Numerical method for designing approximate cloaks with arbitrary shapes

The design of perfect electromagnetic cloaks is usually based on the coordinate transformation method. However, for cloaks with arbitrary shapes, it is difficult to express analytically such coordinate transformation. Thus, we have to resort to numerical methods to design approximate cloaks. In this paper, we propose a numerical method of designing cloaks with arbitrary shapes. According to this method, spatial compressions are treated as homeomorphous mappings and described in numerical forms. The corresponding coordinate transformations are therefore expressed numerically. As an application of this method, we deduced the discrete constitutive parameters of a two-dimensional polygon cloak, and verified the results by numerical simulations. This method can be also used in cases with acoustic waves and matter waves.