Optimal design of nonlinear diffraction gratings

The goal of the paper is to study the optimal design problem for nonlinear diffraction gratings. The problem arises in the study of surface enhanced nonlinear optical effects of second harmonic generation. In order to apply certain gradient based optimization methods, an explicit formula for the partial derivatives of the Rayleigh coefficients with respect to the parameters of the grating profile is derived. Using the formula, numerical results are presented on an optimal design problem of nonlinear binary gratings.