We propose one kind of transformation functions for nonmagnetic invisibility cloak with minimized scattering on the basis of generalized transformation. By matching the impedance at the outer surface of the cloak, the transformations with two parameters are determined. To confirm the performance of the cloak, full wave simulation based on the finite element method is carried out. Furthermore, total scattering cross section is computed to better illustrate the scattering characteristics of cloak with different parameters. In addition, based on the effective media theory, alternating layered system composed of two isotropic materials is employed to realize the cloak practically.
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