基于高阶频域有限差分色散光子准晶电磁仿真快速算法研究

Photonic quasicrystals is better than photonic crystals with respect to photonic band gap property, etc. Hence photonic quasicrystals becomes the excellent candidates of the photonic band gap materials, and one of the hot research issues. The research on photonic quasicrystals involves materials science, optical, computational electromagnetics, and so no. The project intends to build fast algorithm based on finite-difference frequency-domain method (FDFD) and studys the electromagnetic properties of the photonic quasicrystals. The key research contents are as follows: (1). The high order difference method is applied to FDFD in the space, and a linear eigenvalue equation of dispersive photonic crystals is derived, which results in less computing time and storage. (2). By studying systematically on the algebraic multi-grid (AMG), a fast algorithm of high order FDFD and its key techniques (high order sub grid technology, high order conformal technology and high order PML) is constructed. (3). The fast algorithm of high order FDFD is applied to simulation of dispersive photonic quasicrystals. By the research, theory of the fast algorithm of high order FDFD is constructed. The method can simulate dispersive photonic quasicrystals and the project provides theoretical and technical support for the engineering application of dispersive photonic quasicrystals.

由于光子准晶在带隙性能等方面优于光子晶体，使其成为光子带隙材料的优秀候选对象，也是目前的热点研究问题之一。对光子准晶的研究涉及材料科学、光学、计算电磁学等学科领域。项目基于频域有限差分(FDFD)法构建快速仿真算法以研究光子准晶的电磁特性，主要研究内容如下：(1)建立空间高阶差分的FDFD算法，对色散光子晶体建立起线性本征值方程，降低计算时间及内存需求；(2)通过对代数多重网格(AMG)法的系统研究，构建高阶FDFD快速算法理论，建立相关关键技术(高阶子网格技术、高阶共形技术、高阶吸收边界条件);(3)高阶FDFD快速算法在色散光子准晶电磁仿真中的应用。通过本项目的研究，将在电磁计算领域建立起适用于计算色散光子准晶电磁特性的高阶FDFD快速算法，为色散光子准晶的工程应用提供理论技术支持。

项目建立了空间高阶差分的FDFD算法，并针对色散有耗光子晶体推导出了线性本征值方程，有效降低了计算时间及内存需求，另外改进了CPML的吸收效果，并对AMG算法进行了深入研究。项目在以下方面有所延伸，基于FDFD针对含石墨烯二维金属结构中的自发辐射以及小周期有机太阳能电池的光电特性进行了研究；通过建立耦合的Maxwell-Hydrodynamic模型，对等离子体超表面非线性太赫兹波进行了仿真分析；对增益媒质和异常光传输现象间的耦合进行了仿真分析；研究了超表面结构产生的宽频太赫兹的电磁特性，分析了时变等离子体的传播特性；研究了三维AA-HIE-FDTD方法、时变磁化等离子体的 LTJEC-FDTD 方法；通过优化人工各向异性参数降低了WCS-FDTD算法的数值色散误差。项目研究成果，对有耗色散周期结构的电磁问题的仿真分析提供理论指导和算法支撑。