Nonsingular two dimensional cloak of arbitrary shape

We propose a general method to circumvent the singularity (infinitely large values of material parameters) of arbitrary two dimensional (2D) cloaks. 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 a three dimensional (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 demonstrate the method.