Control of wave-front propagation with diffractive elements

In principle, diffractive elements can be designed to control a propagating wave in three dimensions, but no general procedure has been proposed. We present an iterative method that is suitable for the design of such diffractive elements. The resulting complex amplitude distribution will approach any arbitrary requirement, as much as is permitted by basic physical principles. The problem of "nondiffracting-beam" propagation is analyzed as a special case, and intensity peaks are generated that propagate as much as 4 m with a bounded width. The generality of the method, as compared with other techniques, is beams.