Cloaking in shallow-water waves via nonlinear medium transformation
Cloaking in shallow-water waves via nonlinear medium transformation
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DOI：
10.1017/jfm.2015.350
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发表时间：
2015-09-01
影响因子：
3.7
通讯作者：
Alam, Mohammad-Reza
中科院分区：
文献类型：
--
作者：
Zareei, Ahmad;Alam, Mohammad-Reza
在浅水波中为物体设计完美的隐身衣的一个主要障碍是线性变换介质方案（也称为变换光学）需要两个独立介质属性的空间变化。在麦克斯韦方程和电磁隐身的研究问题中，这两个属性是介电常数和磁导率。设计具有可变介电常数和可变磁导率的各向异性材料虽然具有挑战性，但是可以实现的。另一方面，对于长重力波，其控制方程一一映射到单极化麦克斯韦方程，两个所需的空间可变属性是水深和重力加速度;在这种情况下，改变重力加速度是根本不可能的。在这里，我们提出了一个非线性变换，只需要改变介质的属性之一，这在浅水波的情况下，是水深，同时保持重力加速度常数。这种变换保持了控制方程的完整性，并且如果斗篷足够大，则渐近满足必要的边界条件。我们表明，这种非线性变换的对象可以从任何波，仅仅满足长波假设的掩盖。该变换也可用于电磁波无磁光学隐身衣的设计。
A major obstacle in designing a perfect cloak for objects in shallow-water waves is that the linear transformation media scheme (also known as transformation optics) requires spatial variations of two independent medium properties. In the Maxwell's equation and for the well-studied problem of electromagnetic cloaking, these two properties are permittivity and permeability. Designing an anisotropic material with both variable permittivity and variable permeability, while challenging, is achievable. On the other hand, for long gravity waves, whose governing equation maps one-to-one to the single polarization Maxwell's equations, the two required spatially variable properties are the water depth and the gravitational acceleration; in this case changing the gravitational acceleration is simply impossible. Here we present a nonlinear transformation that only requires the change in one of the medium properties, which, in the case of shallow-water waves, is the water depth, while keeping the gravitational acceleration constant. This transformation keeps the governing equation perfectly intact and, if the cloak is large enough, asymptotically satisfies the necessary boundary conditions. We show that with this nonlinear transformation an object can be cloaked from any wave that merely satisfies the long-wave assumption. The presented transformation can be applied as well for the design of non-magnetic optical cloaks for electromagnetic waves.