Generalized transformation for nonmagnetic invisibility cloak with minimized scattering

We propose a generalized transformation for a nonmagnetic invisibility cloak with minimized scattering. In comparison with the previous transformation, it has been demonstrated that the unphysical singularity at the inner boundary and the limitation of the thickness of the cloak shell can be removed by choosing the appropriate transformation function. Furthermore, our generalized transformation is used to design two different nonmagnetic cloaks without considering the unphysical singularity and the limitation of the thickness. Based on the effective medium theory, an alternating layered system composed of two isotropic materials is employed to realize these cloaks. Moreover, through calculating the scattering cross section of the cloak, it is found that such a nonmagnetic cloak can only work in a narrow frequency range.