Oliver Paul at the University of Kaiserslautern in Germany and a few friends reveal an eminently practical way of making invisibility cloaks of any size and shape. Their idea is simple. Creating a cloak that exactly follows the shape of the object it is intended to hide is hard because curve cloaks are hard to make.
Instead, Paul and co approximate the shape using flat facets. These ‘invisibility tiles’ fit together in the same way as the triangular facets in a computer animation. And since each flat tile is relatively simple and easy to make, it becomes much cheaper and easier to build complex cloaks.
(a) Exact circular cloak consisting of metamaterial elements arranged in
concentric circles. (b) and (c) Polygonal cloak shell approximations. In the figures, the grey shading depicts the variation of the geometric dimensions of the metamaterial elements, whereas the short lines indicate the orientation of these elements.
Transformation optics (TO) is a powerful tool for the design of artificial materials with unprecedented optical properties. General TO media are demanding, requiring spatially varying constitutive tensors with both anisotropic electric and magnetic response. Though metamaterials have been proposed as a path to achieving such complex media, the required properties corresponding to the most general transformations remain elusive even in metamaterials leveraging state-of-the-art fabrication methods. Fortunately, in many situations the most significant benefits of a TO medium can be obtained even if approximations to the ideal structures are employed. Here, we propose the approximation of TO structures of arbitrary shape by faceting, in which curved surfaces are approximated by flat metamaterial layers that can be implemented by standard fabrication and stacking techniques. We illustrate the approximation approach for the specific example of a cylindrical “invisibility cloak”. First, we introduce a numerical method for the design of cloaks with arbitrary boundary shapes, and apply it to faceted shapes. Subsequently, we reduce the complexity of the metamaterials needed to implement the perfect faceted cloak by introducing several approximations, whose validity is quantified by an investigation of the scattering cross section.
(Color online) Simulation results for the z-component of the electric field
of a TE-wave incident from the left. (a) The bare conducting object without a cloak.
(b) The exact circular-cylindrical cloak. (c) Approximations APX 1 and (d) APX 2
simulated with the full parameter set.
In this paper, we have proposed an approximation method for the design of transformation-optical (TO) components of arbitrary shape. Starting from the exact transformation, a polygonal approximation of the curved shape of the TO device is introduced. In consecutive approximations the metamaterial elements were aligned parallel to the flat boundaries of the polygons. As a major advantage, the polygonal approximation significantly mitigates the fabrication constraints since the resulting TO components can be implemented by flat metamaterial layers. This can be readily achieved by standard lithographic and stacking techniques. We have validated the approach for the example of a cylindrical cloak and quantified the accuracy of the approximations by comparing the scattering cross-section of the cloak with the exact TO cloak of a circular shape.
Furthermore, we have presented an alternative method for the design of electromagnetic cloaks with virtually arbitrary shapes. The approach is based on the wall distance calculation and is applicable to a large class of cloak geometries including convex shapes and even some non-convex shapes. The new technique has been numerically verified on a specific example of an octagon-shaped cloak.