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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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2
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Fedorov SV, Veretenov NA, Rosanov NN. Control of topology of two-dimensional solitons in a laser with saturable absorption by means of a coherent holding radiation. OPTICS LETTERS 2020; 45:3284-3287. [PMID: 32538963 DOI: 10.1364/ol.394727] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 05/02/2020] [Indexed: 06/11/2023]
Abstract
We propose a simple method to control the topology of laser vortex solitons and their complexes in a wide-aperture laser with saturable absorption by means of weak coherent holding radiation. The holding radiation acting on initial "free" vortex solitons induces the appearance of new peripheral vortices and the splitting of multiple central vortices, as well as reconfiguration of energy flow topology. A wide variety of these stable vortex structures makes the scheme promising for topologically protected information processing.
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Shen Y, Wang X, Xie Z, Min C, Fu X, Liu Q, Gong M, Yuan X. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities. LIGHT, SCIENCE & APPLICATIONS 2019; 8:90. [PMID: 31645934 PMCID: PMC6804826 DOI: 10.1038/s41377-019-0194-2] [Citation(s) in RCA: 376] [Impact Index Per Article: 75.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2019] [Revised: 08/04/2019] [Accepted: 08/20/2019] [Indexed: 05/05/2023]
Abstract
Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.
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Affiliation(s)
- Yijie Shen
- Key Laboratory of Photonic Control Technology (Tsinghua University), Ministry of Education, 100084 Beijing, China
- State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, 100084 Beijing, China
| | - Xuejiao Wang
- National Engineering Laboratory for Public Safety Risk Perception and Control by Big Data (NEL-PSRPC), China Academy of Electronics and Information Technology of CETC, China Electronic Technology Group Corporation, 100041 Beijing, China
| | - Zhenwei Xie
- Nanophotonics Research Center, Shenzhen University, 518060 Shenzhen, China
| | - Changjun Min
- Nanophotonics Research Center, Shenzhen University, 518060 Shenzhen, China
| | - Xing Fu
- Key Laboratory of Photonic Control Technology (Tsinghua University), Ministry of Education, 100084 Beijing, China
- State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, 100084 Beijing, China
| | - Qiang Liu
- Key Laboratory of Photonic Control Technology (Tsinghua University), Ministry of Education, 100084 Beijing, China
- State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, 100084 Beijing, China
| | - Mali Gong
- Key Laboratory of Photonic Control Technology (Tsinghua University), Ministry of Education, 100084 Beijing, China
- State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, 100084 Beijing, China
| | - Xiaocong Yuan
- Nanophotonics Research Center, Shenzhen University, 518060 Shenzhen, China
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Ma X, Schumacher S. Vortex Multistability and Bessel Vortices in Polariton Condensates. PHYSICAL REVIEW LETTERS 2018; 121:227404. [PMID: 30547643 DOI: 10.1103/physrevlett.121.227404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Indexed: 06/09/2023]
Abstract
Vortices are topological objects formed in coherent nonlinear systems. As such they are studied in a wide number of physical systems and promise applications in information storage, processing, and communication. In semiconductor microcavities, vortices in polariton condensates can be conveniently created, studied, and manipulated using solely optical means. For nonresonant excitation with a ring-shaped pump a stable vortex can be formed, leading to bistability with left- and right-handed vorticity. In the present work we report on a much richer vortex multistability, with optically addressable vortices with topological charges m=±1, ±2, and ±3, all stable for the same system and excitation parameters. This unusual multistable behavior is rooted in the inherent nonlinear feedback between reservoir excitations and condensate in the microcavity. For larger radius of the ring-shaped pump we also find a Bessel vortex with its characteristic spiralling phase in the high density region and pronounced self-stabilization ability. Our theoretical results open up exciting possibilities for optical manipulation of vortex multiplets in a compact semiconductor system.
