Computational differential geometry applied to invisibility cloaks in electromagnetism and elastodynamics

继1996年英国John Pendry及其同事发现超材料之后，物理学中出现了负折射的新领域：人们可以将细直线阵列和分裂环谐振器组合在一起，制造出一种复合结构，这种结构颠倒了斯内尔-笛卡儿光学定律（光走错了路）。利用这种超材料，人们可以设计出一种超越衍射极限的会聚式平面透镜：理论上，这种完美的透镜（由彭德里在他的开创性论文《负折射制造完美透镜》中提出，PRL85, 3966, 2000）原则上允许你看到比工作波长小得多的物体（想象一下用你自己的眼睛看DNA !）但还有更多：超材料为材料设计开辟了新的前景，可以使物体隐形。独立的重要工作者提出了几种隐形方法，即：-约翰·彭德里，大卫·舒里格和大卫·史密斯，他们提出了一个几何变换，在空间中打开一个洞，你可以隐藏一个物体。在这种情况下，光在超材料周围被扫过，从另一边出现，就好像它穿过了一个空的空间（就像水在障碍物周围流动一样）。-Ulf Leonhardt，他建议使用共形图，这与Pendry和他的同事的建议有关。-Andrea Alu和Nader Engheta提出使用圆柱形斗篷，其属性取决于隐藏对象的性质（这里需要对象属性的知识）。——格雷姆·米尔顿和尼古拉·尼科罗维奇，他们建议使用一种由负折射率材料组成的圆柱形斗篷（一种不透明的圆柱形完美透镜）。在这里，位于斗篷附近的物体（实际上是在外面，而不是在里面！）被发生在斗篷边界上的场奇点（所谓的反常共振）所隐藏。

Following the 1996 discovery of metamaterials by John Pendry and coworkers in UK, the new field of negative refraction has emerged in physics: one can combine together arrays of thin straight wires and split ring resonators to make a composite structure for which Snell-Descartes laws of optics are inverted (light takes the wrong way). Using such metamaterials, one can design a convergent flat lens which beats the diffraction limit: in theory, such a perfect lens (proposed by Pendry in his seminal paper Negative refraction makes a perfect lens , PRL85, 3966, 2000) allows you in principle to see objects much smaller than the working wavelength (imagine looking at DNA with your own eyes!). But there is even more: metamaterials open new vistas for designs of materials which can make objects invisible. There are few routes to invisibility proposed by independent important workers, namely:-John Pendry, David Schurig and David Smith who propose a geometric transform which opens up a hole in space where you can hide an object. In this case, light is swept around the metamaterial to emerge on the other side as if it had passed through an empty volume of space (in the same way as water flows around an obstacle). -Ulf Leonhardt who suggests to use conformal maps which is relevant to Pendry's and his co-workers proposal.-Andrea Alu and Nader Engheta who propose to use cylindrical cloaks whose properties dependupon the nature about the object to hide (here the knowledge of the object properties is required).-Graeme Milton and Nicolae Nicorovici who propose to use a cylindrical cloak consisting of material of negative refractive index (a cylindrical opaque perfect lens). Here, an object lying in the neighborhood of the cloak (actually outside, not inside!) is hidden by field singularities occuring on the boundary of the cloak (so-called anomalous resonances)