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Zeng L, Shi J, Li J, Li J, Wang Q. Dark soliton families in quintic nonlinear lattices. OPTICS EXPRESS 2022; 30:42504-42511. [PMID: 36366703 DOI: 10.1364/oe.472311] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2022] [Accepted: 10/17/2022] [Indexed: 06/16/2023]
Abstract
We prove that the dark solitons can be stable in the purely quintic nonlinear lattices, including the fundamental, tripole and five-pole solitons. These dark soliton families are generated on the periodic nonlinear backgrounds. The propagation constant affects the forms of these solitons, while the number of poles does not lead to the variation of the backgrounds. The dark solitons are stable only when the propagation constant is moderately large.
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Ma X, Driben R, Malomed BA, Meier T, Schumacher S. Two-dimensional symbiotic solitons and vortices in binary condensates with attractive cross-species interaction. Sci Rep 2016; 6:34847. [PMID: 27703235 PMCID: PMC5050495 DOI: 10.1038/srep34847] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Accepted: 09/12/2016] [Indexed: 11/09/2022] Open
Abstract
We consider a two-dimensional (2D) two-component spinor system with cubic attraction between the components and intra-species self-repulsion, which may be realized in atomic Bose-Einstein condensates, as well as in a quasi-equilibrium condensate of microcavity polaritons. Including a 2D spatially periodic potential, which is necessary for the stabilization of the system against the critical collapse, we use detailed numerical calculations and an analytical variational approximation (VA) to predict the existence and stability of several types of 2D symbiotic solitons in the spinor system. Stability ranges are found for symmetric and asymmetric symbiotic fundamental solitons and vortices, including hidden-vorticity (HV) modes, with opposite vorticities in the two components. The VA produces exceptionally accurate predictions for the fundamental solitons and vortices. The fundamental solitons, both symmetric and asymmetric ones, are completely stable, in either case when they exist as gap solitons or regular ones. The symmetric and asymmetric vortices are stable if the inter-component attraction is stronger than the intra-species repulsion, while the HV modes have their stability region in the opposite case.
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Affiliation(s)
- Xuekai Ma
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
| | - Rodislav Driben
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
| | - Torsten Meier
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
| | - Stefan Schumacher
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
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Driben R, Kartashov YV, Malomed BA, Meier T, Torner L. Soliton gyroscopes in media with spatially growing repulsive nonlinearity. PHYSICAL REVIEW LETTERS 2014; 112:020404. [PMID: 24483996 DOI: 10.1103/physrevlett.112.020404] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2013] [Indexed: 06/03/2023]
Abstract
We find that the recently introduced model of self-trapping supported by a spatially growing strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, i.e., three-dimensional vortex solitons, with topological charges S≥1. The family with S=1 is completely stable, while the one with S=2 has alternating regions of stability and instability. The families are nearly exactly reproduced in an analytical form by the Thomas-Fermi approximation. Unstable states with S=2 and 3 split into persistently rotating pairs or triangles of unitary vortices. Application of a moderate torque to the vortex torus initiates a persistent precession mode, with the torus' axle moving along a conical surface. A strong torque heavily deforms the vortex solitons, but, nonetheless, they restore themselves with the axle oriented according to the vectorial addition of angular momenta.
