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

Abstract

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 coordinates 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.

Hybrid Finite-Difference/Mode-Matching Method for Analysis of Scattering From Arbitrary Configuration of Rotationally-Symmetrical Posts

“…From Equations (17) and (18) it can be found that only E r is used to found other probes of fields in area of discretization. In the case of m = 0 the value of E r at axis AA can be found from Ampere's law [23] and takes the following form:…”

“…In order to consider the arbitrary set of objects in this paper we propose the hybrid approach which is based on the combination of finite-difference frequencydomain/mode matching (FDFD/MM) technique with the analytical iterative scattering procedure (ISP) [17]. In our approach each scatterer or set of scatterers is treated as an effective sphere which encloses investigated elements and is represented by transmission matrix defining the relation between the incident and scattered fields.…”

Light Trapping above the Light Cone in One-Dimensional Arrays of Dielectric Spheres

“…The overwhelming majority of papers since the pioneering papers by Ohtaka and his coauthors [2][3][4] considered the periodical two-and three-dimensional arrays [5][6][7][8]. Surprisingly, less interest has been payed to scattering by a linear array of dielectric nanoparticles mostly restricted to aggregates of a finite number of spheres [9][10][11]. Guiding of electromagnetic waves by a linear array of dielectric spheres below the diffraction limit attracted more attention.…”

Electromagnetic Scattering From Parallel Chiral Cylinders of Circular Cross-Sections Using an Iterative Procedure

“…After calculating the initial scattered fields, interaction between the cylinders is to be considered assuming that this interaction is due to mutual scattering among the cylinders. The initial first order-scattered fields from M −1 cylinders are considered as the incident field on the remaining cylinder inducing the second order scattered fields from all M − 1 cylinders after applying the appropriate boundary conditions on the surface of each cylinder is applied in the first order of interaction [6][7][8]. This iterative scattering procedure between the cylinders yields, after infinite, theoretically, number of interactions, the total scattered field that is the summation of all interactions.…”