Numerical design of arbitrarily shaped electromagnetic cloaks

A methodology to control electromagnetic fields based on the proper design of permeability and permittivity tensors was put forth recently. In particular, it has been suggested that it is possible to achieve electromagnetic cloaking of objects by using metamaterial coatings with properly designed constitutive parameters. However, the necessary coordinate transformation in the original methodology has been carried out analytically. In general, it becomes difficult to design an analytical cloak of arbitrary shape. In this paper, we present a general numerical implementation of cloaking layers and validate it by comparing the numerical results with those from analytical solutions.