Abstract

A self-sufficient algorithm is proposed for solution of a 2D problem of plane electromagnetic wave scattering by a homogeneous magneto-dielectric cylinder of arbitrary cross section. The algorithm is based on a system of surface integral equations for a combination of auxiliary surface electric and magnetic currents, approximation of the original contour of the cross section by a polygon, and a constant approximation of the auxiliary currents on each side of the polygon. The auxiliary currents are determined as a result of solution of a system of linear algebraic equations obtained from the boundary conditions for the fields in the collocation points located in the middle of each side of the polygon. The self-sufficiency of the algorithm is provided by verification of fulfillment of one more system of integral equations written on the basis of the theorem of equivalence for tangential components of the fields on the surface of the cylinder calculated with use of the auxiliary currents determined above. Effectiveness of the algorithm is demonstrated by means of its application for solution of the problem of wave scattering on focusing magneto-dielectric lenses including the lenses made of material with negative index of refraction.

中文翻译：

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磁介质柱电磁散射问题的曲面积分方程法自足算法

摘要

提出了一种自给自足的算法来解决任意横截面的均匀磁电介质圆柱体平面电磁波散射的二维问题。该算法基于辅助表面电流和磁流组合的表面积分方程组、多边形对横截面原始轮廓的近似以及多边形每条边上的辅助电流的恒定近似。辅助电流被确定为线性代数方程组的解的结果，该线性代数方程组是从位于多边形每条边的中间的配置点中的场的边界条件获得的。该算法的自足性是通过验证另一组积分方程的满足来提供的，该积分方程组是根据使用上面确定的辅助电流计算的圆柱体表面上的场的切向分量的等价定理编写的。通过将该算法应用于解决聚焦磁电介质透镜（包括由负折射率材料制成的透镜）的波散射问题，证明了该算法的有效性。