A novel hybrid algorithm for the design of the phase diffractive optical elements for beam shaping

In this paper, a novel hybrid algorithm for the design of a phase diffractive optical elements (PDOE) is proposed. It combines the genetic algorithm (GA) with the transformable scale BEGS (Broyden, Fletcher, Goldfarb, Shanno) algorithm, the penalty function was used in the cost function definition. The novel hybrid algorithm has the global merits of the genetic algorithm as well as the local improvement capabilities of the transformable scale BEGS algorithm. We designed the PDOE using the conventional simulated annealing algorithm and the novel hybrid algorithm. To compare the performance of two algorithms, three indexes of the diffractive efficiency, uniformity error and the signal-to-noise ratio are considered in numerical simulation. The results show that the novel hybrid algorithm has good convergence property and good stability. As an application example, the PDOE was used for the Gaussian beam shaping; high diffractive efficiency, low uniformity error and high signal-to-noise were obtained. The PDOE can be used for high quality beam shaping such as inertial confinement fusion (ICE), excimer laser lithography, fiber coupling laser diode array, laser welding, etc. It shows wide application value. (C) 2012 Elsevier Ltd. All rights reserved.