A general method is proposed to construct an approximate nonsingular two-dimensional (2D) cloak by taking constitutive parameter tensors (CPTs) of a three-dimensional perfect cloak on a mirror-symmetric cross section in order to avoid any singularity at the inner boundary of a perfect 2D cloak. As two examples, reduced 2D models for an elliptic cloak and a bow-tie cloak are derived. The reduced 2D models are characterized explicitly with CPT of finite values and good cloaking effects are verified numerically.
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Zhang et al. (2008) studied this question.
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