摘要
新型电磁结构和材料是当前研究的热点,在微波、毫米波领域具有巨大的应用潜力。但是,新型电磁材料的理论和应用起步不久,在理论研究、数值仿真、实验测试和实际应用等方面还有待深入。有鉴于此,本文首先通过对新型电磁材料所具有特殊性质的分析,抓住Fermat原理,电磁能量和最小作用量原理等电动力学中的基本概念,推广和解决了新型电磁结构相关研究中的一些关键性理论问题。随后,本文并没有仅仅停留于单纯的理论分析,在后面的章节中对几种典型新型材料中的一些新特性进行了探索研究。以具有代表性的矩形栅格PBG周期阵列结构为研究对象,研究了线性和非线性Kerr型掺杂两大类媒质情况下主要的一些特性,对光子晶体的带隙特性、相干孤子特性以及耗散作用的影响进行了深入分析,并给出了计算实例。根据多种新型电磁材料和结构所具有的独特电磁性质的不同特点,对其中相应的结构模型分别进行了全波仿真和实验分析。本文的主要工作体现在以下几个方面：
深入研究了左手媒质形成负折射的机理,提出了广义折射率的表示形式,从而对Fermat原理进行了推广。对Fermat原理与最小作用量原理的进行了对比分析,并通过路径积分运算,使两者在宏观层面上得到了一定的统一。进而揭示了相位在作用量原理中的重要作用。
对新型电磁材料中有关电磁能量的一些问题进行了论述。在Englman等人工作的基础上,发展了电磁作用量以及作用量原理的形式。在引入分数微分的基础上,给出耗散电磁媒质中的Lagrange量,并通过推导相应的Euler-Lagrange方程获得了时域形式的Lorentz媒质模型。重新考虑了Hamilton量,系统时间变换不变量和能量间的关系,由此得到了与近期文献工作中相符合的电磁能量形式。讨论了基于Lorentz媒质模型的色散媒质中的Foster定理。以路模型的形式对电磁能量的进行了分析,在理论上建立了Tretyakov和Boardman各自所定义的电磁能量形式之间的联系。
分别研究了线性媒质和非线性媒质光子晶体周期结构。应用平面波展开法分析了线性媒质光子晶体的带隙结构。通过提出的作用量形式,采用变分方法分析了二维矩形栅格光子晶体X点孤子的相干耦合特性。考虑到耗散效应的普遍性,通过有耗作用量原理对于相应模型中耗散作用对孤子特性的影响进行了研究。
对具有代表性的几种新型电磁媒质进行了仿真和实验研究,从而对新型材料所表现出的一些新现象进行了探索。对平板波导中加载不同分布组合的左、右手媒质块进行了等效媒质模拟,对平面微带复合传输阵列及其单元结构所具有的表面波和空间波特性进行了电路级和全波仿真分析,对在Matematerials阵列中凋落波特性进行了较为全面的比较分析。在EBG高阻表面加载实验测试方面,结合测试对象的具体情况对波导测量法进行了改进,对单向加载电阻元件的Mushroom型EBG结构进行了制作,并以此对样品的反射特性进行了测试,取得了初步的结果。
The attention of electromagnetic researchers is recently focused on new-type electromagnetic structures and materials, which have huge applications in microwave and millimeter wave fields. However, the study on the theory and application of new-type electromagnetic structures and materials is at the initial stage. Lots of efforts should be put into the research on its related theory, numerical simulation, experimental measurement and actual applications. Therefore, the analysis on the special properties of Left-Handed Materials and new-type electromagnetic medium is applied at first. Then, on the basis of basic concepts such as Fermat's principle, electromagnetic energy and least action principle and so on in electrodynamics, generalizing and solving some key theoretical problem in the researches related to new electromagnetic medium. In addition to the theoretical study, several novel properties of some representative electromagnetic or optical structures are studied in the following chapters. Taking typical photonic band-gap structure of square lattice as research model, certain main properties, such as band-gap, coherent solitons and dissipation in photonic critical with linear and non-linear Kerr type media, are investigated respectively. And the numerical example is also given out. Based on the consideration of the properties in several new electromagnetic materials and structures, some structure models are analyzed in full-wave simulation and experiment. The author's major contributions are listed as follows:
After employing the further investigation on negative refraction in Left-handed, the generalized expression of refractive index is proposed and Fermat's principle is also generalized. Through comparing Fermat's principle and least action principle and using path integrals, the two principles are united in macroscopic level. The importance of phase in action principle is pointed out.
The electromagnetic energy in new electromagnetic medium is investigated. Different expression of electromagnetic energy is proposed based on the early works of Englman et al. Lagrangian in dissipative electromagnetic material is proposed on the basis of the introduction of fractional derivative. Lorentz medium model is deduced from Euler-Lagrange equation related. Hamiltonian, invariance of time and energy are investigated, and electromagnetic energy obtained fits early work reported in literature. Foster's theory based on Lorentz model is investigated in dispersive medium. Through using circuit model, electromagnetic energy expressions defined by Tretyakov and Boardman is related theoretically.
Photonic band-gap (PBG) structure in linear and non-linear media is study respectively. Band-gap property of linear photonic crystal is analysis by using plane wave method. Defining action and applying variational method, coherent effects of X-point solitons are investigated. Considering extensive existence of dissipation, the effect of dissipation on solitons is also investigation through introducing dissipative least action principle.
In order to explore novel performance, numerical simulation and experiment is employed for several typical new-type electromagnetic. Left handed materials blocks lying in Planar waveguide with different spatial distribution is simulated. Surface and spatial wave in planar microstrip composite periodic structure and it unit are analyzed in circuit and full wave levels. Evanescent wave performance is study in different type matematerials. Applying improved waveguide measurement, Mushroom-like electromagnetic band-gap (EBG) structure loaded resisters in single direction is produced and its reflection is measured. Preliminary result has been obtained.
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