AI 中文总结
针对周期非均匀手性介质的电磁散射问题，研究结合几何正则扰动理论的高阶谱方法，提出HOPE算法并证明相关解析性，实现高效数值模拟。
AI 中文摘要
手性在许多光学现象中发挥重要作用，拥有高效且精确的数值算法来模拟该场景下的解至关重要。本文讨论了一种结合几何正则扰动理论的高阶谱方法，该方法正是这样的算法。我们将横向周期、介电常数/磁导率恒定结构的手性视为与背景值的偏差，并证明平面电磁波散射场关于该形变的解析性，这种解析性不仅针对任意大实际尺寸的手性形变，还在空间变量上具有联合性。我们还展示了用于建立这些结果的高阶包络扰动（HOPE）递推如何实现为一种快速、鲁棒且可靠的数值算法。
英文摘要
Chirality plays an important role in many optical phenomena, and it is crucial to have efficient and accurate numerical algorithms to simulate solutions in this setting. In this paper, we discuss a High-Order Spectral method coupled to geometric regular perturbation theory, which results in just such a method. We view the chirality of the laterally periodic, constant permittivity/permeability structure as deviating from a background value, and demonstrate analyticity of the field scattered by a plane electromagnetic wave with respect to this deformation. This analyticity is not only with respect to chirality deformations of arbitrarily large real size, but also joint in the spatial variables. We also show how the High--Order Perturbation of Envelopes (HOPE) recursions, which we used to establish these results, can be implemented as a rapid, robust, and reliable numerical algorithm.
