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Dong L, Fan M, Malomed BA. Stable higher-charge vortex solitons in the cubic-quintic medium with a ring potential. OPTICS LETTERS 2023; 48:4817-4820. [PMID: 37707910 DOI: 10.1364/ol.500054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 08/19/2023] [Indexed: 09/15/2023]
Abstract
We put forward a model for trapping stable optical vortex solitons (VSs) with high topological charges m. The cubic-quintic nonlinear medium with an imprinted ring-shaped modulation of the refractive index is shown to support two branches of VSs, which are controlled by the radius, width, and depth of the modulation profile. While the lower-branch VSs are unstable in their nearly whole existence domain, the upper branch is completely stable. Vortex solitons with m ≤ 12 obey the anti-Vakhitov-Kolokolov stability criterion. The results suggest possibilities for the creation of stable narrow optical VSs with a low power, carrying higher vorticities.
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2
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Luo Z, Liu Y, Li Y, Batle J, Malomed BA. Stability limits for modes held in alternating trapping-expulsive potentials. Phys Rev E 2022; 106:014201. [PMID: 35974589 DOI: 10.1103/physreve.106.014201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Accepted: 06/09/2022] [Indexed: 06/15/2023]
Abstract
We elaborate a scheme of trapping-expulsion management (TEM), in the form of the quadratic potential periodically switching between confinement and expulsion, as a means of stabilization of two-dimensional dynamical states against the backdrop of the critical collapse driven by the cubic self-attraction with strength g. The TEM scheme may be implemented, as spatially or temporally periodic modulations, in optics or BEC, respectively. The consideration is carried out by dint of numerical simulations and variational approximation (VA). In terms of the VA, the dynamics amounts to a nonlinear Ermakov equation, which, in turn, is tantamount to a linear Mathieu equation. Stability boundaries are found as functions of g and parameters of the periodic modulation of the trapping potential. Below the usual collapse threshold, which is known, in the numerical form, as g<g_{c}^{(num)}≈5.85 (in the standard notation), the stability is limited by the onset of the parametric resonance. This stability limit, including the setup with the self-repulsive sign of the cubic term (g<0), is accurately predicted by the VA. At g>g_{c}^{(num)}, the collapse threshold is found with the help of full numerical simulations. The relative increase of g_{c} above g_{c}^{(num)} is ≈1.5%. It is a meaningful result, even if its size is small, because the collapse threshold is a universal constant which is difficult to change.
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Affiliation(s)
- Zhihuan Luo
- Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China
| | - Yan Liu
- Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China
| | - Yongyao Li
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Josep Batle
- CRISP Centre de Recerca Independent de sa Pobla, C. Albéniz 12, 07420 sa Pobla, Balearic Islands, Spain
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
- Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile
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Interplay between Binary and Three-Body Interactions and Enhancement of Stability in Trapless Dipolar Bose–Einstein Condensates. APPLIED SCIENCES-BASEL 2022. [DOI: 10.3390/app12031135] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
We investigate the nonlocal Gross–Pitaevskii (GP) equation with long-range dipole-dipole and contact interactions (including binary and three-body collisions). We address the impact of the three-body interaction on stabilizing trapless dipolar Bose–Einstein condensates (BECs). It is found that the dipolar BECs exhibit stability not only for the usual combination of attractive binary and repulsive three-body interactions, but also for the case when these terms have opposite signs. The trapless stability of the dipolar BECs may be further enhanced by time-periodic modulation of the three-body interaction imposed by means of Feshbach resonance. The results are produced analytically using the variational approach and confirmed by numerical simulations.
