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.
We present the numerical modeling of two different randomization methods of two-dimensional aperiodic photonic lattices based on Mathieu beams, optically induced in a photorefractive media. We numerically study light propagation in such lattices. For both methods, we compare light transport and localization in such lattices along the propagation and for various disorder strengths. For all disorder strengths, a disorder-enhanced light transport is observed. With increasing disorder strength light transport becomes diffusive-like while with further increase of disorder strength, the Anderson localization is observed. For longer propagation distances this transition is more pronounced. The influence of input lattice intensity on the localization effects is studied. We observe more pronounced localization for one of the methods, and different diffraction and localization along different directions, due to the crystal and lattice anisotropy. The difference in light transport and localization between two randomization methods is attributed to various levels of input lattice intensity.
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