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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
| | - Stefan Schumacher
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
- College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
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Mayteevarunyoo T, Malomed BA, Skryabin DV. One- and two-dimensional modes in the complex Ginzburg-Landau equation with a trapping potential. OPTICS EXPRESS 2018; 26:8849-8865. [PMID: 29715847 DOI: 10.1364/oe.26.008849] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2018] [Accepted: 03/08/2018] [Indexed: 06/08/2023]
Abstract
We propose a new mechanism for the stabilization of confined modes in lasers and semiconductor microcavities holding exciton-polariton condensates, with spatially uniform linear gain, cubic loss, and cubic self-focusing or defocusing nonlinearity. We demonstrated that the commonly known background instability driven by the linear gain can be suppressed by a combination of a harmonic-oscillator trapping potential and effective diffusion. Systematic numerical analysis of one- and two-dimensional (1D and 2D) versions of the model reveals a variety of stable modes, including stationary ones, breathers, and quasi-regular patterns filling the trapping area in the 1D case. In 2D, the analysis produces stationary modes, breathers, axisymmetric and rotating crescent-shaped vortices, stably rotating complexes built of up to 8 individual vortices, and, in addition, patterns featuring vortex turbulence. Existence boundaries for both 1D and 2D stationary modes are found in an exact analytical form, and an analytical approximation is developed for the full stationary states.
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Li H, Lai S, Qui Y, Zhu X, Xie J, Mihalache D, He Y. Stable dissipative optical vortex clusters by inhomogeneous effective diffusion. OPTICS EXPRESS 2017; 25:27948-27967. [PMID: 29092262 DOI: 10.1364/oe.25.027948] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2017] [Accepted: 09/29/2017] [Indexed: 06/07/2023]
Abstract
We numerically show the generation of robust vortex clusters embedded in a two-dimensional beam propagating in a dissipative medium described by the generic cubic-quintic complex Ginzburg-Landau equation with an inhomogeneous effective diffusion term, which is asymmetrical in the two transverse directions and periodically modulated in the longitudinal direction. We show the generation of stable optical vortex clusters for different values of the winding number (topological charge) of the input optical beam. We have found that the number of individual vortex solitons that form the robust vortex cluster is equal to the winding number of the input beam. We have obtained the relationships between the amplitudes and oscillation periods of the inhomogeneous effective diffusion and the cubic gain and diffusion (viscosity) parameters, which depict the regions of existence and stability of vortex clusters. The obtained results offer a method to form robust vortex clusters embedded in two-dimensional optical beams, and we envisage potential applications in the area of structured light.
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Jimenez-Garcia J, Rodriguez P, Guillet T, Ackemann T. Spontaneous Formation of Vector Vortex Beams in Vertical-Cavity Surface-Emitting Lasers with Feedback. PHYSICAL REVIEW LETTERS 2017; 119:113902. [PMID: 28949217 DOI: 10.1103/physrevlett.119.113902] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2016] [Indexed: 06/07/2023]
Abstract
The spontaneous emergence of vector vortex beams with nonuniform polarization distribution is reported in a vertical-cavity surface-emitting laser (VCSEL) with frequency-selective feedback. Antivortices with a hyperbolic polarization structure and radially polarized vortices are demonstrated. They exist close to and partially coexist with vortices with uniform and nonuniform polarization distributions characterized by four domains of pairwise orthogonal polarization. The spontaneous formation of these nontrivial structures in a simple, nearly isotropic VCSEL system is remarkable and the vector vortices are argued to have solitonlike properties.
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Affiliation(s)
- Jesus Jimenez-Garcia
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
| | - Pedro Rodriguez
- Departamento de Fisica, Universidad de Cordoba, 14071 Cordoba, Spain
| | - T Guillet
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - T Ackemann
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
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Descalzi O, Brand HR. Non-unique results of collisions of quasi-one-dimensional dissipative solitons. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2015; 373:rsta.2015.0115. [PMID: 26527813 DOI: 10.1098/rsta.2015.0115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/10/2015] [Indexed: 06/05/2023]
Abstract
We investigate collisions of quasi-one-dimensional dissipative solitons (DSs) for a large class of initial conditions, which are not temporally asymptotic quasi-one-dimensional DSs. For the case of sufficiently small approach velocity and sufficiently large values of the dissipative cross-coupling between the counter-propagating DSs, we find non-unique results for the outcome of collisions. We demonstrate that these non-unique results are intrinsically related to a modulation instability along the crest of the quasi-one-dimensional objects. As a model, we use coupled cubic-quintic complex Ginzburg-Landau equations. Among the final results found are stationary and oscillatory compound states as well as more complex assemblies consisting of quasi-one-dimensional and localized states. We analyse to what extent the final results can be described by the solutions of one cubic-quintic complex Ginzburg-Landau equation with effective parameters.
