Hybrid approaches that combine genetic algorithms (GA’s) with traditional gradient-based local search techniques are proposed for the optimization design of diffractive phase elements (DPE’s) for laser beam shaping. These hybrid methods exploit the global nature of the GA’s as well as the local improvement capabilities of the gradient-based local search techniques and will perform a more improved search in comparison with each of the individual approaches. The incorporated local search technique that we used here is the Davidon–Fletcher–Powell method. A cost function that can directly control the performance of the final solutions is also used. By performing the DPE 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 diffraction efficiency. Reasonable solutions can be chosen on the basis of the knowledge of the problem. Simulation computations are detailed for two rotationally symmetric beam-shaping systems, in which an incident Gaussian profile laser beam is converted into a uniform beam and a zero-order Bessel beam. Numerical results demonstrate that the proposed algorithm is highly efficient and robust. DPE’s that have high diffraction efficiency and excellent SNR can be achieved by using the algorithm that we propose.
© 2001 Optical Society of America
Original Manuscript: June 5, 2000
Revised Manuscript: October 19, 2000
Manuscript Accepted: November 1, 2000
Published: April 1, 2001
Guangya Zhou, Xiaocong Yuan, Philip Dowd, Yee-Loy Lam, and Yuen-Chuen Chan, "Design of diffractive phase elements for beam shaping: hybrid approach," J. Opt. Soc. Am. A 18, 791-800 (2001)