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Abstract
We demonstrate that the commonly known concept which treats solitons as nonsingular solutions produced by the interplay of nonlinear self-attraction and linear dispersion may be extended to include modes with a relatively weak singularity at the central point, which keeps their integral norm convergent. Such states are generated by self-repulsion, which should be strong enough, represented by septimal, quintic, and usual cubic terms in the framework of the one-, two-, and three-dimensional (1D, 2D, and 3D) nonlinear Schrödinger equations (NLSEs), respectively. Although such solutions seem counterintuitive, we demonstrate that they admit a straightforward interpretation as a result of screening of an additionally introduced attractive δ-functional potential by the defocusing nonlinearity. The strength ("bare charge") of the attractive potential is infinite in 1D, finite in 2D, and vanishingly small in 3D. Analytical asymptotics of the singular solitons at small and large distances are found, entire shapes of the solitons being produced in a numerical form. Complete stability of the singular modes is accurately predicted by the anti-Vakhitov-Kolokolov criterion (under the assumption that it applies to the model), as verified by means of numerical methods. In 2D, the NLSE with a quintic self-focusing term admits singular-soliton solutions with intrinsic vorticity too, but they are fully unstable. We also mention that dissipative singular solitons can be produced by the model with a complex coefficient in front of the nonlinear term.
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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
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
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Two-Dimensional Vortex Solitons in Spin-Orbit-Coupled Dipolar Bose–Einstein Condensates. APPLIED SCIENCES-BASEL 2018. [DOI: 10.3390/app8101771] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Solitons are self-trapped modes existing in various nonlinear systems. Creating stable solitons in two- and three-dimensional settings is a challenging goal in various branches of physics. Several methods have been developed theoretically and experimentally to achieve this, but few of them can support stable multi-dimensional solitons in free space. Recently, a new scheme using spin-orbit-coupling (SOC) has been proposed to create stable 2D solitons in Bose–Einstein condensates (BECs). This paper reviews recent theoretical progress on creating stable 2D solitons in spinor dipolar BEC with SOC, combined with long-range dipole-dipole interaction (DDI), Zeeman splitting (ZS) and contact nonlinearity, in free space. The continuous family of stable symmetric vortex solitons (SVS), asymmetric vortex solitons (AVS), as well as gap solitons (GS) is found via different settings. Their existence and stability conditions are summarized and discussed in detail. The mobility properties of these types of solitons are also addressed. For SVS, a potential method to manipulate its shape and mobility is investigated. These results are supposed to enrich our understanding of 2D solitons and help create multi-dimensional solitons in experiments.
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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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7
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Sakaguchi H, Malomed BA. Vortical light bullets in second-harmonic-generating media supported by a trapping potential. OPTICS EXPRESS 2013; 21:9813-9823. [PMID: 23609688 DOI: 10.1364/oe.21.009813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We introduce a three-dimensional (3D) model of optical media with the quadratic (χ((2))) nonlinearity and an effective 2D isotropic harmonic-oscillator (HO) potential. While it is well known that 3D χ((2)) solitons with embedded vorticity ("vortical light bullets") are unstable in the free space, we demonstrate that they have a broad stability region in the present model, being supported by the HO potential against the splitting instability. The shape of the vortical solitons may be accurately predicted by the variational approximation (VA). They exist above a threshold value of the total energy (norm) and below another critical value, which determines a stability boundary. The existence threshold vanishes is a part of the parameter space, depending on the mismatch parameter, which is explained by means of the comparison with the 2D counterpart of the system. Above the stability boundary, the vortex features shape oscillations, periodically breaking its axisymmetric form and restoring it. Collisions between vortices moving in the longitudinal direction are studied too. The collision is strongly inelastic at relatively small values of the velocities, breaking the two colliding vortices into three, with the same vorticity. The results suggest a possibility of the creation of stable 3D optical solitons with the intrinsic vorticity.
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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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Grow TD, Ishaaya AA, Vuong LT, Gaeta AL. Collapse and stability of necklace beams in Kerr media. PHYSICAL REVIEW LETTERS 2007; 99:133902. [PMID: 17930591 DOI: 10.1103/physrevlett.99.133902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2006] [Indexed: 05/25/2023]
Abstract
We investigate the spatial dynamics of optical necklace beams in Kerr media. For powers corresponding to less than the critical power for self-focusing per bead, we experimentally confirm the confinement of these necklace beams as proposed in [Phys. Rev. Lett. 81, 4851 (1998)10.1103/PhysRevLett.81.4851]. At higher powers, we observe a transition from collective necklace behavior to one in which the beads of the necklace collapse independently. We observe that, below the transition power, the perturbed necklace still behaves in a collective manner with coupling between individual beads but that, at higher powers, it undergoes a similar transition to a decoupled state of the necklace.
