Nonlinear photonic lattices in anisotropic nonlocal self-focusing media

Abstract

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 ...

Matter-wave solitons supported by field-induced dipole-dipole repulsion with spatially modulated strength

“…Numerical computations yield stable even and odd states trapped in the double-well modulation profile (29). Typical examples of such localized modes are shown in Fig.…”

“…The comparison of the corresponding values of Hamiltonian (12), as a function of parameter g 0 in Eq. (29), is shown in Fig. 12(a).…”

“…The DDIs account for a number of remarkable phenomena in ultracold Bose gases [9]- [11], such as various pattern-formation scenarios [12][13][14][15][16], fractional domain walls [17], d -wave collapse [18,19], specific possibilities for precision measurements [20][21][22], stabilization of the dipolar BEC by optical lattices [23,24], the Einstein -de Haas effect [25], etc. Dipolar BECs can be also used as matter-wave simulators [26], to emulate, in particular, the creation of multi-dimensional solitons via the nonlocal nonlinearity-a subject which has also drawn much attention in optics, where nonlocal interactions of other types (with different interaction kernels) occur too [27][28][29]. In fact, the dipolar condensates not only emulate the situation known in optics, but also make it possible to predict the existence of solitons with novel properties.…”

Structure analysis of two-dimensional nonlinear self-trapped photonic lattices in anisotropic photorefractive media

“…When the lattice constant gets too small, the nonlocality of the induced refractive index change leads to interactions between neighboring solitons and these interactions result in a strong instability of in-phase soliton arrays. In contrast, the recently demonstrated twodimensional lattices of out-of-phase solitons can be made robust with smaller lattice spacing [9]. The phase profile of such waves resembles a chessboard pattern with lines of π-phase jumps between neighboring sites.…”

“…To analyze the structure of the induced refractive index change, two different methods can be used. The first method is given by observing the waveguiding properties of the lattice [9,10,11]. As the incident light pattern induces a periodic array of waveguides in the medium, illuminating the lattice with a broad plane wave leads to guiding of this wave and the output intensity pattern of the guided wave qualitatively maps the induced refractive index change.…”