Abstract
This paper extends the proposal of Li and Pendry [Phys. Rev. Lett. 101, 203901-4 (2008)] to invisibility carpets for infinite conducting planes and cylinders (or rigid planes and cylinders in the context of acoustic waves propagating in a compressible fluid). Carpets under consideration here do not touch the ground: they levitate in mid-air (or float in mid-water), which leads to approximate cloaking for an object hidden underneath, or touch either sides of a square cylinder on, or over, the ground. The tentlike carpets attached to the sides of a square cylinder illustrate how the notion of a carpet on a wall naturally generalizes to sides of other small compact objects. We then extend the concept of flying carpets to circular cylinders and show that one can hide any type of defects under such circular carpets, and yet they still scatter waves just like a smaller cylinder on its own. Interestingly, all these carpets are described by non-singular parameters. To exemplify this important aspect, we propose a multi-layered carpet consisting of isotropic homogeneous dielectrics rings (or fluids with constant bulk modulus and varying density) which works over a finite range of wavelengths.
Highlights
There is currently a keen interest in electromagnetic metamaterials within which very unusual phenomena such as negative refraction and focussing effects involving the near field can occur [1, 2, 3, 4]
We have proposed some models of flying carpets which levitate in mid-air. Such cloaks can be built from acoustic metafluids: as explained by Pendry and Li in a recent work, one can for instance emulate required anisotropic density and heterogeneous bulk modulus with arrays of rigid plates with a hemispherical sack of gaz attached to them [42]
Other designs proposed by Torrent and Sanchez-Dehesa would work well [17]. Such flying carpets lead to some approximate cloaking as they do not touch the ground
Summary
There is currently a keen interest in electromagnetic metamaterials within which very unusual phenomena such as negative refraction and focussing effects involving the near field can occur [1, 2, 3, 4]. Whereas cloaking of pressure waves in two-dimensional [18, 17] and three-dimensional [20, 21] fluids, antiplane shear waves in cylindrical bodies [22], and flexural waves in thin-elastic plates [23, 24] is well understood cloaking of in-plane coupled shear and pressure elastic waves still remains elusive [26, 25] as the Navier equations do not retain their form under geometric transforms Such cloaks might involve (complex) pentamode materials such as proposed in [27]. We would like to render e.g. pipelines lying at the bottom of the sea or floating in mid-water undetectable for a boat sonar These pipelines are considered to be infinitely long straight cylinders with a cross-section which is of circular or square shape. We would like to show that we can hide the pipeline under a cylindrical carpet (a metafluid) so that the sonar only detects the wave reflected by the bottom of the sea
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