Abstract:We study numerically the counterpropagating vector solitons in SBN:60 photorefractive crystals. A simple theory is provided for explaining the symmetry-breaking transverse instability of these solitons. Phase diagram is produced that depicts the transition from stable counterpropagating solitons to bidirectional waveguides to unstable optical structures. Numerical simulations are performed that predict novel dynamical beam structures, such as the standing-wave and rotating multipole vector solitonic clusters. For larger coupling strengths and/or thicker crystals the beams form unstable self-trapped optical structures that have no counterparts in the copropagating geometry.

We investigate numerically and theoretically solitons in highly nonlocal three-dimensional nematic liquid crystals. We calculate the fundamental soliton profiles using the modified Petviashvili method. We apply the variational method to the widely accepted scalar model of beam propagation in uniaxial nematic liquid crystals and compare the results with numerical simulations. To check the stability of such solutions, we propagate them in the presence of noise. We discover that the presence of any noise induces the fundamental solitons-the so-called nematicons-to breathe. Our results explain the difficulties in experimental observation of steady nematicons.

Physics of counterpropagating optical beams and spatial optical solitons is reviewed, including the formation of stationary states and spatiotemporal instabilities. First, several models describing the evolution and interactions between optical beams and spatial solitons are discussed, that propagate in opposite directions in nonlinear media. It is shown that coherent collisions between counterpropagating beams give rise to an interesting focusing mechanism resulting from the interference between the beams, and that interactions between such beams are insensitive to the relative phase between them. Second, recent experimental observations of the counterpropagation effects and instabilities in waveguides and bulk geometries, as well as in one-and two-dimensional photonic lattices are discussed. A variety of different generalizations of this concept are summarized, including the counterpropagating beams of complex structures, such as multipole beams and optical vortices, as well as the beams in different media, such as photorefractive materials and liquid crystals.

We demonstrate experimentally the existence of two transverse-dimensional counterpropagating (CP) incoherent spatial solitons in a 5 x 5 x 23 mm SBN:60Ce photorefractive crystal and investigate their dynamical behavior. We carry out numerical simulations that confirm our experimental findings. Substantially different behavior from the copropagating incoherent solitons is found. A symmetry breaking transition from stable overlapping CP solitons to unstable transversely displaced CP solitons is observed. We perform linear stability analysis that predicts the threshold for the split-up transition, in qualitative agreement with numerical simulations and experimental results.

Two-dimensional spatial solitonic lattices are generated and investigated experimentally and numerically in an SBN:Ce crystal. An enhanced stability of these lattices is achieved by exploiting the anisotropy of coherent soliton interaction, in particular the relative phase between soliton rows. Manipulation of individual soliton channels is achieved by use of supplementary control beams.PACS numbers: 05.45. Yv, 42.65Tg, 42.65.Sf. Wide (∼1 mm) Gaussian beams launched in a photorefractive (PR) crystal in the self-focusing regime tend to break into spatially disordered arrays of filaments, owing to transverse modulational instabilities [1]. However, ordered arrays of Gaussian beamlets (∼10 µm), launched in conditions appropriate to the generation of spatial screening solitons [2], form much more stable solitonic lattices. Weakly interacting pixel-like arrangements of solitons that can individually be addressed are interesting for applications as self-adaptive waveguides [3,4].Adaptive waveguides are of particular interest in alloptical information processing for their potential to generate large arrays, as well as for allowing many configurations with different interconnection possibilities. Spatial optical solitons are natural candidates for such applications, owing to their ability for self-adjustable waveguiding and versatile interaction capabilities, as demonstrated in light-induced Y and X couplers, beam splitters, directional couplers and waveguides. In addition to such few-beam configurations, the geometries with many solitons propagating in parallel-the so-called soliton pixels, arrays, or lattices-have been suggested for applications in information processing and image reconstruction [5,6,7,8]. Recently several groups demonstrated the formation of quadratic arrays of solitons in parametric amplifiers [8,9] and PR media, with coherent [7,10] and incoherent [4] beams.In this communication we combine the properties of spatial PR solitons to form pixel-like lattices, to investigate experimentally and numerically the generation and interactions in large arrays of spatial solitons. We achieve improved stability of solitonic lattices by utilizing anisotropic interaction between solitons, in particular the phase-dependent interaction between solitonic rows. We manipulate individual or pairs of solitons using incoherent and phase-sensitive control beams.Creation of solitonic lattices requires stable noninteracting propagation of arrays of self-focusing beams. A crucial feature in the parallel propagation of PR spatial solitons is their anisotropic mutual interaction [11]. Because the refractive index modulation induced by a single soliton reaches beyond its effective waveguide, phasedependent coherent as well as separation-dependent incoherent interactions, such as repulsion or attraction, may appear between the neighboring array elements. These interactions also affect the waveguiding characteristics of an individual solitonic channel. Therefore, the separation between solitons and their nearest-neighbor (NN) a...

The transfer of orbital angular momentum from vortex beams to optically induced photonic lattices is demonstrated. It is found that the sum of the angular momenta of interacting incoherent counterpropagating ͑CP͒ beams is not conserved, whereas their difference is. The sum of angular momenta of copropagating ͑CO͒ interacting beams is strictly conserved. It is also found that the transfer of angular momentum in CP interacting beams is minimal, amounting to a few percent, whereas the transfer in CO interacting beams is substantial, amounting to tens of percent. In fixed lattices, for both CP and CO beams, angular momentum is never conserved.

We investigate the propagation of light beams including Hermite-Gauss, Bessel-Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams -that is, the beams whose Fourier transforms are the beams themselves.

We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a π phase shift; no other recurrences are observed. Different from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.