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Li C, Kartashov YV. Stable Vortex Solitons Sustained by Localized Gain in a Cubic Medium. PHYSICAL REVIEW LETTERS 2024; 132:213802. [PMID: 38856259 DOI: 10.1103/physrevlett.132.213802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Revised: 03/19/2024] [Accepted: 04/22/2024] [Indexed: 06/11/2024]
Abstract
We propose a simple dissipative system with purely cubic defocusing nonlinearity and nonuniform linear gain that can support stable localized dissipative vortex solitons with high topological charges without the utilization of competing nonlinearities and nonlinear gain or losses. Localization of such solitons is achieved due to an intriguing mechanism when defocusing nonlinearity stimulates energy flow from the ringlike region with linear gain to the periphery of the medium where energy is absorbed due to linear background losses. Vortex solitons bifurcate from linear gain-guided vortical modes with eigenvalues depending on topological charges that become purely real only at specific gain amplitudes. Increasing gain amplitude leads to transverse expansion of vortex solitons, but simultaneously it usually also leads to stability enhancement. Increasing background losses allows creation of stable vortex solitons with high topological charges that are usually prone to instabilities in conservative and dissipative systems. Propagation of the perturbed unstable vortex solitons in this system reveals unusual dynamical regimes, when instead of decay or breakup, the initial state transforms into stable vortex solitons with lower or sometimes even with higher topological charge. Our results suggest an efficient mechanism for the formation of nonlinear excited vortex-carrying states with suppressed destructive azimuthal modulational instabilities in a simple setting relevant to a wide class of systems, including polaritonic systems, structured microcavities, and lasers.
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Affiliation(s)
- Chunyan Li
- School of Physics, Xidian University, Xi'an 710071, China
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
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Dong L, Kartashov YV, Torner L, Ferrando A. Vortex Solitons in Twisted Circular Waveguide Arrays. PHYSICAL REVIEW LETTERS 2022; 129:123903. [PMID: 36179208 DOI: 10.1103/physrevlett.129.123903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Revised: 06/19/2022] [Accepted: 08/08/2022] [Indexed: 06/16/2023]
Abstract
We address the formation of topological states in twisted circular waveguide arrays and find that twisting leads to important differences of the fundamental properties of new vortex solitons with opposite topological charges that arise in the nonlinear regime. We find that such system features the rare property that clockwise and counterclockwise vortex states are nonequivalent. Focusing on arrays with C_{6v} discrete rotation symmetry, we find that a longitudinal twist stabilizes the vortex solitons with the lowest topological charges m=±1, which are always unstable in untwisted arrays with the same symmetry. Twisting also leads to the appearance of instability domains for otherwise stable solitons with m=±2 and generates vortex modes with topological charges m=±3 that are forbidden in untwisted arrays. By and large, we establish a rigorous relation between the discrete rotation symmetry of the array, its twist direction, and the possible soliton topological charges.
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Affiliation(s)
- Liangwei Dong
- Department of Physics, Shaanxi University of Science and Technology, Xi'an 710021, China
| | - Yaroslav V Kartashov
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
| | - Lluis Torner
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
| | - Albert Ferrando
- Institut de Ciència de Materials (ICMUV), Universitat de València, C/ Catedrático José Beltrán, 2, E-46980 Paterna, Spain
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3
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Barkhausen F, Schumacher S, Ma X. Multistable circular currents of polariton condensates trapped in ring potentials. OPTICS LETTERS 2020; 45:1192-1195. [PMID: 32108803 DOI: 10.1364/ol.386250] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Accepted: 01/27/2020] [Indexed: 06/10/2023]
Abstract
We demonstrate the formation and trapping of different stationary solutions, oscillatory solutions, and rotating solutions of a polariton condensate in a planar semiconductor microcavity with a built-in ring-shaped potential well. Multistable ring-shaped solutions are trapped in shallow potential wells. These solutions have the same ring-shaped density distribution but different topological charges, corresponding to different orbital angular momentum (OAM) of the emitted light. For stronger confinement potentials, besides the fundamental modes, higher excited (dipole) modes can also be trapped. If two modes are excited simultaneously, their beating produces a complex oscillation or rotation dynamics. When the two modes have the same OAM, a double-ring solution forms for which the density oscillates between the inner and the outer ring. When the two modes have different OAM, a rotating solution with fractional OAM is created.
