Two-dimensional dissimilar electromagnetic cloak for irregular regions

A general method to design a 2D dissimilar cloak for irregular regions is presented by operating a nonlinear transformation in polar coordinates. The material parameters avoid discontinuities while the thickness of the cloak shell is effectively limited in elongated directions. Full-wave simulations of an elliptic cloak, a rectangular cloak, and an arbitrary-shape cloak are performed to verify the validity of the design. Both the material parameters and the scattering widths of different models are calculated and illustrated for comparison. This method provides a possible approach for designing complex shaped cloaks.