<title>Diffractive optical elements designed by hybrid genetic algorithm for the generation of nondiffracting beams</title>

Abstract

The concept of nondiffracting beams was first introduced by Durnin. The beam spot of nondiffracting beam undergoes diffraction-free spreading over a long propagating distance. Therefore, nondiffracting beams could have potential applications in precision alignment, optical interconnections, and power transport. 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 optical elements (DOE's) for the generation of nondiffracting beams. In the hybrid genetic algorithms, an offspring obtained by genetic operators, such as crossover and mutation, is not included in the next generation directly but used as a seed for the sequent local search. The local search method searches the neighborhood of each offspring, and selects a better point, which is included in the next generation. In such a manner, the efficient exploitation of local information is provided by the incorporated local search procedure and the reliable locating of the global minimum is provided by the use of mechanisms of nature selection. 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. The incorporated local search technique we used here is the Davidon-Fletcher-Powell (DFP) method, which is well known for its good convergence property. Numerical results demonstrate that the designed DOE's can successfully produce both zero-order and high-order nondiffracting beams.