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Zhang X, Xu X, Zheng Y, Chen Z, Liu B, Huang C, Malomed BA, Li Y. Semidiscrete Quantum Droplets and Vortices. PHYSICAL REVIEW LETTERS 2019; 123:133901. [PMID: 31697515 DOI: 10.1103/physrevlett.123.133901] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2019] [Revised: 08/01/2019] [Indexed: 06/10/2023]
Abstract
We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap by the Lee-Hung-Yang correction (produced by quantum fluctuations around the MF state), stable on-site- and intersite-centered semidiscrete quantum droplets (QDs) emerge in the array, as fundamental ones and self-trapped vortices, with winding numbers, at least, up to five, in both tightly bound and quasicontinuum forms. The application of a relatively strong trapping potential leads to squeezing transitions, which increase the number of sites in fundamental QDs and eventually replace vortex modes by fundamental or dipole ones. The results provide the first realization of stable semidiscrete vortex QDs, including ones with multiple vorticity.
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Affiliation(s)
- Xiliang Zhang
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Xiaoxi Xu
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Yiyin Zheng
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Zhaopin Chen
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and the Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
| | - Bin Liu
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Chunqing Huang
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Boris A Malomed
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and the Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
| | - Yongyao Li
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and the Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
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He ZM, Wen L, Wang YJ, Chen GP, Tan RB, Dai CQ, Zhang XF. Dynamics and pattern formation of ring dark solitons in a two-dimensional binary Bose-Einstein condensate with tunable interactions. Phys Rev E 2019; 99:062216. [PMID: 31330622 DOI: 10.1103/physreve.99.062216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Indexed: 06/10/2023]
Abstract
We investigate the dynamics and pattern formation of two ring dark solitons in a two-dimensional binary Bose-Einstein condensate with tunable intercomponent interaction via numerical simulation of the time-dependent Gross-Pitaevskii equation. Both the black and gray ring dark solitons are considered for cases where the modulation frequency of the intercomponent interaction is resonant or nonresonant with the one of the trapping potential. Our results show that in the presence of periodic modulation of the intercomponent interaction not only are the lifetimes of the ring dark solitons largely extended but also their decaying dynamics are dramatically affected. Before snaking instability sets in, new ring dark solitons are formed, and both the numbers and depths of the ring dark solitons exhibit collective oscillations. With the development of instability, the system exhibits different decaying processes, and a variety of decay profiles, such as vortex necklace, distorted octagon, vortex-antivortex ring, and cross, are formed, showing a strong dependence on the modulation frequency of the intercomponent interaction and the initial depth of the ring dark soliton.