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Affiliation(s)
- Taylor D Grow
- School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA
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9
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Leblond H, Malomed BA, Mihalache D. Three-dimensional vortex solitons in quasi-two-dimensional lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:026604. [PMID: 17930164 DOI: 10.1103/physreve.76.026604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2006] [Indexed: 05/25/2023]
Abstract
We consider the three-dimensional (3D) Gross-Pitaevskii or nonlinear Schrödinger equation with a quasi-2D square-lattice potential (which corresponds to the optical lattice trapping a self-attractive Bose-Einstein condensate, or, in some approximation, to a photonic-crystal fiber, in terms of nonlinear optics). Stable 3D solitons, with embedded vorticity S=1 and 2, are found by means of the variational approximation and in a numerical form. They are built, basically, as sets of four fundamental solitons forming a rhombus, with phase shifts piS2 between adjacent sites, and an empty site in the middle. The results demonstrate two species of stable 3D solitons, which were not studied before, viz., localized vortices ("spinning light bullets," in terms of optics) with S>1 , and vortex solitons (with any S not equal 0 ) supported by a lattice in the 3D space. Typical scenarios of instability development (collapse or decay) of unstable localized vortices are identified too.
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Affiliation(s)
- Hervé Leblond
- Laboratoire POMA, UMR 6136, Université d'Angers, 2 Bd Lavoisier, 49000 Angers, France
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Efremidis NK, Hizanidis K, Malomed BA, Di Trapani P. Three-dimensional vortex solitons in self-defocusing media. PHYSICAL REVIEW LETTERS 2007; 98:113901. [PMID: 17501055 DOI: 10.1103/physrevlett.98.113901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2006] [Indexed: 05/15/2023]
Abstract
We demonstrate that families of vortex solitons are possible in a bidispersive three-dimensional nonlinear Schrödinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity. Such vortex solitons can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity.
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Affiliation(s)
- Nikolaos K Efremidis
- Department of Applied Mathematics, University of Crete, 71409 Heraklion, Crete, Greece
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11
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Mihalache D, Mazilu D, Malomed BA, Lederer F, Crasovan LC, Kartashov YV, Torner L. Stable three-dimensional optical solitons supported by competing quadratic and self-focusing cubic nonlinearities. Phys Rev E 2006; 74:047601. [PMID: 17155219 DOI: 10.1103/physreve.74.047601] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2006] [Revised: 06/28/2006] [Indexed: 11/07/2022]
Abstract
We show that the quadratic (chi(2)) interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-focusing cubic (chi(3)) nonlinearity, give rise to stable three-dimensional spatiotemporal solitons (STSs), despite the possibility of the supercritical collapse, induced by the chi(3) nonlinearity. At exact phase matching (beta = 0) , the STSs are stable for energies from zero up to a certain maximum value, while for beta not equal 0 the solitons are stable in energy intervals between finite limits.
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Affiliation(s)
- D Mihalache
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
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12
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Mihalache D, Mazilu D, Lederer F, Crasovan LC, Kartashov YV, Torner L, Malomed BA. Stable solitons of even and odd parities supported by competing nonlocal nonlinearities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:066614. [PMID: 17280169 DOI: 10.1103/physreve.74.066614] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2006] [Indexed: 05/13/2023]
Abstract
We introduce a one-dimensional phenomenological model of a nonlocal medium featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, we find families of solitons of two types, even-parity (fundamental) and dipole-mode (odd-parity) ones. Stability of the solitons is explored by means of computation of eigenvalues associated with modes of small perturbations, and tested in direct simulations. We find that the stability of the fundamental solitons strictly follows the Vakhitov-Kolokolov criterion, whereas the dipole solitons can be destabilized through a Hamiltonian-Hopf bifurcation. The solitons of both types may be stable in the nonlocal model with only quintic self-attractive nonlinearity, in contrast with the instability of all solitons in the local version of the quintic model.
