Diffractive optical elements designed by hybrid genetic algorithm for the generation of nondiffracting beams

In this paper, hybrid genetic algorithms that combine genetic algorithms (GAs) with traditional gradient-based local search techniques are proposed for the optimization design of diffractive phase elements (DPE`s) for the generation of nondiffracting beams. The proposed hybrid methods exploit the global nature of the GAs as well as the local improvement capabilities of the gradient-based local search techniques, and will perform a more improved search while comparing with both of the single ones. A cost function that can directly control the performance of the final solutions is also used. By performing the DPE's design with different desired diffraction efficiencies, we obtain a set of results that approximately reflect the trade-off between the design objectives, namely signal-to-noise ratio (SNR) and the diffraction efficiency. Reasonable solutions can be chosen on the basis of the knowledge of the problem. Numerical results demonstrate that the designed DPE's can successfully produce both zero-order and high-order nondiffracting beams.