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Affiliation(s)
- Orazio Descalzi
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. Mons. Álvaro del Portillo 12.455, Las Condes, Santiago, Chile Department of Physics, University of Bayreuth, Bayreuth 95440, Germany
| | - Helmut R Brand
- Department of Physics, University of Bayreuth, Bayreuth 95440, Germany
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Pasquazi A, Peccianti M, Clerici M, Conti C, Morandotti R. Collapse arrest in instantaneous Kerr media via parametric interactions. PHYSICAL REVIEW LETTERS 2014; 113:133901. [PMID: 25302888 DOI: 10.1103/physrevlett.113.133901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Indexed: 06/04/2023]
Abstract
We demonstrate, theoretically and experimentally, that a four-wave mixing parametric interaction is able to arrest the collapse of a two-dimensional multicolor beam in an instantaneous Kerr medium. We consider two weak idlers interacting via a third order nonlinearity with two pump beams and we show that a class of collapse-free quasisolitary solutions can be experimentally observed in a normal dispersion Kerr glass. This observation is sustained by rigorous theoretical analysis demonstrating the stability of the observed self-trapped beams.
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Affiliation(s)
- Alessia Pasquazi
- Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom
| | - Marco Peccianti
- Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom
| | - Matteo Clerici
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, Québec J3X 1S2, Canada and School of Engineering and Physical Sciences, Heriot-Watt University, SUPA, Edinburgh EH14 4AS, United Kingdom
| | - Claudio Conti
- ISC-CNR and Department of Physics, University Sapienza, Piazzale Aldo Moro 5, I-00185 Rome, Italy
| | - Roberto Morandotti
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, Québec J3X 1S2, Canada
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10
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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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Liu B, He XD, Li SJ. Continuous emission of fundamental solitons from vortices in dissipative media by a radial-azimuthal potential. OPTICS EXPRESS 2013; 21:5561-5566. [PMID: 23482127 DOI: 10.1364/oe.21.005561] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We report novel dynamical regimes of dissipative vortices supported by a radial-azimuthal potential (RAP) in the 2D complex Ginzburg-Landau (CGL) equation with the cubic-quintic nonlinearity. First, the stable solutions of vortices with intrinsic vorticity S = 1 and 2 are obtained in the CGL equation without potential. The RAP is a model of an active optical medium with respective expanding anti-waveguiding structures with m (integer) annularly periodic modulation. If the potential is strong enough, m jets fundamental of solitons are continuously emitted from the vortices. The influence of m, diffusivity term (viscosity) β, and cubic-gain coefficient ε on the dynamic region is studied. For a weak potential, the shape of vortices are stretched into the polygon, such as square for m = 4. But for a stronger potential, the vortices will be broke into m fundamental solitons.
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Affiliation(s)
- Bin Liu
- Key Laboratory of Nondestructive Test, Ministry of Education, Nanchang Hangkong University, China.
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12
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Besse V, Leblond H, Mihalache D, Malomed BA. Pattern formation by kicked solitons in the two-dimensional Ginzburg-Landau medium with a transverse grating. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012916. [PMID: 23410413 DOI: 10.1103/physreve.87.012916] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2012] [Revised: 09/13/2012] [Indexed: 06/01/2023]
Abstract
We consider the kick- (tilt-) induced mobility of two-dimensional (2D) fundamental dissipative solitons in models of bulk lasing media based on the 2D complex Ginzburg-Landau equation including a spatially periodic potential (transverse grating). The depinning threshold, which depends on the orientation of the kick, is identified by means of systematic simulations and estimated by means of an analytical approximation. Various pattern-formation scenarios are found above the threshold. Most typically, the soliton, hopping between potential cells, leaves arrayed patterns of different sizes in its wake. In the single-pass-amplifier setup, this effect may be used as a mechanism for the selective pattern formation controlled by the tilt of the input beam. Freely moving solitons feature two distinct values of the established velocity. Elastic and inelastic collisions between free solitons and pinned arrayed patterns are studied too.
