Iterative algorithms for holographic shaping of non-diffracting and self-imaging light beams

We have developed iterative algorithms for the calculation of holograms for non-diffracting or self-imaging light beams. Our methods make use of the special Fourier-space properties of the target beams. We demonstrate experimentally the holographic generation of perhaps the most challenging type of beam: a self-imaging beam shaped in more than one plane. Potential applications include the generation of light "crystals" for optical trapping and atomic diffraction studies.