Gap solitons attached to a gapless layer

We consider linear and nonlinear modes pinned to a grating-free (gapless) layer placed between two symmetric or asymmetric semi-infinite Bragg gratings (BGs), with a possible phase shift between them, in a medium with the uniform Kerr nonlinearity. The asymmetry is defined by a difference between bandgap widths in the two BGs. In the linear system, exact defect modes (DMs) are found. Composite gap solitons pinned to the central layer are found too, in analytical and numerical forms, in the nonlinear model. In the asymmetric system, existence boundaries for the DMs and gap solitons, due to the competition between attraction to the gapless layer and repulsion from the reflectivity step, are obtained analytically. Stability boundaries for solitons in the asymmetric system are identified by means of direct simulations. Collisions of moving BG solitons with the gapless layer are studied too.Comment: 18 pages, 11 figures, J. Opt. Soc. Am. B, in pres

Two-dimensional χ2\chi^{2} solitons generated by the downconversion of Airy waves

Conversion of truncated Airy waves (AWs) carried by the second-harmonic (SH) component into axisymmetric $\chi^{2}$ solitons is considered in the 2D system with the quadratic nonlinearity. The spontaneous conversion is driven by the parametric instability of the SH wave. The input in the form of the AW vortex is considered too. As a result, one, two, or three stable solitons emerge in a well-defined form, unlike the recently studied 1D setting, where the picture is obscured by radiation jets. Shares of the total power captured by the emerging solitons and conversion efficiency are found as functions of parameters of the AW input.Comment: 4 pages, 6 figures, Optics Letters 2016 (in press

Generation of \c{hi}2 solitons from the Airy wave through the parametric instability

Spontaneous creation of solitons in quadratic media by the downconversion, i.e., parametric instability against the generation of fundamental-frequency excitations, from the truncated Airy-wave (AW) mode in the second-harmonic component is studied. Parameter regions are identified for the generation of one, two, and three solitons, with additional small-amplitude "jets". Shares of the total power carried by individual solitons are found. Also considered are soliton patterns generated by the downconversion from a pair of AWs bending in opposite directions.Comment: 4 pages, 6 figures, Optics Letters, in pres

Spontaneous symmetry breaking in a nonlinear double-well structure

We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates (BECs) and optical media, under the action of a potential with two symmetric minima. In the limit case when the NDWP structure is induced by the local nonlinearity coefficient represented by a set of two delta-functions, a fully analytical solution is obtained for symmetric, antisymmetric and asymmetric states. In this solvable model, the SSB bifurcation has a fully subcritical character. Numerical analysis, based on both direct simulations and computation of stability eigenvalues, demonstrates that, while the symmetric states are stable up to the SSB bifurcation point, both symmetric and emerging asymmetric states, as well as all antisymmetric ones, are unstable in the model with the delta-functions. In the general model with a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the SSB bifurcation from the subcritical to supercritical type. Antisymmetric solutions may also get stabilized in the NDWP structure of the general type, which gives rise to a bistability between them and asymmetric states. The symmetric states require a finite norm for their existence, an explanation to which is given. A full diagram for the existence and stability of the trapped states in the model is produced. Experimental observation of the predicted effects should be possible in BEC formed by several hundred atoms.Comment: submitted to Physical Review

Collapse and revival of oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap

In this work, we study parametric resonances in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical and analytical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric resonances (collapse and revival of the oscillations of the BEC width). Parametric resonances disappear when one of the competing factors i.e strength of harmonic trap or the strength of optical lattice dominates. Parametric instabilities (exponential growth of Bogoliubov modes) arise for large variations in the strength of the optical lattice.Comment: 9 pages, 20 figure

Coupled-mode theory for spatial gap solitons in optically-induced lattices

We develop a coupled-mode theory for spatial gap solitons in the one-dimensional photonic lattices induced by interfering optical beams in a nonlinear photorefractive crystal. We derive a novel system of coupled-mode equations for two counter-propagating probe waves, and find its analytical solutions for stationary gap solitons. We also predict the existence of moving (or tilted) gap solitons and study numerically soliton collisions.Comment: 3 pages, submitted to Optics Letter