【作者】 燕保荣；

【导师】 胡希伟；

【作者基本信息】 华中科技大学 ， 脉冲功率与等离子体， 2010， 博士

【摘要】 伴随着电磁异性材料(Electromagnetic Metamaterial)的发展,表面等离体子(Surface Plasmons)因其潜在的发展前景而受到人们的广泛关注,特别是电磁异性材料界面表面等离体子的研究更是近年来的热点。本论文从表面等离体子的基本原理及性质出发,详细研究了电磁异性材料界面本征模式对入射电磁波的响应特性,并利用衰减全反射方法分析了入射电磁波与表面等离体子的相互作用,分析了影响反射率变化的物理因素及机制。另外,基于绝对零温时低维固体等离体子的电磁响应特性,本文还讨论了温度对自由电子系统色散关系的影响。本论文的第一部分主要研究电磁异性材料界面表面等离体子的本征模式,及其在入射电磁波作用下的衰减全反射波谱。其主要内容和创新如下：首先,详细分析了电磁异性材料单界面的本征模式,通过计算发现,在这种材料界面上,表面等离体子不仅可以由p-极化(TM modes)的入射波激发,也可以由s-极化(TE modes)的入射波激发,形成表面等离体子激元,且其传播特性随着参数值的改变而不同。除此之外,和金属界面不同,电磁异性材料界面的表面等离体子激元既能在材料的禁带(Stop-band)区域内传播,也能在材料的通带(Pass-band)区域内传播,且可能由一条变为低频和高频的两条分支。接着,利用衰减全反射方法详细的讨论了两种极化模式下入射电磁波与表面等离体子的相互作用,并计算和分析了影响耦合的几个因素,结果证明：(1)当入射电磁波与表面等离体子满足波矢匹配条件时,两者能够相互耦合,且其耦合强度受中间层厚度、电磁异性材料阻尼系数的影响；(2)入射角度和电磁异性材料占空比等参数对其相互耦合的频率和强度大小都有重要的影响。其次,计算了电磁异性材料平板结构上下界面本征模式的相互耦合,包括对称型和非对称型结构。文中指出,随着平板厚度的增加,上下界面表面等离体子本征模式的相互耦合逐渐减弱,直至演化为半无限大情形。同样的,本文也分析了衰减全反射波谱中反射率随中间层厚度和平板厚度的变化关系,结果再次表明中间层厚度不影响耦合频率而影响耦合的强度,但电磁异性材料平板厚度却对两者都有影响。本论文的第二部分主要探讨了自由电子气系统中,非零温度对Lindhard函数和色散关系的影响。从微观理论出发,首先给出在绝对零温时不同维数(三维、二维、一维)下Lindhard函数和色散关系的解析表达式,接着,详细计算了温度对两者的影响,并给出了物理解释。数值计算的结果表明,温度在不同维数下对Lindhard函数和色散关系的影响与费米波矢(或费米温度)的取值有关,而且温度不改变频率对波矢的函数关系。小波矢极限下,室温范围附近,当费米波矢较大时,随着温度的增加,色散关系接近零温时的曲线,但当费米波矢较小时,色散曲线则远离零温值。更多还原

【Abstract】 Along with the development of the electromagnetic metamaterials, the surface plas-mons retrieve much more attention due to their potential applications, especially for the study of the surface plasmons associated with the metamaterials in recent years. Started with the fundamental principles and the properties of the surface plasmons, we investigate the responses of the eigen modes to the incident waves in detail. Furthermore, the interac-tion between the surface plasmon and the incident wave has been analyzed by the attenuated total reflectivity (ATR) technique. We present the physics factor and the mechanism influ-encing the reflectivity. Beside, we discuss the impacts of the temperature on the dispersion relations based on the analysis forms at the absolute zero.In the first part of this thesis, we demonstrate the eigen modes on the interfaces of the electromagnetic metamaterials and calculate the ATR spectra. The contents and the conclusions are presented as follows:Firstly, the eigen modes on the semi-infinite metamaterial are studied. All the results show that the interfaces associated with metamaterial can support the surface plasmon po-laritons, which are excited by p- or s-polarized incident waves (i.e.TM or TE modes). The propagating properties are dependent on the coefficients of the metamaterial. Moreover, the surface plasmon polaritons not only propagate in the frequency regions of the stop-bands, but also propagate in the pass-bands of the metamaterial, which is different from metal. The dispersion relations may become two branches with lower and higher frequency, respec-tively. After that, using the ATR spectra, the coupling between the incident waves and the surface plasmons are detail discussed. Then, several factors contributed to the coupling are calculated and analyzed. When the matching conditions are satisfied, the incident waves couple with the surface plasmons and the coupling strengths are influenced by the thickness of the middle layer or the damping of metamaterial. However, the incident angle and the fractional ratio of the unit cell occupied by the interior of the split ring in metamaterial will affect the coupling frequency and the coupling strengths.Secondly, we calculate the eigen modes on the upper and lower interface of the mate-material slab with finite thickness. The coupling of the eigen modes for the symmetry and antisymmetry case are given successfully. We point that the interactions decrease with the increasing thickness of the slab, which will evolve into the case of the semi-infinite when the thickness is large enough. Similarly, the ATR spectra dependent on the thicknesses of the air and the slab are presented. We conclude that the thickness of the air influences the cou- pling strength without changing the coupling frequency, whereas the slab thickness effects the coupling strength and frequency simultaneously.In the second part of this thesis, based on the free electrons system, we discuss the influence of temperature on the Lindhard function and the dispersion relations. Firstly, at the absolute zero, the analysis forms of Lindhard function are derived for different dimensions (three dimension two dimension、one dimension). Secondly, we calculate the change of Lindhard and the dispersion numerically. At the same time, the explanations are presented. We find that the influence of temperature is correspond to the Fermi wavevector (or the Fermi Temperature), which does not change the relation between frequency and wavevector. At the limit of small wavevector, the dispersion relations near the room temperature are close to the zero one with the increasing temperature when the Fermi wavevector is larger. However, the tendency is contrary when the Fermi wavevector is smaller.更多还原