Dimensionality crossover of radial discrete diffraction in optically induced Mathieu photonic lattices

We demonstrate transitional dimensionality crossover of radial discrete diffraction in optically induced radial-elliptical Mathieu photonic lattices. Varying the order, characteristic structure size, and ellipticity of the Mathieu beams used for the photonic lattices generation, we control the shape of discrete diffraction distribution over the combination of the radial direction with the circular or elliptic. We also investigate the transition from one-dimensional to two-dimensional discrete diffraction by varying the input probe beam position. Discrete diffraction is the most pronounced along the crystal anisotropy direction.