【作者】 吴刚；

【导师】 黄志祥；

【作者基本信息】 安徽大学 ， 电磁场与微波技术， 2019， 硕士

【摘要】 随着计算电磁学的发展,频域有限差分方法(Finite-Difference Finite-Domain Method,FDFD)作为一种传统的频域数值方法备受关注。在所有的电磁场数值方法中,FDFD方法应该是最容易理解的方法。在处理谐振问题、求解单频点问题、处理色散媒质问题、处理周期结构斜入射问题上有很大优势。由于矩阵求解的复杂度,目前普遍研究二维FDFD方法。本文主要进行了基于二维FDFD方法的传输和散射研究。通过简单介绍有限差分法的基本理论来推导出二维FDFD方程的矩阵形式,简单研究了双脊金属矩形波导的模式特性问题来验证有限差分法的可行性。在推导出二维FDFD方程的矩阵形式后,进一步进行了基于二维FDFD方法的传输和散射研究。传输研究主要包括通过二维FDFD方法仿真点源和平面波源的传播情况以及对双层金属线栅宽带偏振器的反射率和透射率的仿真。散射研究主要讨论金属圆柱和金属扇形圆柱在总场/散射场平面波源激励下的空间场强分布情况。论文的主要工作有:1.认真了解了有限差分方法的基础理论,充分调研了FDFD方法的研究现状,阐明了FDFD方法在求解特殊电磁问题下凸显的算法优势。2.为了验证有限差分法的可行性,研究双脊金属矩形波导的模式特性问题,绘制波导主模、一阶高次模、二阶高次模的色散特性曲线。将频域的麦克斯韦方程组和完美匹配层吸收边界条件进行耦合,推导出最终的二维频域有限差分方程矩阵形式。3.基于二维的FDFD方法对点源和平面波源的传播情况进行研究,进一步对金属圆柱和金属扇形圆柱在总场/散射场平面波源激励下的空间场强分布情况进行仿真讨论。4.进一步进行了基于二维FDFD方法的传输研究,设计一种双层金属线栅宽带偏振器。主要研究三种周期光栅(40nm、80nm、160nm)在TM波入射双层金属线栅宽带偏振器传输后的光学反射率和透射率,同时考虑到TM波的垂直入射和斜入射两种情况。更多还原

【Abstract】 With the development of computational electromagnetics,the finite-difference frequency-domain method(FDFD)has been attracting attention as a traditional frequency domain numerical method.The FDFD method should be the easiest to understand method in all electromagnetic field numerical methods.There are great advantages in dealing with resonance problems,solving single-frequency point problems,dealing with dispersive media problems and dealing with oblique incidence problem of periodic structure.Due to the complexity of matrix solving,two-dimensional FDFD method is currently widely studied.In this thesis,the transmission and scattering based on the two-dimensional FDFD method are investigated.Deducing the matrix form of two-dimensional FDFD equation by briefly introducing the basic theory of finite-difference method,the mode characteristics of double-ridged metal rectangular waveguide is simply studied to verify the feasibility of finite-difference method.After deriving the matrix form of the two-dimensional FDFD equation,further research on transmission and scattering based on two-dimensional FDFD method.Transmission studies mainly include simulation of the propagation of point source and plane wave source by two-dimensional FDFD method and simulation of reflectance and transmittance of dual-layer metallic wire grids broadband polarizers.The scattering study mainly discusses the spatial field intensity distribution of metal cylinder and metal sector cylinder excited by the total-field/scattered-field plane wave source.The main work of this paper includes:1 The basic theory of finite-difference method is carefully understood,the research status of FDFD method is fully investigated and the advantages of FDFD method in solving special electromagnetic problems are clarified.2.In order to verify the feasibility of the finite-difference method,the mode characteristics of the double-ridged metal rectangular waveguide is studied,drawing the dispersion characteristic curves of the main mode,the first-order mode and the second-order mode of the waveguide.The Maxwell’s equations in the frequency domain and the perfectly matched layer absorption boundary conditions are coupled to derive the final two-dimensional FDFD equations matrix form.3.Research on the propagation of point source and plane wave source based on two-dimensional FDFD method,furthermore,the spatial field distribution of metal cylinder and metal sector cylinder excited by the total field/scatter field plane wave source are discussed.4.Further research on the transmission based on two-dimensional FDFD method,a dual-layer metallic wire grids broadband polarizers is designed.The optical reflectance and transmittance of three periodic gratings(40nm,80nm,160nm)after TM wave incident on dual-layer metallic wire grids broadband polarizers are mainly studied,considering the normal and oblique incidence of TM wave.更多还原