Flat-face approximations of invisibility cloaks with planar metamaterial layers

Transformation optics (TO) is a powerful tool for the design of artiffcial materials with unprecedented optical properties. Here, we propose the approximation of TO structures of arbitrary shape by faceting, in which curved surfaces are approximated by at 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.