Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces

We study the design of arbitrarily shaped electromagnetic (EM) concentrators and their potential applications. To obtain closed-form formulas of EM parameters for an arbitrarily shaped concentrator, we employ nonuniform rational B-spline (NURBS) to represent the geometrical boundary. Using the conformally optical transformation of NURBS surfaces, we propose the analytical design of arbitrarily shaped concentrators, which are composed of anisotropic and inhomogeneous metamaterials with closed-form constitutive tensors. The designed concentrators are numerically validated by full-wave simulations, which show perfectly directed EM behaviors. As one of the potential applications, we demonstrate a way to amplify plane waves using a rectangular concentrator, which is much more efficient and easier than the existing techniques. Using NURBS expands the generality of the transformation optics and could lead toward making a very general tool that would interface with commercial softwares such as 3D STUDIOMAX and MAYA.