Scattering by an isolated defect embedded in a dielectric medium of two-dimensional periodicity is of interest in many sub-fields of electrodynamics. Present approaches to compute this scattering rely on either the Born approximation and its quasi-analytic extensions or ab initio computation that requires large domain sizes to reduce the effects of boundary conditions. The Born approximation and its extensions are limited in scope, while the ab initio approach suffers from its high numerical cost. In this paper, I introduce a hybrid scheme in which an effective local electric susceptibility tensor of a defect is estimated by solving an inverse problem efficiently. The estimated tensor is embedded into an S-matrix formula based on the reciprocity theorem. With this embedding, the computation of the S-matrix of the defect requires field solutions only in the unit cell of the background. In practice, this scheme reduces the computational cost by almost two orders of magnitude, while sacrificing little in accuracy. The scheme demonstrates that statistical estimation can capture sufficient information from cheap calculations to compute quantities in the far field. I outline the fundamental theory and algorithms to carry out the computations in high dielectric contrast materials, including metals. I demonstrate the capabilities of this approach with examples from optical inspection of nano-electronic circuitry where the Born approximation fails and the existing methods for its extension are also inapplicable.

中文翻译：

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周期性电介质中孤立缺陷散射的快速计算

在电动力学的许多子领域中，嵌入在二维周期性电介质中的孤立缺陷的散射是令人感兴趣的。目前计算这种散射的方法依赖于 Born 近似及其准解析扩展或需要大域尺寸以减少边界条件影响的从头计算。Born 近似及其扩展的范围有限，而ab initio方法受到其高数值成本的影响。在本文中，我介绍了一种混合方案，其中通过有效地求解逆问题来估计缺陷的有效局部电化率张量。估计的张量嵌入到基于互易定理的 S 矩阵公式中。通过这种嵌入，缺陷的 S 矩阵的计算只需要背景单元中的场解。在实践中，该方案将计算成本降低了近两个数量级，同时几乎没有牺牲准确性。该方案表明，统计估计可以从廉价计算中捕获足够的信息来计算远场中的数量。我概述了在高介电对比度材料（包括金属）中进行计算的基本理论和算法。