【作者】 王辉；

【导师】 黄志祥； 吴先良；

【作者基本信息】 安徽大学 ， 电磁场与微波技术， 2014， 博士

【摘要】 目前自然界中材料的电磁特性已经限制了电磁器件性能的进一步提升及其应用,而具有独特电磁特性的新型人工材料越来越受到人们的关注,对其展开研究可以为电磁器件的设计和应用提供更广阔的发展空间。一般新型人工材料具有色散性或者周期性,而色散性、周期性使电磁系统变得更为复杂,如何能够便捷、有效地分析这类复杂电磁系统的电磁特性成为人们迫切需要解决的问题。得益于计算机技术和数值算法的快速发展,相对于实验测量技术,计算电磁学在分析这类复杂电磁系统时的优越性得到进一步体现。基于此,论文对色散材料,典型周期结构建立了相应的数值分析方法,为研究色散材料、周期结构的电磁特性提供了有效的计算工具。具体来说,本文做了如下三点创新工作：1.在辛时域有限差分算法(SFDTD)中引入斜入射平面波源会造成入射场泄漏到散射场区,首先分析了泄漏产生的主要原因,然后建立了SFDTD中高效平面波源的引入方法—分裂平面波FDTD方法(SP-FDTD),并通过数值算例证明了算法的有效性(泄漏误差在-300dB水平)。2.建立了双色散模型SFDTD算法,利用Drude及Lorentz模型拟合媒质电磁参数脚μr和εr,并基于辅助差分方程、辛传播算子、矩阵分裂技术,经过严格而巧妙地公式推导,实现了双色散模型媒质SFDTD的离散描述。为了验证算法的有效性和精确性,首先计算了一维空间双色散平板的透射系数,并与解析解对比,结果较好地吻合；然后仿真了三维空间中具有实际意义的U型开口谐振银环(SRRs),计算了该结构的反射系数、传输系数和吸收系数并与有限元(FEM)方法对比。3.针对有耗色散光子晶体带隙结构的数值计算方法展开研究,建立了两种本征值分析方法。(1)在二维空间中从波动方程出发,根据FEM方法推导出其等效积分弱形式,按照Galerkin方法最终得到一个基于FEM求解的二次本征值方程,求解该二次本征值方程即可得到有耗色散光子晶体带隙结构。首先通过计算介质光子晶体带隙结构验证了方法的有效性,接着研究了损耗对有耗色散光子晶体带隙结构的影响。(2)为避免求解复杂的二次本征值问题,建立了基于频域有限差分(FDFD)方法求解的本征值分析新方法,该方法借助于量子输运问题中的思想,在本征值方程的推导过程中进行了巧妙地变换,将复杂的非线性本征值问题转化为线性本征值问题,并利用FDFD方法直接求解该线性本征值方程,最终得到有耗色散光子晶体结构的相关物理参数。该方法较其它方法最大的特点为概念清晰、计算简便,最终节省了计算时间及所需内存量。利用该方法,计算介质光子晶体的带隙结构,结果与传统FDFD方法吻合较好,从而验证了该方法的有效性。此外,利用该方法计算有耗色散光子晶体的带隙结构,得到了表面等离子波激发的区域。进一步讨论了损耗对其光子带隙及场分布的影响。相关结果对色散有耗光子晶体的研究具有一定的理论指导意义。更多还原

【Abstract】 Presently, the further development and application of the electromagnetic devices are limited by electromagnetic properties of materials in the nature. And people pay more and more attentions to the new manmade materials, which have unique electromagnetic properties and provide a broad space for development of electromagnetic devices. In gen-eral, the new manmade materials are dispersive and/or periodic, which complicate systems even more. How to conveniently and effectively analyze the electromagnetic characteristic of the complex systems is urgent needs to solve. Comparing with experimental measure-ment and benefited from the rapid development of computer technology and numerical methods, the advantage of computational electromagnetism is gradually showing.Specifically, the following three innovations are addressed in this thesis.1. The incident field could leak into the scatter field domain when introducing the oblique plan-wave to symplectic finite-difference time-domain (SFDTD) method. First we find the causes. And then, it presents an efficient plane-wave injection method-splitting plane-wave FDTD method. Finally, numerical simulations show that the method is valid for SFDTD (the leakage error is at the level of-300dB).2. The SFDTD method for the double dispersive materials are well established. Intro-ducing the Drude and Lorentz model for fitting the electromagnetic parameters μγande∈γ, based on the auxiliary differential equation method, the symplectic integrator propaga-tor, and the matrix splitting, the method is constructed with rigorous and artful formula derivation. To verify the efficiency and accuracy, the transmission coefficient of a double dispersive slab in one-dimension is calculated by the method, which agrees well with the analytic solution. Moreover, the silver split resonance ring structure (SRRs) is simulated in three dimensional, and the structure is U-shaped. The reflection, transmission and absorption coefficients of the SRRs are obtained by the method and compared with FEM method.3. Two kinds of eigenvalue methods are presented for calculating the band structure of Photonic Crystals (PCs) with lossy and dispersive materials.(1)The weak form of the equations are derived from wave equations in two dimension by FEM process. According to Galerkin method, quadratic eigenvalue equations are obtained and can be solved by FEM method. The band structure of the lossy and dispersive PCs are obtained by solving the quadratic eigenvalue equation.(2) To avoid solving a quadratic eigenvalue equation, a novel eigenvalue method, based on FDFD method,is proposed to calculated the band structure of PCs with lossy and dispersive materials. Borrowing an idea from quantum transport problem, a standard linear eigenvalue equation rather than a nonlinear eigen-value equation is obtained by a rigorous and artful transformation. And the physical parameters of PCs with lossy and dispersive materials is obtained by solving the linear eigenvalue equation using FDFD method. Comparing with others, the proposed method has greatest features of clear concept and simple calculation, which saves computing time and storage. A dielectric PCs is simulated by the proposed method, and the results agree well with that of traditional FDFD method, which verify the validity of the proposed method. Moreover, the band structure of the PCs with lossy and dispersive materials is calculated by the proposed method, and the surface plasmon frequency is obtained. Fur-ther more, the influence of lossy upon the band structure and the distribution of field is studied. The results provide some theoretical guidance for studying on the PCs with lossy and dispersive materials.更多还原