Iterative solution of the scattering by an arbitrary configuration of conducting or dielectric spheres

An analytic solution to the problem of the scattering of a plane electromagnetic wave by an arbitrary configuration of dielectric spheres is presented using an iterative procedure to account for the multiple scattered fields between the spheres. To compute the higher order terms of the scattered fields, the translation addition theorem for the vector spherical wave functions is used to express the field scattered by one sphere in terms of the spherical co-ordinates of the other spheres to impose the boundary conditions. Coefficients of the various order scattered fields are obtained in matrix form. Numerical results for the normalised backscattering and bistatic cross-section patterns are presented for one- and two-dimensional arrays, and these show that scattered fields up to the fourth order are needed in the special case of contacting conducting linear arrays of spheres to achieve results in excellent agreement with the available data published in the literature