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Affiliation(s)
- D Mihalache
- Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, 077125, Romania
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Mihalache D, Mazilu D, Lederer F, Kartashov YV, Crasovan LC, Torner L, Malomed BA. Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation. PHYSICAL REVIEW LETTERS 2006; 97:073904. [PMID: 17026230 DOI: 10.1103/physrevlett.97.073904] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2006] [Indexed: 05/09/2023]
Abstract
We demonstrate the existence of stable toroidal dissipative solitons with the inner phase field in the form of rotating spirals, corresponding to vorticity S=0, 1, and 2, in the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. The stable solitons easily self-trap from pulses with embedded vorticity. The stability is corroborated by accurate computation of growth rates for perturbation eigenmodes. The results provide the first example of stable vortex tori in a 3D dissipative medium, as well as the first example of higher-order tori (with S=2) in any nonlinear medium. It is found that all stable vortical solitons coexist in a large domain of the parameter space; in smaller regions, there coexist stable solitons with either S=0 and S=1, or S=1 and S=2.
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Affiliation(s)
- D Mihalache
- Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest 077125, Romania
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Mihalache D, Mazilu D, Lederer F, Malomed BA, Kartashov YV, Crasovan LC, Torner L. Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:025601. [PMID: 16605390 DOI: 10.1103/physreve.73.025601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2005] [Indexed: 05/08/2023]
Abstract
We demonstrate the existence of stable three-dimensional spatiotemporal solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental (nonspinning) STSs forming one-parameter families are stable if their propagation constant exceeds a certain critical value that is inversely proportional to the range of nonlocality of nonlinear response. All spinning three-dimensional STSs are found to be unstable.
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Affiliation(s)
- D Mihalache
- National Institute of Physics and Nuclear Engineering, Institute of Atomic Physics, Department of Theoretical Physics, P.O. Box MG-6, Bucharest, Romania
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Leblond H, Malomed BA, Mihalache D. Quasistable two-dimensional solitons with hidden and explicit vorticity in a medium with competing nonlinearities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036608. [PMID: 15903606 DOI: 10.1103/physreve.71.036608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2004] [Indexed: 05/02/2023]
Abstract
We consider basic types of two-dimensional (2D) vortex solitons in a three-wave model combining quadratic chi((2)) and self-defocusing cubic chi((3))(-) nonlinearities. The system involves two fundamental-frequency (FF) waves with orthogonal polarizations and a single second-harmonic (SH) one. The model makes it possible to introduce a 2D soliton, with hidden vorticity (HV). Its vorticities in the two FF components are S(1,2) = +/-1 , whereas the SH carries no vorticity, S(3) = 0 . We also consider an ordinary compound vortex, with 2S(1) = 2S(2) = S(3) = 2 . Without the chi((3))(-) terms, the HV soliton and the ordinary vortex are moderately unstable. Within the propagation distance z approximately 15 diffraction lengths, Z(diffr), the former one turns itself into a usual zero-vorticity (ZV) soliton, while the latter splits into three ZV solitons (the splinters form a necklace pattern, with its own intrinsic dynamics). To gain analytical insight into the azimuthal instability of the HV solitons, we also consider its one-dimensional counterpart, viz., the modulational instability (MI) of a one-dimensional CW (continuous-wave) state with "hidden momentum," i.e., opposite wave numbers in its two components, concluding that such wave numbers may partly suppress the MI. As concerns analytical results, we also find exact solutions for spreading localized vortices in the 2D linear model; in terms of quantum mechanics, these are coherent states with angular momentum (we need these solutions to accurately define the diffraction length of the true solitons). The addition of the chi((3))(-) interaction strongly stabilizes both the HV solitons and the ordinary vortices, helping them to persist over z up to 50 Z(diffr). In terms of the possible experiment, they are completely stable objects. After very long propagation, the HV soliton splits into two ZV solitons, while the vortex with S(3) = 2S(1,2) = 2 splits into a set of three or four ZV solitons.
