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.

Numerical methods for generation and characterization of disordered aperiodic photonic lattices.

We introduce numerical modeling of two different methods for the deterministic randomization of two-dimensional aperiodic photonic lattices based on Mathieu beams, optically induced in a photorefractive media. For both methods we compare light transport and localization in such lattices along the propagation, for various disorder strengths. A disorder-enhanced light transport is observed for all disorder strengths. With increasing disorder strength light transport becomes diffusive-like and with further increase of disorder strength the Anderson localization is observed. This trend is more noticeable for longer propagation distances. The influence of input lattice intensity on the localization effects is studied. The difference in light transport between two randomization methods is attributed to various levels of input lattice intensity. We observe more pronounced localization for one of the methods. Localization lengths differ along different directions, due to the crystal and lattice anisotropy. We analyze localization effects comparing uniform and on-site probe beam excitation positions and different probe beam widths.

Light transport and localization in disordered aperiodic Mathieu lattices.

Complex optical systems such as deterministic aperiodic Mathieu lattices are known to hinder light diffraction in a manner comparable to randomized optical systems. We systematically incorporate randomness in our complex optical system, measuring its relative contribution of randomness, to understand the relationship between randomness and complexity. We introduce an experimental method for the realization of disordered aperiodic Mathieu lattices with numerically controlled disorder degree. Added disorder always enhances light transport. For lower disorder degrees, we observe diffusive-like transport, and in the range of highest light transport, we detect Anderson localization. With further increase of disorder degree, light transport is slowly decreasing and localization length decreases indicating more pronounced Anderson localization. Numerical investigation at longer propagation distances indicates that the threshold of Anderson localization detection is shifted to lower disorder degrees.

Morphing discrete diffraction in nonlinear Mathieu lattices.

Discrete optical gratings are essential components to customize structured light waves, determined by the band structure of the periodic potential. Beyond fabricating static devices, light-driven diffraction management requires nonlinear materials. Up to now, nonlinear self-action has been limited mainly to discrete spatial solitons. Discrete solitons, however, are restricted to the eigenstates of the photonic lattice. Here, we control light formation by nonlinear discrete diffraction, allowing for versatile output diffraction states. We observe morphing of diffraction structures for discrete Mathieu beams propagating nonlinearly in photosensitive media. The self-action of a zero-order Mathieu beam in a nonlinear medium shows characteristics similar to discrete diffraction in one-dimensional waveguide arrays. Mathieu beams of higher orders show discrete diffraction along curved paths, showing the fingerprint of respective two-dimensional photonic lattices.

Soliton formation by decelerating interacting Airy beams.

We demonstrate a new type of soliton formation arising from the interaction of multiple two-dimensional Airy beams in a nonlinear medium. While in linear regime, interference effects of two or four spatially displaced Airy beams lead to accelerated intensity structures that can be used for optical induction of novel light guiding refractive index structures, the nonlinear cross-interaction between the Airy beams decelerates their bending and enables the formation of straight propagating solitary states. Our experimental results represent an intriguing combination of two fundamental effects, accelerated optical beams and nonlinearity, together enable novel mechanisms of soliton formation that will find applications in all-optical light localization and switching architectures. Our experimental results are supported by corresponding numerical simulations.

Counterpropagating solitons at boundary of photonic lattices.

We study numerically the interaction of two counterpropagating (CP) optical beams near the boundary of a truncated one-dimensional photonic lattice. We demonstrate that the mutual coupling of beams suppresses the effective repulsion from the lattice edge, resulting in the formation of CP surface solitons. Such localized beams may propagate in the same, as well as in neighboring, waveguides. We also reveal that the lattice disorder reduces substantially the threshold power for the formation of CP surface states.