Metamaterials and metasurfaces for water waves and marine structures

在电磁学、光学、弹性学和声学等应用领域，超材料被用来以不寻常的方式控制波。超材料是一种介质，在这种介质中，场的特性可以以一种自然产生的材料中通常找不到的方式传播。它们通常由比潜在场变量固有的自然长度尺度小得多的微观结构组成，其方式是使其对场的宏观影响允许展示复杂的现象。在上面列出的应用领域中，例子包括斜波进入超材料时向后弯曲的“负折射”、“完全透镜”和“隐形隐身”，它们都依赖于负折射率。同样，元曲面是以一种不寻常的方式与场交互的域的边界。这些微结构通常是人为的，而不是在自然产生的材料中发现的。经典的线性化水波理论是势场理论的一个例子，它与电磁场、声场和弹性场理论有一些共同的特征。特别是，这是一个支持波浪的环境。除了少数几个值得注意的例外，许多在其他应用领域发展起来的超材料和超表面的想法还没有扩展到水波中或纳入到水波中。那些经常利用近似的“线性化浅水理论”或“长波理论”将想法和结果传递到水波中的人。这导致了一些有趣的想法和发展，特别是在水波中的“隐身隐身”领域(博士导师在这一领域做出了一些贡献)。然而，定义水波的一组方程具有特殊的特征，这使它们不同于其他场论。在深度方向上对场的依赖不同于其他两个水平波浪方向，区域上横向边界的存在构成了水波问题的一个基本部分，这是其他场论所不具备的。浅水理论使用深度平均作为克服这些困难的一种手段，但这样做的代价是引入了一个近似值，并限制了近似值合理的参数范围。

In application areas such as electromagnetics, optics, elasticity and acoustics, metamaterials are used to control waves in unusual ways. A metamaterial is a medium in which properties of a field can be propagated in a manner not normally found in naturally-occurring materials. They are most often comprised of microstructures much smaller than the natural lengthscales intrinsic to the underlying field variables in such a way that their macroscopic effect on the field allows complex phenomena to be exhibited. In the application areas listed above examples include "negative refraction" in which oblique waves bend backwards as they enter the metamaterial, "perfect lensing" and "invisibility cloaking", which both rely on negative refractivity. Likewise, metasurfaces are boundaries to domains which interact with a field in an unusual way. These are often comprised of microstructres that are man made rather than being found in naturally-occurring materials.The classical theory of linearised water waves is an example of a potential field theory sharing some common features with electromagnetic, acoustic and elastic field theories. In particular it is a wave-supporting environment. With a few notable exceptions, many of the ideas of metamaterials and metasurfaces developed in other application areas have not been extended or incorporated into water waves. Those that have have often taken advantage of an approximate "linearised shallow water theory" or "long wave theory" to transfer ideas and results across to water waves. This has led to some interesting ideas and developments particularly in the area of "invisibility cloaking" in water waves (an area which the PhD supervisor has made some contributions). However, the set of equations which define water waves have particular features which make them different to other field theories. The dependence on the field in the depth direction is different to the other two horizontal wave-bearing directions and the existence of lateral boundaries on the domain form an essential part of a water-wave problem in a way not shared by other field theories. Shallow water theory uses depth-averaging as a means of overcoming these difficulties but does so at the expense of introducing an approximation and restricting the range of parameters for which the approximation is justified.