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.
An analytic solution is obtained for the problem of plane electromagnetic-wave scattering by an arbitrary configuration of N dielectric spheres. The multipole expansion method is employed, and the boundary condition is imposed using the translational addition theorem for vector spherical wave functions. A system of simultaneous linear equations is given in matrix form for the scattering coefficients. An approximate solution, which has been developed and employed by the authors for the scattering by N conducting spheres, is extended to the dielectric spheres case. Plots for the normalized backscattering, bistatic, and forward-scattering cross sections are presented over wide ranges of permittivity, size, and electrical separations between the neighbouring spheres. The results show a reduction in the normalized backscattering and bistatic cross sections for certain choices of permittivity relative to conducting arrays of spheres of the same dimensions and separations.
An exact analytic solution is presented, by using the method of separation of variables, to the problem of electromagnetic wave scattering by an optically active (chiral) spheroid. Fields outside as well as inside the spheroid are expanded in terms of vector spheroidal eigenfunctions, and a set of simultaneous linear equations is obtained by imposing boundary conditions on the surface of the spheroid. Solution of these equations results in the unknown coefficients in the series expansions of the associated fields. The behavior of the scattered fields is illustrated by plots of scattering cross sections for both prolate and oblate spheroids of different sizes and materials in the resonance region.
Given volume distributions of stationary or quasistationary electric current are replaced by equivalent distributions of fictitious magnetization and, eventually, of surface current, on the basis of the Ampèrian model for magnetized media. The fictitious magnetization is subsequently replaced by the equivalent distribution of fictitious magnetic charge. Consequently, the magnetic field due to given volume currents is determined from that produced by the corresponding charges and surface currents. This modeling method is also presented for generalized distributions of current. A scalar potential is introduced to describe the field in the models constructed. This scalar potential is a single-valued function of position when the current distribution is modeled by using a fictitious magnetization and only an equivalent charge distribution within the region considered. The modeling procedure is flexible and the models proposed yield an easier physical interpretation and a substantially reduced amount of computation with respect to vector or combined vector and scalar potential methods used so far. A few illustrative examples are given. This paper relates to stationary or quasistationary magnetic fields, but the modeling technique and the scalar potential presented are applicable to problems relative to any physical fields governed by the same equations.
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