色散介质FDTD方法及其应用研究

发布时间：2018-04-01 12:08

本文选题：色散介质　切入点：时域有限差分方法　出处：《延安大学》2016年硕士论文

【摘要】：基于自然界中色散介质的普遍存在性,以及色散介质电波传播问题在雷达目标散射、生物医学诊疗、电磁探测及光学元件检测等领域的重要性,本文针对色散介质时域有限差分(Finite Difference Time Domain,FDTD)方法进行了深入研究,并将其应用于色散介质相关电磁问题分析,所做的工作主要包括以下几方面:1、借鉴数字信号处理中信号与系统的时域关系,讨论了色散介质的通用半解析递归卷积(Semi-Analytical Recursive Convolution,SARC)FDTD方法,并推导了基于SARC算法的色散介质UPML吸收边界条件更新公式,最后通过电偶极子源的辐射验证了UPML吸收边界好的吸收效果,通过常见色散介质板反射系数和介质球雷达散射截面的计算验证了SARC-FDTD方法的正确性和通用性。2、将色散介质SARC算法应用到金属光学特性分析。对可见光和红外光波段金属常用的色散介质模型进行总结,并给出极化率函数的统一表达式,针对该表达式推导了适用于金属光学特性分析的通用改进SARC-FDTD方法,最后应用该方法计算了不同色散模型金属铝板反射系数。3、将色散介质SARC算法应用到分层色散介质FDTD分析。从二维Maxwell旋度方程出发,讨论了TE、TM两种模式下斜入射平面波引入的色散介质通用SARC-FDTD修正方法,并推导了基于SARC-FDTD方法的分层色散介质UPML吸收边界条件的更新公式,进而结合理论解研究了通用SARC-FDTD修正方法的斜入射角度适用范围,最后将SARC-FDTD修正方法用于肿瘤组织电磁特性的分析。
[Abstract]:Due to the prevalence of dispersive media in nature, and the importance of dispersive dielectric wave propagation in the fields of radar target scattering, biomedical diagnosis, electromagnetic detection and optical element detection, etc.In this paper, the finite Difference Time FDTD method for dispersive media is studied and applied to the analysis of electromagnetic problems related to dispersive media.The work done mainly includes the following aspects: 1. Referring to the time-domain relationship between the signal and the system in digital signal processing, the general semi-analytical recursive convolution Recursive solution SARCU FDTD method for dispersive media is discussed.The updating formula of UPML absorbing boundary conditions in dispersive media based on SARC algorithm is derived. Finally, the good absorption effect of UPML absorbing boundary is verified by the radiation of electric dipole source.The correctness and generality of the SARC-FDTD method is verified by the calculation of the reflection coefficient of the dispersive dielectric plate and the radar cross section of the dielectric sphere. The dispersion dielectric SARC algorithm is applied to the analysis of the optical properties of metals.In this paper, the dispersion media models of metals in visible and infrared light bands are summarized, and the unified expression of polarizability function is given. A general improved SARC-FDTD method for the analysis of metal optical properties is derived.Finally, the reflection coefficient of aluminum plate with different dispersion models is calculated by using this method, and the dispersion medium SARC algorithm is applied to the FDTD analysis of layered dispersion medium.Based on the two-dimensional Maxwell curl equation, the general SARC-FDTD correction method for dispersive media introduced by oblique incident plane waves in two modes is discussed, and the updating formula of UPML absorbing boundary conditions for layered dispersive media based on SARC-FDTD method is derived.Then the application range of the oblique incidence angle of the general SARC-FDTD correction method is studied with the theoretical solution. Finally, the SARC-FDTD correction method is applied to the analysis of the electromagnetic characteristics of tumor tissue.
【学位授予单位】：延安大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN011

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