Design of two dimensional nonsingular internal-external cloaks with arbitrary cross-section

Abstract

According to the combination of the complementary medium and transformation optics, the shape of two-dimensional (2D) internal-external cloaks has been generalized into any geometry to adapt to the variety of object shapes. In order to adapt to the practical application, some approximations have been introduced to eliminate the infinite singularity of the parameters in the compressed region by adjusting the principle sketch out of the plane. Firstly, the general parameter equations of the nonsingular cloak with arbitrary cross-section are deduced strictly by the mathematical method based on coordinate transformations in the cylindrical coordinate system. Secondly, taking into account the discontinuous property of the curve functions of arbitrary polygons, a supplementary investigation is given for the nonsingular cloak with arbitrary polygonal cross-section. The transformations in the supplementary study are carried out in the Cartesian coordinate system directly and referred to the coordinates of the polygon’s vertices rather than the curve function of the polygon. Last, the invisibility effect of the corresponding cloak is studied by full-wave simulations based on the finite element method. The applicable scope of the 2D internal-external cloak is expanded greatly by the methods and results given in this paper.