Optimal design of diffractive optical elements with functional relationship between phase and amplitude modulations using nonlinear optimization methods

Abstract

In this paper, the optimal design problem of diffractive optical elements having a functional relationship between phase and amplitude modulations is investigated by using nonlinear optimization methods. Comparative analysis on formulations and performances of three important iterative methods (iterative Fourier-transform algorithm, nonlinear conjugate gradient method, and Gauss-Newton-Levenberg-Marquardt method) is provided. The detailed design equations of each method are described and numerical results are presented. The stable convergences of three investigated algorithms are confirmed. In our design problem, the conventional phase-only modulation is not assumed but the inherent functional relationship between phase and amplitude modulations of real diffractive optical elements are taken into account. It is shown that considering the functional relationship of phase and amplitude modulations in the design of diffractive optical elements leads to improvements in uniformity and diffraction efficiency.