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Affiliation(s)
- Zhang-Ming He
- College of Science, Hunan University of Technology, Zhuzhou 412007, China
| | - L Wen
- College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 400047, China
| | - Ya-Jun Wang
- Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China
- School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China
| | - G P Chen
- School of Physics and Mechtronic Engineering, Sichuan University of Art and Science, Dazhou 635000, China
| | - R-B Tan
- College of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing 401331, China
| | - C-Q Dai
- School of Sciences, Zhejiang A&F University, Lin'an, Zhejiang 311300, China
| | - Xiao-Fei Zhang
- Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China
- School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China
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Kartashov YV, Zezyulin DA. Stable Multiring and Rotating Solitons in Two-Dimensional Spin-Orbit-Coupled Bose-Einstein Condensates with a Radially Periodic Potential. PHYSICAL REVIEW LETTERS 2019; 122:123201. [PMID: 30978069 DOI: 10.1103/physrevlett.122.123201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Revised: 12/10/2018] [Indexed: 06/09/2023]
Abstract
We consider two-dimensional spin-orbit-coupled atomic Bose-Einstein condensate in a radially periodic potential. The system supports different types of stable self-sustained states including radially symmetric vorticity-carrying modes with different topological charges in two spinor components that may have multiring profiles and at the same time remain remarkably stable for repulsive interactions. Solitons of the second type show persistent rotation with constant angular frequency. They can be stable for both repulsive and attractive interatomic interactions. Because of the inequivalence between clockwise and counterclockwise rotation directions introduced by spin-orbit coupling, the properties of such solitons strongly differ for positive and negative rotation frequencies. The collision of solitons located in the same or different rings is accompanied by a change of the rotation frequency that depends on the phase difference between colliding solitons.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
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Izdebskaya YV, Shvedov VG, Jung PS, Krolikowski W. Stable vortex soliton in nonlocal media with orientational nonlinearity. OPTICS LETTERS 2018; 43:66-69. [PMID: 29328198 DOI: 10.1364/ol.43.000066] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2017] [Accepted: 11/23/2017] [Indexed: 06/07/2023]
Abstract
We report on the first experimental observation of stable vortex solitons in nematic liquid crystals with nonlocal nonlinear reorientational response. We show how these nonlinear vortex beams can be formed and confined in extraordinary optical waves by employing the cell with no lateral boundary conditions and the application of an external magnetic field that effectively controls the molecular direction and propagation of the self-trapped beams. We also find that these vortex solitons can be generated in certain ranges of the input beam power.
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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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9
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Diebel F, Boguslawski M, Dadalyan T, Drampyan R, Denz C. Controlled soliton formation in tailored Bessel photonic lattices. OPTICS EXPRESS 2016; 24:12933-12940. [PMID: 27410312 DOI: 10.1364/oe.24.012933] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Azimuthally modulated higher order rotationally symmetric Bessel-like optical patterns were generated by coherent superposition of two co-propagating Bessel beams - either in or out of phase. By changing the distance between the beam centers, a whole variety of transition states can be realized. As one prominent example, a 4-fold symmetry quadrupole-like photonic structure was optically inducted in an SBN crystal and nonlinear beam propagation in such a photonic wave-guiding structure is investigated in both self-focusing and self-defocusing regimes. The proposed device serves as an all-optical 2d 1 × 4 photonic interconnect.
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Kartashov YV, Konotop VV, Torner L. Topological States in Partially-PT-Symmetric Azimuthal Potentials. PHYSICAL REVIEW LETTERS 2015; 115:193902. [PMID: 26588383 DOI: 10.1103/physrevlett.115.193902] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2015] [Indexed: 06/05/2023]
Abstract
We introduce partially-parity-time (pPT)-symmetric azimuthal potentials composed from individual PT-symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potential excitations carrying topological dislocations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such nonconservative ratchetlike structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully-PT-symmetric potentials. The vortex solitons in the pPT- and PT-symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region 142190, Russia
| | - Vladimir V Konotop
- Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande 2, Edifício C8, Lisboa 1749-016, Portugal
| | - Lluis Torner
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Universitat Politecnica de Catalunya, 08034 Barcelona, Spain
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11
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Huang C, Ye F, Malomed BA, Kartashov YV, Chen X. Solitary vortices supported by localized parametric gain. OPTICS LETTERS 2013; 38:2177-2180. [PMID: 23811869 DOI: 10.1364/ol.38.002177] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We demonstrate the existence and stability of bright vortex solitons sustained by a ring-shaped parametric gain, for both focusing and defocusing Kerr nonlinearities in lossy optical media. With the defocusing nonlinearity, the vortices are stable at all values of the detuning parameter, while under the focusing nonlinearity their stability region is limited to some positive values of the detuning. Unstable vortices in the focusing medium transform into stable rotating azimuthons.
