Computational differential geometry applied to invisibility cloaks in electromagnetism and elastodynamics

1996年，约翰·彭德利和他的同事在英国发现了超材料，在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，形成一个复合结构，其中斯内尔-笛卡尔光学定律是颠倒的(光走错了方向)。使用这种超材料，人们可以设计一种会聚的平板透镜，它可以超过衍射极限：理论上，这种完美透镜(由彭德里在他的开创性论文《负折射制造完美透镜》，PRL85,3966,2000)中提出，原则上可以让你看到比工作波长小得多的物体(想象一下你用自己的眼睛看DNA！)。但还有更多的东西：超材料为可以使物体看不见的材料的设计开辟了新的前景。由独立的重要工作者提出的隐身方法很少，即：-约翰·彭德里、大卫·舒里格和大卫·史密斯，他们提出了一种几何变换，在空间中打开一个洞，你可以在那里隐藏物体。在这种情况下，光在超材料周围扫过，出现在另一边，就像它穿过了一片空白的空间一样(就像水绕着障碍物流动一样)。-Ulf Leonhardt，他建议使用与Pendry和他的同事的建议相关的保形贴图。-Andrea Alu和Nader Engheta，他们建议使用圆柱形斗篷，其性质取决于要隐藏的对象的性质(这里需要对象属性的知识)。-Graeme Milton和Nicolae Nicorovici，他们建议使用由负折射率材料组成的圆柱形斗篷(圆柱形不透明完美透镜)。在这里，一个物体躺在斗篷附近(实际上是外面，而不是里面！)被出现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)