Alavikia Babak, Ramahi Omar M
Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada.
J Opt Soc Am A Opt Image Sci Vis. 2011 Oct 1;28(10):2192-9. doi: 10.1364/JOSAA.28.002192.
This work presents a hybrid finite element-boundary integral algorithm to solve the problem of scattering from a finite array of two-dimensional cavities engraved in a perfectly electric conducting screen covered with multilayer stratified dielectric coating. The solution region is divided into interior regions containing the cavities and the region exterior to the cavities. The finite element formulation is applied only inside the interior regions to derive a linear system of equations associated with unknown field values. Using a two-boundary formulation, the surface integral equation employing a closed-form multilayer Green's function in the spatial domain is applied at the opening of the cavities as a boundary constraint to truncate the solution region. The closed-form Green's function in the spatial domain for multilayer planar coating is expressed in terms of complex images using the generalized pencil-of-function method in conjunction with a two-level sampling approach. Placing the truncation boundary at the opening of the cavities and inside the dielectric coating results in a highly efficient solution in terms of computational resources, which makes the algorithm well suited for optimization problems involving scattering from grating surfaces. The near fields are generated for array of cavities with different dimensions and inhomogeneous fillings covered with dielectric layers.
本文提出了一种混合有限元-边界积分算法，用于解决刻在覆盖有多层分层介质涂层的理想导电屏幕上的二维有限阵列腔体的散射问题。求解区域被划分为包含腔体的内部区域和腔体外部区域。仅在内部区域内应用有限元公式，以推导与未知场值相关的线性方程组。采用双边界公式，在腔体开口处应用采用空间域中封闭形式多层格林函数的表面积分方程作为边界约束，以截断求解区域。多层平面涂层在空间域中的封闭形式格林函数通过广义函数束方法结合两级采样方法用复镜像表示。将截断边界置于腔体开口处和介质涂层内部，在计算资源方面产生了高效的解决方案，这使得该算法非常适合涉及光栅表面散射的优化问题。针对覆盖有介质层的不同尺寸和非均匀填充物的腔体阵列生成了近场。