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Affiliation(s)
- Changming Huang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Physics Department, Shanghai Jiao Tong University, Shanghai 200240, China
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12
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Kartashov YV, Vysloukh VA, Torner L. Solitons in spiraling Vogel lattices. OPTICS LETTERS 2013; 38:190-192. [PMID: 23454958 DOI: 10.1364/ol.38.000190] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We address light propagation in Vogel optical lattices and show that such lattices support a variety of stable soliton solutions in both self-focusing and self-defocusing media, whose propagation constants belong to domains resembling gaps in the spectrum of a truly periodic lattice. The azimuthally rich structure of Vogel lattices allows generation of spiraling soliton motion.
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Affiliation(s)
- Yaroslav V Kartashov
- Institut de Ciencies Fotoniques (ICFO) and Universitat Politecnica de Catalunya, Castelldefels, Barcelona 08860, Spain.
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Soto-Crespo JM, Akhmediev N, Mejia-Cortés C, Devine N. Dissipative ring solitons with vorticity. OPTICS EXPRESS 2009; 17:4236-4250. [PMID: 19293847 DOI: 10.1364/oe.17.004236] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation. In dissipative media, radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters. Beyond the region of stability, the solitons lose the radial symmetry but may remain stable, keeping the same value of the topological charge. We have found bifurcations into solitons with n-fold bending symmetry, with n independent on m. Solitons without circular symmetry can also display (m + 1)-fold modulation behaviour. A sequence of bifurcations can transform the ring soliton into a pulsating or chaotic state which keeps the same value of the topological charge as the original ring.
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Affiliation(s)
- J M Soto-Crespo
- Instituto de Optica, C.S.I.C., Serrano 121, 28006 Madrid, Spain.
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Dong L, Wang J, Wang H, Yin G. Broken ring solitons in Bessel optical lattices. OPTICS LETTERS 2008; 33:2989-2991. [PMID: 19079516 DOI: 10.1364/ol.33.002989] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We address the existence of ring solitons broken by several nodes in a defocusing saturable nonlinear medium with an imprinted Bessel optical lattice. Such a multipolelike soliton is composed of two or more arc patterns with opposite phase between the adjacent components. The width of existence domain is determined only by the saturation degree of medium. The maximum number of soliton components depends on the radius of the lattice ring, where they reside. Those novel solitons can be trapped entirely on any ring of the Bessel lattice provided that the lattice is modulated deep enough. This study offers a smooth transition from the multipole soliton to necklace soliton.
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Affiliation(s)
- Liangwei Dong
- Institute of Information Optics, Zhejiang Normal University, Jinhua, China.
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Kartashov YV, Vysloukh VA, Torner L. Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index. OPTICS LETTERS 2008; 33:2173-2175. [PMID: 18830342 DOI: 10.1364/ol.33.002173] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We address vortex solitons supported by optical lattices featuring modulation of both the linear and nonlinear refractive indices. We find that when the modulation is out of phase the competition between both effects results in remarkable shape transformations of the solitons that profoundly affect their properties and stability. Nonlinear refractive index modulation is found to impose restrictions on the maximal power of off-site solitons, which are shown to be stable only below a maximum nonlinearity modulation depth.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, Barcelona, Spain.
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16
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Dong L, Wang H. Surface solitons supported by Bessel optical potential. OPTICS EXPRESS 2007; 15:1706-1711. [PMID: 19532407 DOI: 10.1364/oe.15.001706] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
A simple but new model, an interface separated by 1-D Bessel optical potential with different modulation depth on the opposite side of the interface was proposed. We show this model can support stable surface solitons. Surface solitons form because diffraction and defocusing nonlinearity are balanced by the Bessel potential. We demonstrate numerically such solitons are stable in their entire existence domain even for higher-order Bessel potential.
