Discretization of an square electromagneic cloak based on transformation optics

Existing discrete electromagnetic cloaks are often limited to circular shape and always based on one dimensional discretization of radius variable in cylindrical coordinates. In this paper, we proposed a two dimensional (2D) discrete square invisible cloak which really does not require any continuous constitutive material parameters. The discrete square cloak consists of several homogeneous blocks, and they are discretized from the original transform medium whose material parameters are often continuous spatial functions of both x and y variables in Cartesian coordinates. With proper design of numbers of blocks, we demonstrated the scattering properties of the proposed cloaking structure through rigorous analysis of the scattered electromagnetic fields. The proposed cloaking structure could be possibly realized, therefore may lead to a practical path to an experimental demonstration of electromagnetic cloaking.