Nonlinear lattice structures based on families of complex nondiffracting beams

We present a new concept for the generation of optical lattice waves. For all four families of nondiffracting beams, we are able to realize corresponding nondiffracting intensity patterns in one single setup. The potential of our approach is shown by demonstrating the optical induction of complex photonic discrete, Bessel, Mathieu, and Weber lattices in a nonlinear photorefractive medium. However, our technique itself is very general and can be transferred to optical lattices in other fields like atom optics or cold gases in order to add such complex optical potentials as a new concept to these areas as well.