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17
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Baizakov BB, Malomed BA, Salerno M. Matter-wave solitons in radially periodic potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:066615. [PMID: 17280170 DOI: 10.1103/physreve.74.066615] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2006] [Revised: 08/16/2006] [Indexed: 05/13/2023]
Abstract
We investigate two-dimensional (2D) states in Bose-Einstein condensates with self-attraction or self-repulsion, trapped in an axially symmetric optical-lattice potential periodic along the radius. The states trapped both in the central potential well and in remote circular troughs are studied. In the repulsive mode, a new soliton species is found, in the form of radial gap solitons. The latter solitons are completely stable if they carry zero vorticity (l=0) , while with l not equal 0 they develop a weak azimuthal modulation, which makes them rotating patterns, that persist indefinitely long. In addition, annular gap solitons may support stable azimuthal dark-soliton pairs on their crests. In remote troughs of the attractive model, stable localized states may assume a ringlike shape with weak azimuthal modulation, or shrink into solitons strongly localized in the azimuthal direction, which is explained in the framework of an averaged 1D equation with the cyclic azimuthal coordinate. Numerical simulations of the attractive model also reveal stable necklacelike patterns, built of several strongly localized peaks. Dynamics of strongly localized solitons circulating in the troughs is studied too. While the solitons with sufficiently small velocities are completely stable, fast solitons gradually decay, due to the leakage of matter into the adjacent trough, under the action of the centrifugal force. Investigation of head-on collisions between strongly localized solitons traveling in circular troughs shows that collisions between in-phase solitons in a common trough lead to collapse, while pi-out-of-phase solitons bounce many times, but eventually merge into a single one, without collapsing. In-phase solitons colliding in adjacent circular troughs also tend to merge into a single soliton.
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Affiliation(s)
- Bakhtiyor B Baizakov
- Physical-Technical Institute of the Uzbek Academy of Sciences, 2-b, G. Mavlyanov Strasse, 700084, Tashkent, Uzbekistan
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Wang X, Chen Z, Yang J. Guiding light in optically induced ring lattices with a low-refractive-index core. OPTICS LETTERS 2006; 31:1887-9. [PMID: 16729104 DOI: 10.1364/ol.31.001887] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
We demonstrate a ring-shaped Bessel-like photonic lattice akin to a photonic bandgap fiber with a low-index core. While the ring lattice is optically induced in a bulk crystal with a self-defocusing nonlinearity, guidance of a probe beam propagating linearly through the core is clearly observed. The possible mechanism for such guidance is also discussed.
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Affiliation(s)
- Xiaosheng Wang
- Department of Physics and Astronomy, San Francisco State University, California 94132, USA
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Sakaguchi H, Malomed BA. Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:026601. [PMID: 16605465 DOI: 10.1103/physreve.73.026601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2005] [Indexed: 05/08/2023]
Abstract
We introduce a dynamical model of a Bose-Einstein condensate based on the two-dimensional Gross-Pitaevskii equation, in which the nonlinear coefficient is a function of radius. The model describes a situation with spatial modulation of the negative atomic scattering length, via the Feshbach resonance controlled by a properly shaped magnetic of optical field. We focus on the configuration with the nonlinear coefficient different from zero in a circle or annulus, including the case of a narrow ring. Two-dimensional axisymmetric solitons are found in a numerical form, and also by means of a variational approximation; for an infinitely narrow ring, the soliton is found in an exact form (in the latter case, exact solitons are also found in a two-component model). A stability region for the solitons is identified by means of numerical and analytical methods. In particular, if the nonlinearity is supported on the annulus, the upper stability border is determined by azimuthal perturbations; the stability region disappears if the ratio of the inner and outer radii of the annulus exceeds a critical value . The model gives rise to bistability, as the stationary solitons coexist with stable axisymmetric breathers, whose stability region extends to higher values of the norm than that of the static solitons. The collapse threshold strongly increases with the radius of the inner hole of the annulus. Vortex solitons are found too, but they are unstable.