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Affiliation(s)
- Rodislav Driben
- Department of Physics & CeOPP, University of Paderborn, Warburger Straße 100, Paderborn D-33098, Germany and Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
| | - Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain and Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 142190, Russia
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
| | - Torsten Meier
- Department of Physics & CeOPP, University of Paderborn, Warburger Straße 100, Paderborn D-33098, Germany
| | - Lluis Torner
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain
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Mayteevarunyoo T, Malomed BA, Roeksabutr A. Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type. OPTICS EXPRESS 2011; 19:17834-17851. [PMID: 21935151 DOI: 10.1364/oe.19.017834] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Solitons in the model of nonlinear photonic crystals with the transverse structure based on two-dimensional (2D) quadratic- or rhombic-shaped Kronig-Penney (KP) lattices are studied by means of numerical methods. The model can also applies to a Bose-Einstein condensate (BEC) trapped in a superposition of linear and nonlinear 2D periodic potentials. The analysis is chiefly presented for the self-repulsive nonlinearity, which gives rise to several species of stable fundamental gap solitons, dipoles, four-peak complexes, and vortices in two finite bandgaps of the underlying spectrum. Stable solitons with complex shapes are found, in particular, in the second bandgap of the KP lattice with the rhombic structure. The stability of the localized modes is analyzed in terms of eigenvalues of small perturbations, and tested in direct simulations. Depending on the value of the KP's duty cycle (DC, i.e., the ratio of the void's width to the lattice period), an internal stability boundary for the solitons and vortices may exist inside of the first bandgap. Otherwise, the families of the localized modes are entirely stable or unstable in the bandgaps. With the self-attractive nonlinearity, only unstable solitons and vortices are found in the semi-infinite gap.
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Affiliation(s)
- Thawatchai Mayteevarunyoo
- Department of Telecommunication Engineering, Mahanakorn University of Technology, Bangkok, Thailand.
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Feng M, Liu Y, Li Y, Xie X, Zhou J. Light propagation in a resonantly absorbing waveguide array. OPTICS EXPRESS 2011; 19:7222-7229. [PMID: 21503034 DOI: 10.1364/oe.19.007222] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Light propagation behavior in a resonantly absorbing waveguide array is analyzed. Both a Lorentzian line shape and an inhomogeneous broadened absorbing line shape are considered, with their imaginary and real part of the refractive index determined by a Kramers-Kronig relationship. The diffracted wave is shown to have the frequency spectra determined by the material absorption, dispersion as well as the waveguide structure. An interesting phenomenon is that a spectral hole is produced and becomes deeper in the diffraction spectrum as the thickness of the resonantly absorbing waveguide array increases. The experimental measurements conducted in a waveguide array are found to be in good agreement with the numerical results.
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Affiliation(s)
- Mingneng Feng
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China
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Wang C, Theocharis G, Kevrekidis PG, Whitaker N, Law KJH, Frantzeskakis DJ, Malomed BA. Two-dimensional paradigm for symmetry breaking: the nonlinear Schrödinger equation with a four-well potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:046611. [PMID: 19905475 DOI: 10.1103/physreve.80.046611] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2009] [Revised: 08/27/2009] [Indexed: 05/28/2023]
Abstract
We study the existence and stability of localized modes in the two-dimensional (2D) nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation with a symmetric four-well potential. Using the corresponding four-mode approximation, we trace the parametric evolution of the trapped stationary modes, starting from the linear limit, and thus derive a complete bifurcation diagram for families of the stationary modes. This provides the picture of spontaneous symmetry breaking in the fundamental 2D setting. In a broad parameter region, the predictions based on the four-mode decomposition are found to be in good agreement with full numerical solutions of the NLS/GP equation. Stability properties of the stationary states coincide with those suggested by the corresponding discrete model in the large-amplitude limit. The dynamics of unstable modes is explored by means of direct simulations. Finally, in addition to the full analysis for the case of the self-attractive nonlinearity, the bifurcation diagram for the case of self-repulsion is briefly considered too.
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Affiliation(s)
- C Wang
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
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Maluckov A, Hadzievski L, Malomed BA. Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:036604. [PMID: 18517540 DOI: 10.1103/physreve.77.036604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2007] [Indexed: 05/26/2023]
Abstract
Results of a comprehensive dynamical analysis are reported for several fundamental species of bright solitons in the one-dimensional lattice modeled by the discrete nonlinear Schrödinger equation with the cubic-quintic nonlinearity. Staggered solitons, which were not previously considered in this model, are studied numerically, through the computation of the eigenvalue spectrum for modes of small perturbations, and analytically, by means of the variational approximation. The numerical results confirm the analytical predictions. The mobility of discrete solitons is studied by means of direct simulations, and semianalytically, in the framework of the Peierls-Nabarro barrier, which is introduced in terms of two different concepts, free energy and mapping analysis. It is found that persistently moving localized modes may only be of the unstaggered type.
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