辛时域离散伽略金算法及其在典型微纳结构电磁仿真中的应用

Currently, a hot research issues is the application of nanomaterials in field of metamaterials, nanoantenna, and optic devices containing graphene and so on. The development of nanomaterials offers new chances to make breakthroughs in the filed of solid-state physics, materials science, optics, and applied electromagnetics. New types of electromagnetic simulation method are needed for the micro- and nano-structures which contains dispersive and multiscal nanomaterials. Based on symplectic discontinuous Galerkin time domain method, the project mainly studies on the electromagnetic problem of typical micro- and nano-structures. The key research contents are as follows: (1)The constructions of the explicit and implicit symplectic discontinuous Galerkin time domain methods, and the research on its stability and numerical dispersion. (2)Research on some techniques of symplectic discontinuous Galerkin time domain method, which involves the introduction of excitation sources, implementation of boundary condition (connection boundary conditions, absorbing boundary condition, periodic boundary conditions), post-processing techniques (S-parameters extraction, the calculation of extinction, scattering, and absorption cross-section) and so on. (3)The theory study on the construction of symplectic discontinuous Galerkin time domain method for dispersive materials, and the electromagnetic simulation of typical micro- and nano-structures. Our research provides theory basis and technical support for the design of new nanodevices.

目前纳米材料在新型人工电磁超材料、纳米天线及含石墨烯结构的光学器件等中的应用成为热点研究问题，纳米材料的发展也为固体物理、材料科学、光学和应用电磁学等领域取得突破提供了契机。而由纳米材料所构成的微纳结构涉及色散、多尺度问题的电磁仿真，需要发展与之相适应的新型电磁仿真技术。项目基于辛时域离散伽略金算法研究典型微纳结构的电磁计算问题，具体研究内容如下：(1)显式、隐式辛时域离散伽略金算法的构建及其稳定度与数值色散特性研究；(2) 辛时域离散伽略金算法相关技术处理，主要涉及到各类激励波源的引入、边界条件的构造(连接边界条件、吸收边界条件、周期边界条件)及相关后处理技术(散射参数的提取，消光截面、散射截面、吸收截面的计算)等；(3)色散媒质的辛时域离散伽略金算法的构建与理论研究及其在典型微纳结构电磁仿真中的应用。我们的研究可为新型纳米结构器件的设计提供理论依据与技术支持。

项目构建了DGTD基础算法，在DGTD算法中引入了PML，并将DGTD方法与压缩感知技术相结合，以及将辛算法与DGTD算法相结合。同时项目在以下方面有所延伸，建立了用于模拟电磁场-粒子相互作用的麦克斯韦-薛定谔耦合系统及高阶辛时域有限差分算法的离散框架，研究了有耗色散光子晶体的带隙结构、非线性介质混合表面等离子波导，建立了三维人工各向异性弱条件稳定的时域有限差分方法、三维AA-HIE-FDTD方法，并对增益媒质和异常光传输现象间的耦合以及新型亚网格技术进行了深入研究。项目研究成果对新型纳米结构器件的设计提供理论依据和技术支持。