Three-dimensional invisible cloaks with arbitrary shapes based on partial differential equation

The method of designing electromagnetic invisible cloak is usually based on the form-invariance of Maxwell's equations in coordinate transformation. By solving the partial differential equations (PDEs) that describe how the coordinates transform, three-dimensional (3-D) electromagnetic and acoustic invisible cloaks with arbitrary shapes can be designed provided the boundary conditions of the cloaks can be determined by the corresponding transformation. Full wave simulations based on finite element method verify the designed cloaks. The proposed method can be easily used in designing other transformation media such as matter-wave cloaks.