Acoustic cloaking and mirages with flying carpets

Carpets under consideration here, in the context of pressure acoustic waves propagating in a compressible fluid, 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 touching 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. However, instead of reducing its scattering cross-section like in acoustic cloaks, we rather mimic that of another obstacle, say a square rigid cylinder. For instance, 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 acoustic parameters. To exemplify this important aspect, we propose a multi-layered carpet consisting of isotropic homogeneous fluids with constant bulk modulus and varying density which works over a finite range of wavelengths. We have discussed some applications, with the sonar boats or radars cases as typical examples. For instance, we would like to render a pipeline lying on the bottom of the sea or floating in mid-water undetectable for a boat with a sonar at rest just above it on the surface of the sea. Another possible application would be protecting parabolic antennas.