We investigate, experimentally and theoretically, light propagation in one-dimensional waveguide arrays exhibiting a saturable self-defocusing nonlinearity. We demonstrate low-intensity “discrete diffraction”, and the high-intensity formation of spatial gap solitons arising from the first band of the transmission spectrum. The waveguide arrays are fabricated by titanium in-diffusion in a photorefractive copper-doped lithium niobate crystal, and the optical nonlinearity arises from the bulk photovoltaic effect.

The observation of nonlinear staggered surface states at the interface between a substrate and a one-dimensional self-defocusing nonlinear waveguide array is reported. Launching of staggered input beams of different power in the first channel of the array results in formation of localized structures in different channels. Our experimental results are confirmed numerically.

Dynamical properties of discrete solitons in nonlinear Schrödinger lattices with saturable nonlinearity are studied in the framework of the one-dimensional discrete Vinetskii-Kukhtarev model. Two stationary strongly localized modes, centered on site ($A$) and between two neighboring sites ($B$), are obtained. The associated Peierls-Nabarro potential is bounded and has multiple zeros indicating strong implications on the stability and dynamics of the localized modes. Besides a stable propagation of mode $A$, a stable propagation of mode $B$ is also possible. The enhanced ability of the large power solitons to move across the lattice is pointed out and numerically verified.

A problem of pulse propagation in a homogeneous nonlinear waveguide array with saturable nonlinearity is studied. The corresponding model equation is the discretized Vinetskii-Kukhtarev equation with neglected influence of diffusion of charge carriers. For periodic boundary conditions, exact homogeneous and oscillating stationary solutions are found. A wide instability region of the homogeneous, array-independent solution is identified. An approximate analytical solution for the bright one-dimensional discrete soliton where the energy is concentrated mainly in a few waveguides is obtained. The soliton stability is investigated both analytically and numerically and a cascade nature of the saturation mechanism is revealed.

We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disk’s plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, which differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying three-dimensional Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on the effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site, and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial.

We report on the formation of dark discrete solitons in a nonlinear periodic system consisting of evanescently coupled channel waveguides in defocusing lithium niobate. Localized nonlinear dark modes displaying a phase jump in the center that is located either on-channel (mode $A$) or in-between channels (mode $B$) are formed, which is to our knowledge the first experimental observation of mode $B$. By numerical simulations we find that the saturable nature of the nonlinearity is responsible for the improved stability of mode $B$. The ability of the induced refractive index structures to guide light of a low-power probe beam is demonstrated.