Alavikia Babak, Ramahi Omar M
Department of Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L3G1, Canada.
J Opt Soc Am A Opt Image Sci Vis. 2011 Jun 1;28(6):1022-31. doi: 10.1364/JOSAA.28.001022.
This work presents a hybrid finite-element-boundary integral algorithm to solve the problem of scattering from a finite and infinite array of two-dimensional cavities engraved in a perfectly electric conducting screen covered with a stratified dielectric layer. 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 the grounded dielectric slab Green's function in the spatial domain is applied at the opening of the cavities as a boundary constraint to truncate the solution region. Placing the truncation boundary at the opening of the cavities and inside the dielectric layer results in a highly efficient solution in terms of computational resources, which makes the algorithm well suited for the optimization problems involving scattering from grating surfaces. The near fields are generated for an 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分层介质层的理想导电屏幕上的有限和无限二维腔阵列的散射问题。求解区域分为包含腔体的内部区域和腔体外部区域。有限元公式仅应用于内部区域内部，以导出与未知场值相关的线性方程组。采用双边界公式，在腔体开口处应用在空间域中采用接地介质平板格林函数的表面积分方程作为边界约束，以截断求解区域。将截断边界置于腔体开口处和介质层内部，在计算资源方面可得到高效的解，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阵列生成近场。