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Affiliation(s)
- Hervé Leblond
- Laboratoire POMA, UMR 6136, Université d'Angers, France
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17
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Panoiu NC, Osgood RM, Malomed BA, Lederer F, Mazilu D, Mihalache D. Parametric light bullets supported by quasi-phase-matched quadratically nonlinear crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036615. [PMID: 15903613 DOI: 10.1103/physreve.71.036615] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2004] [Indexed: 05/02/2023]
Abstract
We present a comprehensive analysis of the dynamics of three-dimensional spatiotemporal nonspinning and spinning solitons in quasi-phased-matched (QPM) gratings. By employing an averaging approach based on perturbation theory, we show that the soliton's stability is strongly affected by the QPM-induced third-order nonlinearity (which is always of a mixed type, with opposite signs in front of the corresponding self-phase and cross-phase modulation terms). We study the dependence of the stability of the spatiotemporal soliton (STS) on its energy, spin, the wave-vector mismatch between the fundamental and second harmonics, and the relative strength of the intrinsic quadratic and QPM-induced cubic nonlinearities. In particular, all the spinning solitons are unstable against fragmentation, while zero-spin STS's have their stability regions on the system's parameter space.
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Affiliation(s)
- N-C Panoiu
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
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18
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Kartashov YV, Vysloukh VA, Torner L. Stable ring-profile vortex solitons in bessel optical lattices. PHYSICAL REVIEW LETTERS 2005; 94:043902. [PMID: 15783560 DOI: 10.1103/physrevlett.94.043902] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2004] [Indexed: 05/24/2023]
Abstract
Stable ring-profile vortex solitons, featuring a bright shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex solitons and reveal their salient properties, including the conditions required for their stability. We show that the higher the soliton topological charge, the deeper the lattice modulation necessary for stabilization.
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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, 08034, Barcelona, Spain
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Xu Z, Kartashov YV, Crasovan LC, Mihalache D, Torner L. Spatiotemporal discrete multicolor solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:066618. [PMID: 15697537 DOI: 10.1103/physreve.70.066618] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2004] [Revised: 07/27/2004] [Indexed: 05/24/2023]
Abstract
We have found various families of two-dimensional spatiotemporal solitons in quadratically nonlinear waveguide arrays. The families of unstaggered odd, even, and twisted stationary solutions are thoroughly characterized and their stability against perturbations is investigated. We show that the twisted and even solitons display instability, while most of the odd solitons show remarkable stability upon evolution.
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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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Kevrekidis PG, Malomed BA, Frantzeskakis DJ, Carretero-González R. Three-dimensional solitary waves and vortices in a discrete nonlinear Schrödinger lattice. PHYSICAL REVIEW LETTERS 2004; 93:080403. [PMID: 15447160 DOI: 10.1103/physrevlett.93.080403] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2004] [Indexed: 05/24/2023]
Abstract
In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schrödinger equation, we find discrete vortex solitons with various values of the topological charge S. Stability regions for the vortices with S=0,1,3 are investigated. The S=2 vortex is unstable and may spontaneously rearranging into a stable one with S=3. In a two-component extension of the model, we find a novel class of stable structures, consisting of vortices in the different components, perpendicularly oriented to each other. Self-localized states of the proposed types can be observed experimentally in Bose-Einstein condensates trapped in optical lattices and in photonic crystals built of microresonators.
