Carpet cloak for water waves

Cloaking is a challenging topic in the field of wave motion, and is of significant theoretical value. In this article, a type of carpet cloak has been theoretically designed for water waves by using the effective medium and transformation theory. This carpet cloak device, created by a three-dimensional printer, is composed of a periodic structure which realizes the equivalent anisotropic water depth. We demonstrate its excellent cloaking performance numerically and experimentally in a wide range of frequencies and angles of incidence, with low wave attenuation characteristics and simple device realization of this carpet cloak illustrating that water wave transformation is a powerful method with which to manipulate water waves.

Figure 1

Carpet cloak device. (a) Physical space; (b) virtual space using coordinate transformations; (c) distribution of alternate water depths; (d) experimental component.

Figure 2

Diagram of the experimental setup.

Figure 3

Numerical simulations with $\theta ={30}^{\circ }$ and $f=9\mathrm{Hz}$. (a) The wave is obliquely incident upon a flat plane. (b) The wave is obliquely incident upon a bare protruded plane.

Figure 4

Experimental demonstrations with $\theta ={30}^{\circ }$ and $f=9\mathrm{Hz}$. (a) The wave is obliquely incident upon a flat plane. (b) The wave is obliquely incident upon a bare protruded plane.

Figure 5

Numerical simulations and experimental results for the carpet cloak with $\theta ={30}^{\circ }$. (a) Simulation for $f=12\mathrm{Hz}$; (b) experiment for $f=12\mathrm{Hz}$; (c) simulation for $f=9\mathrm{Hz}$; (d) experiment for $f=9\mathrm{Hz}$; (e) simulation for $f=7\mathrm{Hz}$; (f) experiment for $f=7\mathrm{Hz}$.

Figure 6

Numerical simulations and experimental results for the carpet cloak with $\theta ={40}^{\circ }$. (a) Simulation for $f=12\mathrm{Hz}$; (b) experiment for $f=12\mathrm{Hz}$; (c) simulation for $f=9\mathrm{Hz}$; (d) experiment for $f=9\mathrm{Hz}$; (e) simulation for $f=7\mathrm{Hz}$; (f) experiment for $f=7\mathrm{Hz}$.

Figure 7

Numerical simulations and experimental results for the carpet cloak with $\theta ={50}^{\circ }$. (a) Simulation for $f=12\mathrm{Hz}$; (b) experiment for $f=12\mathrm{Hz}$; (c) simulation for $f=9\mathrm{Hz}$; (d) experiment for $f=9\mathrm{Hz}$; (e) simulation for $f=7\mathrm{Hz}$; (f) experiment for $f=7\mathrm{Hz}$.