Zhang Xiujuan, Wu Ying
Division of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia.
Sci Rep. 2015 Jan 20;5:7892. doi: 10.1038/srep07892.
Materials with anisotropic material parameters can be utilized to fabricate many fascinating devices, such as hyperlenses, metasolids, and one-way waveguides. In this study, we analyze the effects of geometric anisotropy on a two-dimensional metamaterial composed of a rectangular array of elliptic cylinders and derive an effective medium theory for such a metamaterial. We find that it is possible to obtain a closed-form analytical solution for the anisotropic effective medium parameters, provided the aspect ratio of the lattice and the eccentricity of the elliptic cylinder satisfy certain conditions. The derived effective medium theory not only recovers the well-known Maxwell-Garnett results in the quasi-static regime, but is also valid beyond the long-wavelength limit, where the wavelength in the host medium is comparable to the size of the lattice so that previous anisotropic effective medium theories fail. Such an advance greatly broadens the applicable realm of the effective medium theory and introduces many possibilities in the design of structures with desired anisotropic material characteristics. A real sample of a recently theoretically proposed anisotropic medium, with a near-zero index to control the flux, is achieved using the derived effective medium theory, and control of the electromagnetic waves in the sample is clearly demonstrated.
具有各向异性材料参数的材料可用于制造许多引人入胜的器件，如超透镜、超固体和单向波导。在本研究中，我们分析了几何各向异性对由椭圆形圆柱矩形阵列组成的二维超材料的影响，并推导了这种超材料的有效介质理论。我们发现，只要晶格的纵横比和椭圆形圆柱的偏心率满足一定条件，就有可能获得各向异性有效介质参数的闭式解析解。推导得到的有效介质理论不仅在准静态区域恢复了著名的麦克斯韦-加尼特结果，而且在长波长极限之外也有效，在该极限下，主体介质中的波长与晶格尺寸相当，使得先前的各向异性有效介质理论失效。这一进展极大地拓宽了有效介质理论的适用范围，并在设计具有所需各向异性材料特性的结构方面引入了许多可能性。利用推导得到的有效介质理论实现了最近理论上提出的具有近零折射率以控制通量的各向异性介质的实际样品，并清楚地展示了对样品中电磁波的控制。