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Affiliation(s)
- P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA
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Mihalache D, Mazilu D, Malomed BA, Lederer F. Stable vortex solitons supported by competing quadratic and cubic nonlinearities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:066614. [PMID: 15244771 DOI: 10.1103/physreve.69.066614] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2003] [Revised: 03/17/2004] [Indexed: 05/24/2023]
Abstract
We address the stability problem for vortex solitons in two-dimensional media combining quadratic and self-defocusing cubic [chi(2):chi(3)- ] nonlinearities. We consider the propagation of spatial beams with intrinsic vorticity S in such bulk optical media. It was earlier found that the S=1 and S=2 solitons can be stable, provided that their power (i.e., transverse size) is large enough, and it was conjectured that all the higher-order vortices with S> or =3 are always unstable. On the other hand, it was recently shown that vortex solitons with S>2 and very large transverse size may be stable in media combining cubic self-focusing and quintic self-defocusing nonlinearities. Here, we demonstrate that the same is true in the chi(2):chi(3)- model, the vortices with S=3 and S=4 being stable in regions occupying, respectively, approximately 3% and 1.5% of their existence domain. The vortex solitons with S>4 are also stable in tiny regions. The results are obtained through computation of stability eigenvalues, and are then checked in direct simulations, with a conclusion that the stable vortices are truly robust ones, easily self-trapping from initial beams with embedded vorticity. The dependence of the stability region on the chi(2) phase-mismatch parameter is specially investigated. We thus conclude that the stability of higher-order two-dimensional vortex solitons in narrow regions is a generic feature of optical media featuring the competition between self-focusing and self-defocusing nonlinearities. A qualitative analytical explanation to this feature is proposed.
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Affiliation(s)
- D Mihalache
- Department of Theoretical Physics, Institute of Atomic Physics, P.O. Box MG-6, Bucharest, Romania
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Bigelow MS, Zerom P, Boyd RW. Breakup of ring beams carrying orbital angular momentum in sodium vapor. PHYSICAL REVIEW LETTERS 2004; 92:083902. [PMID: 14995774 DOI: 10.1103/physrevlett.92.083902] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2003] [Indexed: 05/24/2023]
Abstract
We have observed filamentation due to azimuthal modulational instabilities in spinning ring solitons with orbital angular momentum m variant Planck's over 2pi in sodium vapor. We show experimentally that vortex beams with m values of 1, 2, and 3 tend to break into two, four, and six filaments, respectively. Treating the sodium vapor as a Doppler broadened two-level atomic system, we find that we can accurately model the propagation and breakup of these beams with numerical simulations.
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Affiliation(s)
- Matthew S Bigelow
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
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Mihalache D, Mazilu D, Crasovan LC, Malomed BA, Lederer F, Torner L. Robust soliton clusters in media with competing cubic and quintic nonlinearities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:046612. [PMID: 14683070 DOI: 10.1103/physreve.68.046612] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2003] [Indexed: 05/24/2023]
Abstract
Systematic results are reported for dynamics of circular patterns ("necklaces"), composed of fundamental solitons and carrying orbital angular momentum, in the two-dimensional model, which describes the propagation of light beams in bulk media combining self-focusing cubic and self-defocusing quintic nonlinearities. Semianalytical predictions for the existence of quasistable necklace structures are obtained on the basis of an effective interaction potential. Then, direct simulations are run. In the case when the initial pattern is far from an equilibrium size predicted by the potential, it cannot maintain its shape. However, a necklace with the initial shape close to the predicted equilibrium survives very long evolution, featuring persistent oscillations. The quasistable evolution is not essentially disturbed by a large noise component added to the initial configuration. Basic conclusions concerning the necklace dynamics in this model are qualitatively the same as in a recently studied one which combines quadratic and self-defocusing cubic nonlinearities. Thus, we infer that a combination of competing self-focusing and self-defocusing nonlinearities enhances the robustness not only of vortex solitons but also of vorticity-carrying necklace patterns.
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Affiliation(s)
- D Mihalache
- ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, ES 8034 Barcelona, Spain
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Mihalache D, Mazilu D, Towers I, Malomed BA, Lederer F. Stable spatiotemporal spinning solitons in a bimodal cubic-quintic medium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:056608. [PMID: 12786297 DOI: 10.1103/physreve.67.056608] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2002] [Revised: 01/14/2003] [Indexed: 05/24/2023]
Abstract
We investigate the formation of stable spatiotemporal three-dimensional (3D) solitons ("light bullets") with internal vorticity ("spin") in a bimodal system described by coupled cubic-quintic nonlinear Schrödinger equations. Two relevant versions of the model, for the linear and circular polarizations, are considered. In the former case, an important ingredient of the model are four-wave-mixing terms, which give rise to a phase-sensitive nonlinear coupling between two polarization components. Thresholds for the formation of both spinning and nonspinning 3D solitons are found. Instability growth rates of perturbation eigenmodes with different azimuthal indices are calculated as functions of the solitons' propagation constant. As a result, stability domains in the model's parameter plane are identified for solitons with the values of the spins of their components s=0 and s=1, while all the solitons with s> or =2 are unstable. The solitons with s=1 are stable only if their energy exceeds a certain critical value, so that, in typical cases, the stability region occupies approximately 25% of their existence domain. Direct simulations of the full system produce results that are in perfect agreement with the linear-stability analysis: stable 3D spinning solitons readily self-trap from initial Gaussian pulses with embedded vorticity, and easily heal themselves if strong perturbations are imposed, while unstable spinning solitons quickly split into a set of separating zero-spin fragments whose number is exactly equal to the azimuthal index of the strongest unstable perturbation eigenmode.
