arXiv 0704.02482007-04physics.opticsmath-phmath.MP

全波电磁隐身（隐身）的严格时域分析

A Rigorous Time-Domain Analysis of Full--Wave Electromagnetic Cloaking (Invisibility)

Ricardo Weder

备注：: The presentation of the results has been simplified. Comments and references have been added

摘要：

目前，人们对用电磁波掩盖物体的观测在理论和实践上的可能性有很大的兴趣。这些不可见装置\cite{glu1, glu2, le}、\cite{pss1}的基本思想是使用各向异性{ \it变换介质}，其介电常数和磁导率$\var^{λν}, μ^{λν}$通过坐标的奇异变换从各向同性介质的介电常数和磁导率$\var_0^{λν}, μ^{λν}_0$获得。本文利用含时散射理论研究了时域电磁隐身问题。这种形式主义使我们能够以一种明确的方式解决由{ \it变换介质}的介电常数和磁导率的倒数的奇异性在隐身物体的边界上所引起的数学问题。我们将麦克斯韦方程组写成薛定谔形式，电磁传播子扮演哈密顿量的角色。我们证明了隐身物体外的电磁传播子本质上是自伴的。此外，唯一的自伴扩张是酉等价的电磁传播介质$\var_0^{λν}, μ^{λν}_0$。利用这一事实，由于坐标变换是球外的恒等式，我们证明散射算子是恒等式。我们的结果给出了一个严格的证明，\cite{glu1, glu2, le}，\cite{pss1}的建设完美地掩盖被动和主动设备从电磁波的观察。此外，我们证明了一般各向异性材料的隐身。特别是，我们的研究结果证明，有可能将物体隐藏在一般的晶体中。

英文摘要：

There is currently a great deal of interest in the theoretical and practical possibility of cloaking objects from the observation by electromagnetic waves. The basic idea of these invisibility devices \cite{glu1, glu2, le},\cite{pss1} is to use anisotropic {\it transformation media} whose permittivity and permeability $\var^{λν}, μ^{λν}$, are obtained from the ones, $\var_0^{λν}, μ^{λν}_0$, of isotropic media, by singular transformations of coordinates. In this paper we study electromagnetic cloaking in the time-domain using the formalism of time-dependent scattering theory. This formalism allows us to settle in an unambiguous way the mathematical problems posed by the singularities of the inverse of the permittivity and the permeability of the {\it transformation media} on the boundary of the cloaked objects. We write Maxwell's equations in Schrödinger form with the electromagnetic propagator playing the role of the Hamiltonian. We prove that the electromagnetic propagator outside of the cloaked objects is essentially self-adjoint. Moreover, the unique self-adjoint extension is unitarily equivalent to the electromagnetic propagator in the medium $\var_0^{λν}, μ^{λν}_0$. Using this fact, and since the coordinate transformation is the identity outside of a ball, we prove that the scattering operator is the identity. Our results give a rigorous proof that the construction of \cite{glu1, glu2, le}, \cite{pss1} perfectly cloaks passive and active devices from observation by electromagnetic waves. Furthermore, we prove cloaking for general anisotropic materials. In particular, our results prove that it is possible to cloak objects inside general crystals.

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