Interdimensional radial discrete diffraction in Mathieu photonic lattices

We demonstrate transitional dimensionality of discrete diffraction in radial-elliptical 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, elliptic, or hyperbolic. We also investigate the transition from one-dimensional to two-dimensional discrete diffraction by varying the input probe beam position. The most pronounced discrete diffraction is observed along the crystal anisotropy direction

Light propagation in disordered aperiodic Mathieu photonic lattices

We present the numerical modeling of two different randomization methods of photonic lattices. We compare the results of light propagation in disordered aperiodic and disordered periodic lattices. In disordered aperiodic lattice disorder always enhances light transport for both methods, contrary to the disordered periodic lattice. For the highest disorder levels, we detect Anderson localization for both methods and both disordered lattices. More pronounced localization is observed for disordered aperiodic lattice

Light propagation in aperiodic photonic lattices created by synthesized Mathieu–Gauss beams

We investigate light propagation in a two-dimensional aperiodic refractive index lattice realized using the interference of multiple Mathieu–Gauss beams. We demonstrate experimentally and numerically that such a lattice effectively hinders linear light expansion and leads to light localization, compared to periodic photonic lattices in a photorefractive crystal. Most promisingly, we show that such an aperiodic lattice supports the nonlinear confinement of light in the form of soliton-like propagation that is robust with respect to changes in a wide range of intensities