Designing a square invisibility cloak using metamaterials made of stacked positive-negative index slabs

We present a design of a square invisibility cloak based on triangular transformations. In triangular transformations, certain areas of the cloak are squeezed to be infinitesimal in the virtual space. This results in cloak materials whose constitutive parameters are singular. We show rigorously that these prescribed singular materials can be emulated by metamaterials made of stacked positive-negative index slabs. We use numerical simulations to demonstrate the conceived square cloak, which in principle can be constructed using only homogenous and non-singular materials. The proposed square invisibility cloak suggests another important application of negative index media. (C) 2013 AIP Publishing LLC.