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Affiliation(s)
- D Mihalache
- Department of Theoretical Physics, Institute of Atomic Physics, P.O. Box MG-6, Bucharest, Romania
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Crasovan LC, Kartashov YV, Mihalache D, Torner L, Kivshar YS, Pérez-García VM. Soliton "molecules": robust clusters of spatiotemporal optical solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046610. [PMID: 12786512 DOI: 10.1103/physreve.67.046610] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2002] [Indexed: 05/24/2023]
Abstract
We show how to generate robust self-sustained clusters of soliton bullets-spatiotemporal (optical or matter-wave) solitons. The clusters carry an orbital angular momentum being supported by competing nonlinearities. The "atoms" forming the "molecule" are fully three-dimensional solitons linked via a staircaselike macroscopic phase. Recent progress in generating atomic-molecular coherent mixing in the Bose-Einstein condensates might open potential scenarios for the experimental generation of these soliton molecules with matter waves.
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Affiliation(s)
- Lucian-Cornel Crasovan
- Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, ES 08034 Barcelona, Spain
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Davydova TA, Yakimenko AI, Zaliznyak YA. Two-dimensional solitons and vortices in normal and anomalous dispersive media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:026402. [PMID: 12636817 DOI: 10.1103/physreve.67.026402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2002] [Indexed: 05/24/2023]
Abstract
We study solitons and vortices described by the (2+1)-dimensional fourth-order generalized nonlinear Schrödinger equation with cubic-quintic nonlinearity. Necessary conditions for the existence of such structures are investigated analytically using conservation laws and asymptotic behavior of localized solutions. We derive the generalized virial relation, which describes the combined influence of linear and nonlinear effects on the evolution of the wave packet envelope. By means of refined variational analysis, we predict the main features of steady soliton solutions, which have been shown to be in good agreement with our numerical results. Soliton and vortex stability is investigated by linear analysis and direct numerical simulations. We show that stable bright solitons exist in nonlinear Kerr media both in anomalous and normal dispersive regimes, even if only the fourth-order dispersive effect is taken into account. Vortices occur robust with respect to symmetry-breaking azimuthal instability only in the presence of additional defocusing quintic nonlinearity in the strongly nonlinear regime. We apply our results to the theoretical explanation of whistler self-induced waveguide propagation in plasmas, and discuss possible applications to light beam propagation in cubic-quintic optical materials and to solitons in two-dimensional molecular systems.
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Affiliation(s)
- T A Davydova
- Institute for Nuclear Research, Prospect Nauki 47, Kiev 03680, Ukraine.
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Kartashov YV, Crasovan LC, Mihalache D, Torner L. Robust propagation of two-color soliton clusters supported by competing nonlinearities. PHYSICAL REVIEW LETTERS 2002; 89:273902. [PMID: 12513208 DOI: 10.1103/physrevlett.89.273902] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2002] [Indexed: 05/24/2023]
Abstract
We reveal numerically the remarkably robust propagation of quasistationary two-color soliton clusters in media with competing quadratic and cubic nonlinearities. We predict that such clusters carrying nonzero angular momentum can propagate over any practically feasible crystal length before they decay, even in the presence of input random perturbations.
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Affiliation(s)
- Yaroslav V Kartashov
- Institute of Photonic Sciences and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain
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