Zouros Grigorios P, Kanoussis Demetrios P, Roumeliotis John A
J Opt Soc Am A Opt Image Sci Vis. 2013 Sep 1;30(9):1832-44. doi: 10.1364/JOSAA.30.001832.
An analytical, closed-form solution to the scattering problem from an infinite lossless or lossy elliptical cylinder coating a circular metal core is treated in this work. The problem is solved by expressing the electromagnetic field in both elliptical and circular wave functions, connected with one another by well-known expansion formulas. The procedure for solving the problem is cumbersome because of the nonexistence of orthogonality relations for Mathieu functions across the dielectric elliptical boundary. The solution obtained, which is free of Mathieu functions, is given in closed form, and it is valid for small values of the eccentricity h of the elliptical cylinder. Analytical expressions of the form S(h)=S(0)[1+g(2)h2+g(4)h4+O(h6] are obtained, permitting an immediate calculation for the scattering cross sections. The proposed method is an alternative one, for small h, to the standard exact numerical solution obtained after the truncation of the system matrices, composed after the satisfaction of the boundary conditions. Both polarizations are considered for normal incidence. The results are validated against the exact solution, and numerical results are given for various values of the parameters.
本文研究了无限长无损或有损椭圆圆柱包覆圆形金属芯散射问题的解析闭式解。通过用椭圆波函数和圆波函数表示电磁场来解决该问题，二者通过著名的展开公式相互联系。由于马蒂厄函数在介质椭圆边界上不存在正交关系，求解该问题的过程较为繁琐。得到的解不含马蒂厄函数，以闭式给出，并且对于椭圆圆柱偏心率(h)的小值有效。得到了形如(S(h)=S(0)[1 + g(2)h^2 + g(4)h^4 + O(h^6)])的解析表达式，可直接计算散射截面。对于小的(h)，所提出的方法是对满足边界条件后截断系统矩阵得到的标准精确数值解的一种替代方法。考虑了垂直入射时的两种极化情况。结果与精确解进行了验证，并给出了不同参数值的数值结果。
