We analyze theoretically and generate experimentally two-dimensional nonlinear periodic lattices in a photorefractive medium. We demonstrate that the light-induced periodically modulated nonlinear refractive index is highly anisotropic and nonlocal, and it depends on the lattice orientation relative to the crystal axis. We discuss stability of such induced photonic structures and their guiding properties.The study of nonlinear effects in periodic photonic structures recently attracted strong interest because of many novel possibilities to control light propagation, steering and trapping. Periodic modulation of the refractive index modifies the linear spectrum and wave diffraction and consequently strongly affects the nonlinear propagation and localization of light [1].Photonic lattices can be optically induced by linear diffraction-free light patterns created by interfering several plane waves [2]. However, the induced change of the refractive index depends on the light intensity and, in the nonlinear regime, it is accompanied by the selfaction effect [3]. The nonlinear diffraction-free light patterns in the form of stable self-trapped periodic waves can propagate without change in their profile, becoming the eigenmodes of the self-induced periodic potentials. This behavior is generic, since nonlinear periodic waves can exist in many types of nonlinear systems, and they provide a simple realization of nonlinear photonic crystals. Such structures are "flexible" because the lattice is modified and shaped by the nonlinear medium; these flexible lattices extend the concept of optically-induced gratings beyond the limits of weak material nonlinearity. Moreover, the nonlinear lattices offer many novel possibilities for the study of nonlinear effects in periodic systems because they can interact with localized signal beams via the cross-phase modulation and can form a composite bound states [4,5].Nonlinear photonic lattices created by two-dimensional arrays of in-phase solitons have recently been demonstrated experimentally in parametric processes [6], and in photorefractive crystals with both coherent [7] and partially incoherent [3,5,8] light. For the case of twodimensional arrays of in-phase solitons created by the amplitude modulation, every pixel of the lattice induces a waveguide which can be manipulated by an external steering beam [7,8,9]. However, the spatial periodicity of these lattices is limited by attractive soliton interaction that may leads to their strong instability. In contrast, the recently suggested two-dimensional lattices of out-ofphase solitons are known to be robust in isotropic saturable model [10]. The phase profile of such self-trapped waves resembles chessboard with the lines of π-phase jumps between neighboring white and black sites.In this Letter, we study two-dimensional nonlinear lattices with a chessboard phase structure in anisotropic nonlocal self-focusing media and generate such lattices experimentally in a photorefractive crystal. We demonstrate that the light-induced periodically ...

We predict theoretically and generate in a photorefractive crystal two-dimensional self-trapped periodic waves of different symmetries, including vortex lattices-patterns of phase dislocations with internal energy flows. We demonstrate that these nonlinear waves exist even with anisotropic nonlocal nonlinearity when the optically-induced periodic refractive index becomes highly anisotropic, and it depends on the orientation of the two-dimensional lattice relative to the crystallographic c-axis.

As the formation of spatial optical solitons in photorefractive media is governed by modification of the refractive index every single solitons in complex configurations of solitons can act as a single waveguide for other light beams. In this article we demonstrate guiding of amplitude modulated beams in complex configurations of photorefractive solitons carrying information and we analyze the received signal in the kHz frequency range. The possibility of data transmission combined with waveguide couplers opens the route to all-optical networks.

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