A rigorous and nonsingular two dimensional cloaking coordinate transformation

We derive an approximate but rigorous two dimensional electromagnetic cloaking shell in which no parameters are singular. The simplicity of the material parameters makes it potentially easier to realize in practice than other cloaking solutions. The analytical formulation of this shell also provides a simple and explicit analytical trade-off between its scatter reduction performance, its thickness relative to the interior size, and the complexity and realization difficulty of the required permittivity and permeability.