Simulating of electromagnetic scattering on thin parallel ideally conducting and dielectric cylinders

Using the method of auxiliary sources, we solve the problem of electromagnetic-wave scattering by a structure consisting of a thin dielectric cylinder and a thin perfectly conducting cylinder oriented parallel towards dielectric cylinder. The gist of the method to be used is the following. We introduce an unknown continuously distributed auxiliary electric current and an unknown continuously distributed auxiliary magnetic current on the axis of dielectric cylinder and we introduce only unknown continuously distributed auxiliary electric current on the axis of perfectly conducting cylinder. Now we represent the unknown scattered field {E_e,H_e} in outer medium D_e as a sum of the fields from the introduced auxiliary currents. In order to represent field {E_i,H_i} inside the dielectric cylinder we introduce auxiliary surface S_i enclosing the cylinder. Surface S_i is also a circular cylinder with spherically rounded butt-ends. Then we choose finite set of points M_{n i} on auxiliary surface S_i. At each of these points we place a pair of independent auxiliary electric dipoles with the moments which are chosen in the plane tangent to S_i at point M_{n i} . It is assumed that dipoles placed on S_i, radiate into a homogeneous medium with dielectric and magnetic permeabilities which are equal to permeabilities of the dielectric cylinder. Now we represent unknown field {E_i, H,} inside the dielectric cylinder as the sum of the fields of the introduced auxiliary dipoles. The chosen representations of the fields satisfy Maxwell's equations and radiation conditions. To satisfy boundary conditions on the surfaces of the cylinders, we should properly select the unknown dipole moments and axial currents. Before making that, we introduce the piecewise-constant approximation for the axial currents by dividing the axial lines of dielectric cylinder and perfectly conducting cylinder into small sections (current elements) such that the current can be assumed constant within each section. Then we use the boundary conditions on the surfaces of the cylinders, which are satisfied according to the collocation method, to obtain the system of linear algebraic equations for determination of unknown dipole moments and the current elements. For perfectly conducting cylinder we take into account that the contribution of the azimuthal component of the current on the cylinder surface to the scattered radiation can be neglected due to the fact that the cylinder diameter is small compared with the wavelength of the exciting-field. Based on the method described above, we developed a computer code for calculating the scattered-field components. Using this code, we carried out a series of computational calculations aimed at determination the domain of applicability of the proposed method, comparison of the results calculated with the help of proposed method and known results, and analysis of the scattering cross section of different structures.

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