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A singular coordinate transformation leads to extreme materials in a transformation-based cloak. If a non-singular transformation is used, the perfect invisibility is lost. The invisibility is also influenced by the homogenization process. In this paper, we investigate these two influences in 2-D circular cylindrical cloaks, obtained from different non-singular mappings. Considering a further deterministic optimization, we also conclude that it is better to use a non-singular cloak based on a mapping scale up to 20%, since it has lower scattering and simpler materials when compared with cloaks based on other mappings. [ABSTRACT FROM AUTHOR]

A possible strategy for avoiding singular material parameters in a transformation-based invisibility cloak involves an out-of-plane stretching, calculated to compensate the in-plane singular transformation. In this paper, we used numerical simulations to analyze the relation among the out-of-plane transformation, the resulting material anisotropy, and the total scattering cross width. Moreover, we show how this information can be used to optimize a cloak with homogeneous anisotropic layers. [ABSTRACT FROM AUTHOR]