Design of arbitrarily directional cloaks by solving the Laplace's equation

We propose a robust method to design arbitrarily directional cloaks by solving the Laplace's equation. The method is based on the orthogonality between light rays and eikonal curves. By employing the analogy between light rays and electric force lines, and the equivalence between eikonal curves and isopotential lines, the original problem in the geometrical optics is converted into a boundary value problem in electrostatics. Examples are given and the simulation results validate the design. The method can also be used to design other optical-transformation devices and be extended to solve three-dimensional problems. The medium parameters designed by the method are easily realized using metamaterials or normal materials, and hence, the method can find applications in the optical and microwave engineering. (C) 2010 American Institute of Physics. [doi:10.1063/1.3436577]