small as two spheres in contact becomes feasible. Simplification and approximation for various cases are also given. With the availability of exact solution, the usefulness of various approximate solutions can be determined quantitatively. For high frequencies, the ray-optical solution is given for two conducting spheres. In addition to the geometric and creeping wave rays pertaining to each sphere alone, there are rays that undergo multiple reflections, multiple creeps, and combinations of both, called the hybrid rays. Numerical results show that the ray-optical solution can be accurate for spheres as small as\lambda/4in radius is some cases. Despite some shortcomings, this approach provides much physical insight into the multiple scattering phenomena.