Non-Singular Homogeneous Polyhedral Heat Cloak and Its Realization

Abstract

As most arbitrarily shaped cloaks can be approximated by polyhedra and further divided into a series of tetrahedra, we propose in this paper a linear mapping approach to design cloaks with tetrahedron shapes (i. e. tetrahedral cloaks). Homogeneous material properties of the cloak are straightforwardly obtained from coordinates of typical points. Consequently, most arbitrarily shaped thermal cloaks can be designed using homogeneous anisotropic materials only. We construct two polyhedral cloaks and show numerically that they successfully thermally conceal objects after a certain lapse of time. We then demonstrate that cloaks with curved boundaries can also be obtained using our approach. It is further shown how geometrical parameters affect the material properties and cloaking performances. One can flexibly tune the cloaking performances based on practical requirements and material availabilities. We analyze effectiveness of a polygonal cloak composed of an alternation of homogeneous isotropic layers, and note that cloaking deteriorates at short times. We finally sketch an approach to realize 3D homogenized thermal metamaterials.

Elastic Wave Near-Cloaking

“…In numerical simulation, transformations [16,17] created effective infinite domains that led to the PMLs (perfectly matched layers) [18] now widely used. The work of Pendry [19] and Leonhard [20] in designing invisibility cloaks that act to hide an object from outside radiation by producing zero scattering, and zero interaction of the wave with the object, led to an explosion of activity with the idea of invisibility or cloaking then adapted to many physical, scalar problems such as electromagnetic/optical invisibility [19,20]; cloaks for water waves [21,22]; airborne sound [23,24,25,26,27,28,29,3]; vibration cloaks [2,21,22,30,31,6,1,13]; and thermal cloaks [32,33,34]. In parallel with the idea of infinite transformations such as conformal cloaking [20] there were strides to make the transformations more realistic using the truncation of the infinite transformation to a finite one [35].…”

“…In parallel with the idea of infinite transformations such as conformal cloaking [20] there were strides to make the transformations more realistic using the truncation of the infinite transformation to a finite one [35]. An alternative approach called scattering cancellation, or neutral inclusions, has also been used for long wavelength considerations [36,33,6,34]. Carpet cloaks, based around the idea of quasi-conformal mappings [35] have been particularly popular as such cloaks allow one to effectively hide defects or imperfections in a surface, and have implementations in optics [37,38].…”