Approximation approach of designing practical cloaks with arbitrary shapes

The approach of designing cloaks with arbitrary shapes was investigated. The coordinate transformation was considered as a homeomorphous topological mapping and the related geometrical description was proposed by introducing position surfaces and tracing lines. Then an approximation approach was presented, which considers a close shape as a polyhedron and performs the spatial compression in a general method. As an example of this approach, we deduced the material parameter equations for two-dimensional polygon cloaks and confirmed the results through numerical simulations. Our approach opens up possibilities of designing practical cloaks with arbitrary shapes through numerical or/and semi-analytical methods.