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Register a new userSuppression of the critical collapse for one-dimensional solitons by saturable quintic nonlinear lattices
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The stabilization of one-dimensional solitons by a nonlinear lattice against the critical collapse in the focusing quintic medium is a challenging issue. We demonstrate that this purpose can be achieved by combining a nonlinearlatticeandsaturationofthequinticnonlinearity. Thesystemsupportsthreespeciesofsolitons, namely, fundamental (even-parity) ones and dipole (odd-parity) modes of on- and off-site-centered types. Very narrow fundamental solitons are found in an approximate analytical form, and systematic results for very broad unstable and moderately broad partly stable solitons, including their existence and stability areas, are produced by means of numerical methods. Stability regions of the solitons are identified by means of systematic simulations. The stability of all the soliton species obeys the Vakhitov-Kolokolov criterion.
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Thawatchai Mayteevarunyoo (Department of Telecommunicationn Engineering
, Mahanakorn University of Technology
, Bangkok
2008
We report results of a systematic analysis of spatial solitons in the model of 1D photonic crystals, built as a periodic lattice of waveguiding channels, of width D, separated by empty channels of width L-D. The system is characterized by its structural duty cycle, DC = D/L. In the case of the self-defocusing (SDF) intrinsic nonlinearity in the channels, one can predict new effects caused by competition between the linear trapping potential and the effective nonlinear repulsive one. Several species of solitons are found in the first two finite bandgaps of the SDF model, as well as a family of fundamental solitons in the semi-infinite gap of the system with the self-focusing nonlinearity. At moderate values of DC (such as 0.50), both fundamental and higher-order solitons populating the second bandgap of the SDF model suffer destabilization with the increase of the total power. Passing the destabilization point, the solitons assume a flat-top shape, while the shape of unstable solitons gets inverted, with local maxima appearing in empty layers. In the model with narrow channels (around DC =0.25), fundamental and higher-order solitons exist only in the first finite bandgap, where they are stable, despite the fact that they also feature the inverted shape.
We predict the existence of spatial-spectral vortex solitons in one-dimensional periodic waveguide arrays with quadratic nonlinear response. In such vortices the energy flow forms a closed loop through the simultaneous effects of phase gradients at the fundamental frequency and second-harmonic fields, and the parametric frequency conversion between the spectral components. The linear stability analysis shows that such modes are stable in a broad parameter region.
We observe experimentally two-dimensional solitons in superlattices comprising alternating deep and shallow waveguides fabricated via the femtosecond laser direct writing technique. We find that the symmetry of linear diffraction patterns as well as soliton shapes and threshold powers largely differ for excitations centered on deep and shallow sites. Thus, bulk and surface solitons centered on deep waveguides require much lower powers than their counterparts on shallow sites.
We develop stability analysis for matter-wave solitons in a two-dimensional (2D) Bose-Einstein condensate loaded in an optical lattice (OL), to which periodic time modulation is applied, in different forms. The stability is studied by dint of the variational approximation and systematic simulations. For solitons in the semi-infinite gap, well-defined stability patterns are produced under the action of the attractive nonlinearity, clearly exhibiting the presence of resonance frequencies. The analysis is reported for several time-modulation formats, including the case of in-phase modulations of both quasi-1D sublattices, which build the 2D square-shaped OL, and setups with asynchronous modulation of the sublattices. In particular, when the modulations of two sublattices are phase-shifted by {delta}={pi}/2, the stability map is not improved, as the originally well-structured stability pattern becomes fuzzy and the stability at high modulation frequencies is considerably reduced. Mixed results are obtained for anti-phase modulations of the sublattices ({delta}={pi}), where extended stability regions are found for low modulation frequencies, but for high frequencies the stability is weakened. The analysis is also performed in the case of the repulsive nonlinearity, for solitons in the first finite bandgap. It is concluded that, even though stability regions may be found, distinct stability boundaries for the gap solitons cannot be identified clearly. Finally, the stability is also explored for vortex solitons of both the square-shaped and rhombic types (i.e., off- and on-site-centered ones).
We consider self-trapping of topological modes governed by the one- and two-dimensional (1D and 2D) nonlinear-Schrodinger/Gross-Pitaevskii equation with effective single- and double-well (DW) nonlinear potentials induced by spatial modulation of the local strength of the self-defocusing nonlinearity. This setting, which may be implemented in optics and Bose-Einstein condensates, aims to extend previous studies, which dealt with single-well nonlinear potentials. In the 1D setting, we find several types of symmetric, asymmetric and antisymmetric states, focusing on scenarios of the spontaneous symmetry breaking. The single-well model is extended by including rocking motion of the well, which gives rise to Rabi oscillations between the fundamental and dipole modes. Analysis of the 2D single-well setting gives rise to stable modes in the form of ordinary dipoles, vortex-antivortex dipoles (VADs), and vortex triangles (VTs), which may be considered as produced by spontaneous breaking of the axial symmetry. The consideration of the DW configuration in 2D reveals diverse types of modes built of components trapped in the two wells, which may be fundamental states and vortices with topological charges m = 1 and 2, as well as VADs (with m = 0) and VTs (with m = 2).
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