基于宽带格林函数理论的电大周期结构电磁散射分析方法及应用

Recent developments in quantum optics, THz and optical communication techniques have posed new challenges in precisely controlling the propagation of electromagnetic (EM) waves. Artificial electromagnetic materials based on EM wave interactions with periodic structures, including photonic crystals, metamaterials, and metasurfaces, have drawn attention due to their exotic and versatile electromagnetic properties, and they have shown potential in acting as the fundamental blocks of electromagnetic and optical devices of the new generation. However, it is especially difficult to perform accurate full-wave simulations using traditional approaches on EM/ optical devices made of periodic structures of large electrical sizes. The difficulty arises in the extremely large number of unknowns involved in discretizing the bounded periodic structure and has become the bottleneck in analyzing and optimizing the device performances. This proposal aims to develop an effective new technology in deriving the full-wave solution of bounded periodic structures over a broad band of frequency of interest. The new approach is based upon a novel theory of the broadband Green’s function, which links the scattering solution of a bounded periodic structure to the band solution of the infinite periodic array. The broadband Green’s function is the wideband point source response inside an infinite array of periodic scatterers. Being expanded in fast converging series of the band modal solutions, it is the connection between the two problems. Such an approach successfully reduces the computational complexity by one order of magnitude: it converts the volumetric discretization over the periodic array into the surface discretization around the prescribing boundary of the array. Thus, it significantly improves the computing efficiency. The new approach will also be applied to analyzing the novel edge states arising from topological photonics and acoustics. Such bosonic topological insulators have shown extremely robust wave guidance capability along their interfaces. The proposed work will provide new tools to analyze periodic structure scattering, improve our understanding to the wave scattering mechanism associated with periodic structures, and facilitate the engineering applications of periodic structures in various EM/ optical devices.

近年来量子光学、太赫兹及光通信技术的发展对有效控制电磁波传播提出了更高要求。光子晶体、超材料与超表面等人工周期结构以其新颖、多元的电磁特性成为构建新一代电磁、光器件的基础组件。对电大尺寸周期结构进行精确电磁散射分析计算量极大，成为制约电磁、光器件性能优化的瓶颈。本课题致力于发展一套新颖的周期结构宽带格林函数理论，并以此为基础建立一套高效的分析电大周期结构在宽频带内电磁响应的精确方法。这套理论建立了无限大周期结构模态解及色散关系与有限大周期结构散射解之间的关联。它以无限大周期结构中点源电磁响应，即格林函数，为关联两者的纽带。它可将有界周期结构散射的计算复杂度降低一个数量级，从而大大提高分析效率。本课题将此理论和方法用于分析拓扑光子和声子晶体的边界态。本研究将提供分析周期结构散射的有效工具，对认清周期结构的散射机理，将新兴周期结构推向更广泛的工程应用具有重要意义。

本项目面向对光子晶体、超材料、超表面等人造工程周期结构进行电磁散射建模的重大需求，深入发展了对周期结构进行本征模式分析和电磁散射建模的宽带格林函数方法和多次散射理论。本项目发展了周期格林函数的空域、波谱域混合宽带表征形式，并将其与积分方程相结合，再分别通过矩量法和波函数展开法对积分方程进行离散，将周期结构的能带求解问题转化为一个小尺度的线性和非线性特征值问题，可同时获得周期结构在较宽频率范围内的能带及模态场分布。本项目成功将这套方法推广至对磁旋光子结构、非均匀声子结构的能带分析中。本项目也通过构建混合场积分方程和采用高精度的Nystrom方法离散积分方程的思路解决了通过积分方程构造本征值问题的伪解难题。另一方面，本项目就着对拓扑电磁结构的边界态进行有效建模深入发展了Foldy-Lax多次散射理论，成功解决了任意散射体的T-矩阵提取和有限大周期结构及有不连续边界周期结构的散射建模难题。本项目探讨了磁旋光子晶体中格林函数的特殊性，并据此结合波导理论从经典电磁学的角度解释了拓扑单边模态的成因。再一方面，本项目就着借助于数据科学手段来加速电磁散射计算进行了创造性的尝试。本项目将电磁散射问题中的入射场与散射体表面场之间的映射转化为一个神经网络，并通过面积分方程来约束这两组场量的关系以有效地对神经网络进行训练。这构造了一种无需训练数据集的物理驱动神经网络，并最终实现了对电磁散射问题解的有效预测。本研究发展的宽带格林函数思路对于分析复杂腔体谐振问题也有应用价值，本研究所发展的复杂系统格林函数概念和Foldy-Lax多次散射理论对解决复杂平台、复杂环境、复杂介质的电磁散射建模也具有指导意义，本研究所尝试的通过人工智能技术来加速电磁计算的思路在更广泛的物理建模技术中也有借鉴意义。

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