Solitons and vortices in nonlinear potential wells

Abstract

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).

Journal of Optics, in press (a special issue on Singular Optics and Topological Photonics)

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Cited by in corpus (10)

• Multidimensional solitons: Well-established results and novel findings
• Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension
• Rotating vortex clusters in media with inhomogeneous defocusing nonlinearity
• Bubbles and W-shaped solitons in Kerr media with fractional diffraction
• Dipolar bright solitons and solitary vortices in a radial lattice
• Two-color soliton meta-atoms and molecules
• Localized modes in the Gross-Pitaevskii equation with a parabolic trapping potential and a nonlinear lattice pseudopotential
• Symmetry breaking in competing single-well linear-nonlinear potentials
• Quantum Scattering States in a Nonlinear Coherent Medium
• Exact States in Waveguides With Periodically Modulated Nonlinearity