Designing a diffractive optical element used as a ring-beam convertor to control the wave-front propagation in a three-dimensional space

Conventional diffractive optical elements (DOEs) are usually designed to produce a predetermined function or light distribution on a single transverse plane. As we know, the unconventional light distributions are generated within a three-dimensional domain. Such as a ring-beam convertor described in this paper, the distribution with a ring profile must be consistent in any cross section. A phase-only diffractive optical element with 1 6 levels is designed for controlling the wave-front propagation within a given three-dimensional space. And it is a rotation symmetrical binary optical element that is used to convert the input uniform beam to a ring output beam. We designed this convertor by the Simulated Annealing method (SA) the iterative method based on the Block-Iterative weighted projections algorithm (BIWP) and the SA-BIWP hybrid algorithm. In this paper, we emphatically investigated and compared these three phase retrieval algorithms. The results of numerical simulation show that the procedure of the hybrid algorithm converges more stably to an optimal solution close to the global optimum with an acceptable computing time. The diffractive efficiency is higher and the energy of the output beam in the ring domain is more concentrated. Along the direction of the input beam, the intensity of the beam in each transverse plane is accordant. What's more, the hybrid algorithm is applicable to be employed to solve other discrete stochastic optimization problem ofthe design of a DOE.