Divide and conquer algorithm for nondiffracting beams

We put forward a robust technique to encode a plethora of arbitrary images as nondiffracting beams by optimizing their respective phase components. This technique works directly under the constraint of a ring of infinitesimal width in Fourier space. The procedure reported is based on a stochastic direct search and global optimization: the differential evolution method. Unlike previous methods reported, the present approach is also able to optimize the spatial frequency of the image used. Remarkably, this technique also demonstrates that it is possible to encode even more arbitrary images on demand into nondiffracting forms by allowing a segmentation of the profile. We provide some codes to generate nondiffracting beams by using this algorithm.