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arXiv 0711.0507physics.opticsmath-phmath.MP
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高阶电磁隐身衣的严格分析

A rigorous analysis of high order electromagnetic invisibility cloaks

Ricardo Weder

摘要:

Pendry等人最近提出的基于变换方法的隐形斗篷目前引起了很大的兴趣。他们用一阶变换得到了结果。在最近的论文中,Hendi等人和Cai等人考虑了具有高阶变换的隐形斗篷。本文研究了一般各向异性介质经高阶变换后得到的变换介质中的高阶电磁隐身衣。我们考虑的情况下,有一个有限数量的球形斗篷位于空间中的不同点。我们证明了对于任意频率的平面波入射,散射波恒为零。我们还考虑了有限能量波包的散射。我们证明了散射矩阵是恒等式,即,对于任何输入波包,输出波包与输入波包相同。这证明了在任何电磁波在高阶变换介质,特别是Pendry等人的一阶变换介质中的散射实验中都不能探测到隐身衣,并证明了高阶隐身衣与一阶隐身衣一样,也能隐身无源和有源器件.隐形的物体与外部完全分离。实际上,外部的隐身与被隐身对象内部的内容无关。隐身物体内部的电磁波不能离开隐蔽区域,反之亦然,隐身物体外部的电磁波不能进入隐蔽区域。当我们证明我们的结果,从一般的各向异性材料的转换获得的媒体,我们证明,它是可能的斗篷内的一般晶体的对象。

英文摘要:

There is currently a great deal of interest in the invisibility cloaks recently proposed by Pendry et al. that are based in the transformation approach. They obtained their results using first order transformations. In recent papers Hendi et al. and Cai et al. considered invisibility cloaks with high order transformations. In this paper we study high order electromagnetic invisibility cloaks in transformation media obtained by high order transformations from general anisotropic media. We consider the case where there is a finite number of spherical cloaks located in different points in space. We prove that for any incident plane wave, at any frequency, the scattered wave is identically zero. We also consider the scattering of finite energy wave packets. We prove that the scattering matrix is the identity, i.e., that for any incoming wave packet the outgoing wave packet is the same as the incoming one. This proves that the invisibility cloaks can not be detected in any scattering experiment with electromagnetic waves in high order transformation media, and in particular in the first order transformation media of Pendry et al. We also prove that the high order invisibility cloaks, as well as the first order ones, cloak passive and active devices. The cloaked objects completely decouple from the exterior. Actually, the cloaking outside is independent of what is inside the cloaked objects. The electromagnetic waves inside the cloaked objects can not leave the concealed regions and viceversa, the electromagnetic waves outside the cloaked objects can not go inside the concealed regions. As we prove our results for media that are obtained by transformation from general anisotropic materials, we prove that it is possible to cloak objects inside general crystals.

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