【作者】 杨涛；

【导师】 马红孺； 罗旭东；

【作者基本信息】 上海交通大学 ， 理论物理， 2010， 博士

【摘要】 超颖材料(Metamaterials )是指一类具有天然材料所不具备的超常物理性质的人工复合材料,变换介质理论则是设计具有特定功能的超颖材料器件的有效手段.在本文中,基于变换介质理论和补偿介质理论,我们首先提出电磁“超散射体”的概念,分析了它的散射特性,设计了几类基于电磁“超散射体”的超颖材料器件,包括“穿墙术”与开口的完美隐身斗篷等.接着,研究了二维简化隐声斗篷及其分层实现方案,运用散射理论证实了声超散射体的存在性,讨论了它的分层实现方案.最后,我们研究了一种具有特殊结构的声学超颖材料—由不同晶格常数的二维声子晶体叠加而成的复合声子晶体的声学特性.本文提出的“超散射体”的概念,极大的丰富了超颖材料器件的设计研究,也对电磁波以及声波等经典波的实际应用研究开辟了新的空间.论文主要内容安排如下:第一章简单介绍了超颖材料以及变换介质理论的研究背景,以及当前国内外在该领域的研究进展.第二章对本文所要用到的基础知识做了简单的回顾.介绍了左手材料的由来与负折射率产生的原因;展示了变换介质理论的基本思想,并以波集中器与球形隐身斗篷为例做了具体演示;最后简要介绍了补偿介质理论的相关知识.第三章介绍了我们工作的最主要部分.与隐身斗篷着眼于尽量降低物体的散射截面不同,我们发现了超颖材料器件的另一种不寻常的效应,即一个物体甚至可以看起来比该物体以及所包裹着的器件的几何尺度还要大,并称之为“超散射体”.我们不仅从几何的角度出发给出了形象的说明,同时还用严格的Mie散射理论分析了它的散射特性.接着,我们用这个概念设计出了隐藏之门,或者“穿墙术”:在一面墙的缺口处放置特定的超散射体之后,可以使之看上去跟没有缺口的完整墙一样,尽管在缺口处物体仍然可以自由的出入.此外,我们设计了更具应用前景的开口的完美隐身斗篷.最后,对与“超散射体”相关一些其它研究进展进行了简要介绍.第四章是我们工作的另一部分,主要研究变换介质理论在流体中声学问题的一些应用,包括简化的声波集中器,简化的二维和三维隐声斗篷及其分层实现方案等.此外,通过精确散射理论,我们证实了声超散射体的存在,考察了其声压场的分布及其分层实现方案.发现对于许多超散射体,通常的分层方案会在某些层内引起较大的吸收,从而大大影响其散射性能.我们提出了解决这一问题的特殊分层方案.第五章研究特殊结构的人工声学超颖材料—复合型声子晶体材料的声学特性.我们分析了由多层二维声子晶体(不同的层具有不同的晶格常数,相互间有理相关)叠加复合而成的复杂声子晶体中弹性波的传播行为,发现它们不仅表现出了简单晶体的某些特性,同时还可以实现新的传播性质,包括控制弹性波禁带和低频局域共振特性等.通过对这类复杂声子晶体材料的研究,可以为声学超颖材料的制备提供理论指导.最后,我们对研究内容给出了总结和展望.更多还原

【Abstract】 Metamaterials are artificial composite materials that display properties be-yond those available in naturally occurring materials and give enormous choice ofmaterial parameters for electromagnetic applications. Transformation media con-cept provides an e?cient way to design various functional electromagnetics(EM)devices. In this dissertation, we first propose the concept of“superscatterer”based on the transformation optics and the complementary media theory andmake detail investigation on the scattering behaviors of superscatterer and showa few typical applications, including hidden portal, invisible open cloak, etc.Then, we investigate the acoustics metamaterials. We not only give the layeredmethod to realize the reduced acoustic cloak, but also prove the existence ofacoustic superscatterer by means of rigorous scattering theory. At last, we studya special acoustic metamaterial—phononic crystals(PCs), which is composed ofdi?erent 2D lattice structure in unit slab. The concept of“superscatterer”hasgreatly enriched the study of functional devices for metamaterials and provide avast research area for the practical applications of EM and acoustic waves. Thewhole dissertation is organized as follows.In chapter I, we described the background and reviewed the current researchprogress in this area. The related theories and concepts, including the causeof negative refractive index, transformation optics and complementary mediaconcept were brie?y showed in chapter II.The content of Chapter III is the major part of our work. First, comparedwith the optical devices of invisible cloak, we designed a di?erent EM device called“supscatterer”. When we put a special NIM(negative refractive index material)shell on a PEC(perfect electric conductor), the scattering property of this deviceis equivalent to a“virtual”PEC whose scattering cross section is much bigger than the device itself, and the space between the original PEC and virtual PECseems to be removed. In fact, according to the concept of complementary media,the removed space is filled with a pair of complementary media: vacuum andNIM shell. Similar concept can be extended to the case of non PEC. Then, bymeans of the superscatterer, we proposed a design of hidden portal in which theentrance is concealed from the EM wave detection, however the small objectscould pass in and out freely. This design can be as a physics interpretation ofplatform 934. Third, we proposed a perfect invisible open-cloak. There are no anyinformation communications between the inner and outer domains in traditionalinvisible cloak since the object is closed in the cloak shell. Due to the impedancematched in every interface, the open-cloak with gap in cloak shell not only makethe object perfectly invisible, but also keep contact with the outside world. Atlast, we brie?y described the characteristics of deformation and location shift byextending the concept of supersatterer. As the name of deformation suggests,an object with certain shape coated with suitable NIM shell would transforminto another one with di?erent shape. Another application called displacementshift shows the phenomenon which one sees an object somewhere but in factthe real location is not here. These two visual illusions are the straightforwarddevelopment of the concept of superscatterer.Chapter IV is another part of our work. We discussed some applications oftransformation media in acoustic ?uid. In addition, the acoustic superscattereris designed and the distributions of pressure field are also investigated in detail.For the purpose of fabrication in experiment, we proposed a multi-layered sys-tem method which is composed of concentric layered structure with alternatinghomogeneous isotropic materials. We also found that this design can avoid thelarge pressure inside the device.Next, a relatively independent work about the scattering properties of PCs( phononic crystals ) is shown in chapter V. From the the layered MST(multiplescattering theory) in PCs with simple lattice structure, we developed a methodto investigate the“complex”lattice structure PCs. The new method is inspiredby the surface analysis in LEED ( low energy electron di?raction ) where weexpanded the di?erent 2-D reciprocal lattice vector of layers in a new introducedcommon lattice. With this new method, the propagation characters of elastic waves in the rational related structure PCs, i.e., complex PCs, is calculated andwe found some special behaviors, such as band gap from Bragg scattering andlocal resonant properties at low frequency.The last chapter gave the conclusion and outlook of this dissertation.更多还原