用加速笛卡尔展开法（ACE）快速分析周期性介质结构的散射
The Rapid Analysis of Scattering from Periodic Dielectric Structures Using Accelerated Cartesian Expansions (ACE)
摘要：
周期性介电结构中的场的分析出现在最近感兴趣的许多应用中，从光子带隙（PBG）结构和等离子体活性纳米结构到超材料。为了实现在这些结构中使用数值方法的字段的准确表示，密集的空间离散化是必需的。这反过来又会影响分析的成本，特别是对于基于积分方程的方法，传统的迭代方法需要O（N^2）次运算，N是空间自由度的数量。本文介绍了一种快速求解双周期介质结构中体积电场积分方程的方法。我们的方法的核心是ACE算法，这是用来评估在O（N）的成本所需的潜力。提供的结果证实了我们的索赔的加速不影响精度，以及我们的方法的应用程序的一些引人注目的光子学应用。
英文摘要：
The analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap (PBG) structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral equation based methods, for which traditional iterative methods require O(N^2) operations, N being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the ACE algorithm, which is used to evaluate the requisite potentials in O(N) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.
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