A rigorous numerical method for the optimal
نویسنده
چکیده
In this paper we describe recent developments in the application of mathematical and computational techniques to the problem of designing binary gratings on top of a multilayer stack in such a way that the propagating modes have a speci ed intensity or phase pattern for a chosen range of wavelengths or incidence angles. This optimal design problem is solved by a minimization algorithm based on gradient descent, the exact calculation of gradients of certain functionals with respect to the parameters of the grating pro le and the thickness of the layers. For the computation of di raction e ciencies and of the gradients we use a reliable nite element method which originates from variational formulations of the di raction problems. We provide several numerical examples including polarisation gratings and beam splitters to demonstrate the e ciency of the algorithm.
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