周期介质中孤立缺陷散射的快速计算
Fast Computation of Scattering by Isolated Defects in Periodic Dielectric Media
摘要：
二维周期性介质中孤立缺陷的电磁散射问题是电动力学中的一个重要研究课题。目前的方法来计算这种散射依赖于玻恩近似及其准解析扩展，或\emph{ab-initio}计算，需要大的域的大小，以减少边界条件的影响。玻恩近似及其扩展的范围是有限的，而从头算方法遭受其高数值成本。在本文中，我介绍了一个混合计划，其中的一个有效的局部电极化率张量的缺陷估计有效地解决反问题。估计张量嵌入到一个S-矩阵公式的基础上的互易定理。通过这种嵌入，缺陷的S矩阵的计算仅需要背景的单位单元中的场解。在实践中，该方案减少了近两个数量级的计算成本，而牺牲很少的精度。该方案表明，统计估计可以从廉价的计算中捕获足够的信息来计算远场的量。我概述的基本理论和算法进行计算的高介电对比度材料，包括金属。我证明了这种方法的能力与纳米电子电路的光学检查的例子，玻恩近似失败，其扩展的现有方法也不适用。
英文摘要：
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 either on the Born approximation and its quasi-analytic extensions, or on \emph{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.
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