Optimal Control of Light Propagation Governed by Eikonal Equation within Inhomogeneous Media Using Computational Adjoint Approach

Abstract

A mathematical model is presented in the present study to control‎ ‎the light propagation in an inhomogeneous media‎. ‎The method is ‎based on the identification of the optimal materials distribution‎ ‎in the media such that the trajectories of light rays follow the‎ ‎desired path‎. ‎The problem is formulated as a distributed parameter ‎identification problem and it is solved by a numerical method‎. ‎The‎ ‎necessary optimality conditions based on Karush-Kuhm-Tucker (KKT) conditions is derived‎ ‎by means of the adjoint approach and a solution algorithm is‎ ‎introduced to find local minimizers of the original problem‎. ‎The‎ ‎original PDE and its corresponding adjoint are discretized by the‎ ‎finite difference method and they are solved efficiently by the‎ ‎fast sweeping approach‎. ‎The main benefits of the presented‎ ‎algorithm is the computational efficiency‎, ‎flexibility and ability‎ ‎to produce isotropic materials distribution with bounded physical‎ ‎properties‎. ‎The presented algorithm can be used for the optimal‎ ‎design of waveguides and invisibility cloaks in the wavelength ‎spectrum of visible light‎. ‎The feasibility of the‎ ‎presented method is studied by a numerical example‎.