周期性非均匀介质矢量电磁散射的包络高阶微扰（HOPE）方法：解析延拓
A High-Order Perturbation of Envelopes (HOPE) Method for Vector Electromagnetic Scattering by Periodic Inhomogeneous Media: Analytic Continuation
AI总结：
本文提出HOPE方法，将高阶谱算法与正则微扰理论结合，通过解析延拓把三维矢量麦克斯韦方程的小扰动结果推广到大扰动情形，用于周期性非均匀介质的电磁散射模拟。
摘要：
电磁波与三维周期性结构的相互作用出现在许多具有重大科学和工程意义的应用中。这些三维相互作用极其复杂且微妙，因此实践者对其快速、稳健且精确的数值模拟抱有至高兴趣并不令人意外。在众多可能的数值方法中，高阶谱算法通常因其在中等未知量数目下具有卓越的保真度而受到青睐，本文描述了一种属于该类的算法。此外，我们对问题采用微扰方法，将介电常数相对于参考值的偏差视为形变，并进行正则微扰理论分析。本工作总结了这类方法的一条研究路线：该路线始于由亥姆霍兹方程控制的二维问题，随后推进到全三维矢量麦克斯韦方程组中的小扰动情形。我们现在将这些后期结果扩展到构成严格解析延拓的大（实数）扰动。
英文摘要：
Electromagnetic waves interacting with three--dimensional periodic structures occur in many applications of great scientific and engineering interest. These three dimensional interactions are extremely complicated and subtle, so it is unsurprising that practitioners find their rapid, robust, and accurate numerical simulation to be of paramount interest. Among the wide array of possible numerical approaches, the High--Order Spectral algorithms are often preferred due to their surpassing fidelity with a moderate number of unknowns, and here we describe an algorithm that fits into this class. In addition, we take a perturbative approach to the problem which views the deviation of the permittivity from a reference value as the deformation and we conduct a regular perturbation theory. This work concludes a line of research on these methods which began with two-dimensional problems governed by the Helmholtz equation and moved to small perturbations in the fully three-dimensional vector Maxwell equations. We now extend these latter results to large (real) perturbations constituting a rigorous analytic continuation.
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