三维周期结构中电磁散射问题的数值方法研究

With the rapid development of the nano-electronic engineering, many three dimensional nano-components are developed for the design of nano-electronic devices, for instance, the nano-spheres and nano-triangles, etc. For more and more complicated nano-device with periodic structure models, the fast and accurate numerical algorithms for the calculation of the electromagnetic scattered fields are in great need. In this research project, we try our efforts on conducting the efficient algorithms for electromagnetic scattering problems from general three dimensional periodic structures. First, we consider general three dimensional homogeneous medium unit cell in the periodic structure, and then construct the mapping operator by the surface integral equation method. Second, for the layered medium periodic structures with metallic and dielectric material, we construct the integral equation operator marching method to manipulate the propagation of electromagnetic waves in the layered medium structures. Then, from the three dimensional integral equation operator marching method, we construct the high accurate numerical discretization scheme. From the calculation of unknowns of surface electric currents and magnetic currents, we simulate the propagation of electromagnetic wave in the layered medium. On invoking the integral equation operator marching method, we efficiently obtain the electromagnetic fields results from the large scale three dimensional nano-periodic electronic devices with millions of discretization unknowns, and thus provide an efficient algorithm for the design and optimization of the devices. Meanwhile, we explain and analyze the scattered fields from the periodic structure with the novelty experimental physical phenomenon, for instance, the surface plasmonic phenomenon from metallic material. Also, the applicant has studied and done research at department of mathematics from bachelor to PhD period.

随着纳米光电工业的飞速发展，众多三维纳米元件被用于设计光电器件，如纳米球和纳米三角形等。面对日益复杂的光电器件中出现的周期元件模型，快速和高精度的数值方法用来模拟散射场的需求急剧提高。本项目致力于三维周期结构材料电磁散射问题的高性能算法研究。首先，考虑周期结构中出现的三维任意齐次介质单元，基于表面积分方程方法建立映射算子。其次，针对周期分层结构金属和绝缘体材料，建立三维表面积分方程映射算子推进算法。进而，建立三维积分方程映射算子推进算法的高精度数值离散格式。通过计算分片齐次区域的表面电流和磁流未知量，数值模拟电磁场在分层介质中的传播。基于积分方程的映射算子推进方法，高精度计算具有百万离散未知量的三维周期光电器件散射场，从而为光电器件设计提供高性能算法。同时，解释和分析周期材料的一些新颖实验物理现象，如金属材料的表面等离子激元现象。另外，申请人自本科至博士期间，均在数学系从事学习和研究工作。

随着纳米光电工业的飞速发展，众多三维纳米元件被用于设计光电器件，如纳米球和纳米三角形等。面对日益复杂的光电器件中出现的周期元件模型，快速和高精度的数值方法用来模拟散射场的需求急剧提高。本项目致力于三维周期结构材料电磁散射问题的高性能算法研究。首先，考虑周期结构中出现的三维任意齐次介质单元，基于表面积分方程方法建立映射算子。其次，针对周期分层结构金属和绝缘体材料，建立三维表面积分方程映射算子推进算法。进而，建立三维积分方程映射算子推进算法的高精度数值离散格式。通过计算分片齐次区域的表面电流和磁流未知量，数值模拟电磁场在分层介质中的传播。基于积分方程的映射算子推进方法，高精度计算具有百万离散未知量的三维周期光电器件散射场，从而为光电器件设计提供高性能算法。同时，解释和分析周期材料的一些新颖实验物理现象，如金属材料的表面等离子激元现象。另外，申请人自本科至博士期间，均在数学系从事学习和研究工作。

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