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Affiliation(s)
- Hidetsugu Sakaguchi
- Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
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Kartashov YV, Vysloukh VA, Torner L. Topological dragging of solitons. PHYSICAL REVIEW LETTERS 2005; 95:243902. [PMID: 16384380 DOI: 10.1103/physrevlett.95.243902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2005] [Indexed: 05/05/2023]
Abstract
We put forward properties of solitons supported by optical lattices featuring topological dislocations and show that solitons experience attractive and repulsive forces around the dislocations. Suitable arrangements of dislocations are even found to form soliton traps, and the properties of such solitons are shown to crucially depend on the trap topology. The uncovered phenomenon opens a new concept for soliton control and manipulation, e.g., in disk-shaped Bose-Einstein condensates.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institute de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, 08860, Castelldefels, Spain
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Kartashov YV, Ferrando A, Egorov AA, Torner L. Soliton topology versus discrete symmetry in optical lattices. PHYSICAL REVIEW LETTERS 2005; 95:123902. [PMID: 16197075 DOI: 10.1103/physrevlett.95.123902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2005] [Indexed: 05/04/2023]
Abstract
We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the possible topological charges of solitons. We set a general "charge rule" using group-theory techniques, which holds for all lattices belonging to a given symmetry group. Focusing on the case of Bessel lattices allows us to derive also an overall stability rule for the allowed vortex solitons.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, Universitat Politecnica de Catalunya, Barcelona, Spain
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Ferrando A. Discrete-symmetry vortices as angular Bloch modes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:036612. [PMID: 16241597 DOI: 10.1103/physreve.72.036612] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2005] [Indexed: 05/05/2023]
Abstract
The most general form for symmetric modes of nonlinear discrete-symmetry systems with nonlinearity depending on the modulus of the field is presented. Vortex solutions are demonstrated to behave as Bloch modes characterized by an angular Bloch momentum associated to a periodic variable, periodicity being fixed by the order of discrete point-symmetry of the system. The concept of angular Bloch momentum is thus introduced to generalize the usual definition of angular momentum to cases where O2 symmetry no longer holds. The conservation of angular Bloch momentum during propagation is demonstrated.
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Affiliation(s)
- Albert Ferrando
- Departament de Matemàtica Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, E-46022 València, Spain
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23
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Mihalache D, Mazilu D, Lederer F, Malomed BA, Kartashov YV, Crasovan LC, Torner L. Stable spatiotemporal solitons in bessel optical lattices. PHYSICAL REVIEW LETTERS 2005; 95:023902. [PMID: 16090683 DOI: 10.1103/physrevlett.95.023902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2004] [Indexed: 05/03/2023]
Abstract
We investigate the existence and stability of three-dimensional solitons supported by cylindrical Bessel lattices in self-focusing media. If the lattice strength exceeds a threshold value, we show numerically, and using the variational approximation, that the solitons are stable within one or two intervals of values of their norm. In the latter case, the Hamiltonian versus norm diagram has a swallowtail shape with three cuspidal points. The model applies to Bose-Einstein condensates and to optical media with saturable nonlinearity, suggesting new ways of making stable three-dimensional solitons and "light bullets" of an arbitrary size.
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Affiliation(s)
- D Mihalache
- Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller Universität Jena, Max-Wien-Platz 1, D-077743 Jena, Germany
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Xu Z, Kartashov YV, Torner L, Vysloukh VA. Reconfigurable directional couplers and junctions optically induced by nondiffracting Bessel beams. OPTICS LETTERS 2005; 30:1180-2. [PMID: 15943302 DOI: 10.1364/ol.30.001180] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
We put forward the concept of reconfigurable structures optically induced by mutually incoherent nondiffracting Bessel beams in Kerr-type nonlinear media. We address collinear couplers and X junctions and show how one can tune the switching properties of such structures by varying the intensity of the Bessel beams.
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Affiliation(s)
- Zhiyong Xu
- ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain
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Kartashov YV, Vysloukh VA, Torner L. Oscillations of two-dimensional solitons in harmonic and Bessel optical lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036621. [PMID: 15903619 DOI: 10.1103/physreve.71.036621] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2004] [Indexed: 05/02/2023]
Abstract
We consider parametric amplification of two-dimensional spatial soliton oscillations in longitudinally modulated harmonic and Bessel lattices in Kerr-type saturable medium. We show that soliton center oscillations along different axes in two-dimensional lattices are coupled, which gives rise to a number of interesting propagation scenarios including periodic damping and excitation of soliton oscillations along perpendicular axes, selective amplification of soliton oscillations along one transverse axis, and enhancement of soliton spiraling.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, Barcelona, Spain
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