Baczewski Andrew D, Miller Nicholas C, Shanker Balasubramaniam
Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48825, USA.
J Opt Soc Am A Opt Image Sci Vis. 2012 Apr 1;29(4):531-40. doi: 10.1364/JOSAA.29.000531.
The analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap 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(N2) 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 accelerated Cartesian expansion 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.
对周期性介电结构中的场进行分析出现在近期众多备受关注的应用中，从光子带隙结构、等离子体活性纳米结构到超材料。为了使用数值方法准确表示这些结构中的场，需要进行密集的空间离散化。这反过来又会影响分析成本，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)为空间自由度的数量。在本文中，我们介绍一种用于快速求解双周期介电结构分析中使用的体积电场积分方程的方法。我们方法的关键是加速笛卡尔展开算法，它用于以(O(N))的成本评估所需的势。给出的结果证实了我们在不影响准确性的情况下实现加速的说法，以及我们的方法在一些引人注目的光子学应用中的应用。
