Nonsingular two dimensional cloak of arbitrary shape

We propose a general method to circumvent the singularity of arbitrary 2D cloaks, which arises from infinitely large values of material parameters at inner boundaries. The presented method is based on the deformation view of the transformation design method. It is shown that by adjusting the principle stretch out of the cloaking plane, 2D cloaks of arbitrary shapes without singularity can be constructed. It is also demonstrated that the method based on the equivalent dispersion relation and the design method for nonsingular 2D cloak from mirror-symmetric cross section of 3D cloak can be derived from the proposed theory. Examples of a cylindrical electromagnetic cloak and an arbitrary shaped 2D electromagnetic cloak without singularity are provided to illustrate the method.