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Affiliation(s)
- Valentin Besse
- LUNAM Université, Laboratoire de Photonique d'Angers, Université d'Angers, EA 4464, 2 Boulevard Lavoisier, 49000 Angers, France
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13
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He Y, Mihalache D, Malomed BA, Qiu Y, Chen Z, Li Y. Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:066206. [PMID: 23005195 DOI: 10.1103/physreve.85.066206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate that, in a two-dimensional dissipative medium described by the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) equation with the viscous (spectral-filtering) term, necklace rings carrying a mixed radial-azimuthal phase modulation can evolve into polygonal or quasipolygonal stable soliton clusters, and into stable fundamental solitons. The outcome of the evolution is controlled by the depth and azimuthal anharmonicity of the phase-modulation profile, or by the radius and number of "beads" in the initial necklace ring. Threshold characteristics of the evolution of the patterns are identified and explained. Parameter regions for the formation of the stable polygonal and quasipolygonal soliton clusters, and of stable fundamental solitons, are identified. The model with the CQ terms replaced by the full saturable nonlinearity produces essentially the same set of basic dynamical scenarios; hence this set is a universal one for the CGL models.
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Affiliation(s)
- Yingji He
- School of Electronics and Information, Guangdong Polytechnic Normal University, 510665 Guangzhou, China.
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Liu B, He XD. Continuous generation of "light bullets" in dissipative media by an annularly periodic potential. OPTICS EXPRESS 2011; 19:20009-20014. [PMID: 21997011 DOI: 10.1364/oe.19.020009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We report novel dynamical regimes of "light bullets" supported by an annularly periodic potential in the three-dimensional (3D) complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. This is a model of an active optical medium with respective expanding anti-waveguiding structures with m≥2 (integer) annularly periodic modulation. If the potentials are strong enough, they give rise to continuous generation of m jets light bullet by an initial light bullet initially placed at the center. The influence of m and diffusivity term (viscosity) β on the corresponding strength of potential is studied. In the case of m = 0 (conical geometry), these are concentric waves expanding in the radial direction.
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Affiliation(s)
- Bin Liu
- Key Laboratory of Nondestructive Test (Ministry of Education), Nanchang Hangkong University, China.
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15
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Borovkova OV, Kartashov YV, Lobanov VE, Vysloukh VA, Torner L. Vortex twins and anti-twins supported by multiring gain landscapes. OPTICS LETTERS 2011; 36:3783-3785. [PMID: 21964096 DOI: 10.1364/ol.36.003783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We address the properties of multivortex soliton complexes supported by multiring gain landscapes in focusing Kerr nonlinear media with strong two-photon absorption. Stable complexes incorporating two, three, or four vortices featuring opposite or identical topological charges are shown to exist. In the simplest geometries with two amplifying rings vortex twins with equal topological charges exhibit asymmetric intensity distributions, while vortex anti-twins may be symmetric or asymmetric, depending on the gain level and separation between rings.
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Affiliation(s)
- O V Borovkova
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, 08860, Castelldefels (Barcelona), Spain.
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16
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Paulau PV, Gomila D, Colet P, Malomed BA, Firth WJ. From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:036213. [PMID: 22060481 DOI: 10.1103/physreve.84.036213] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2011] [Indexed: 05/31/2023]
Abstract
We use the cubic complex Ginzburg-Landau equation linearly coupled to a dissipative linear equation as a model for lasers with an external frequency-selective feedback. This system may also serve as a general pattern-formation model in media driven by an intrinsic gain and selective feedback. While, strictly speaking, the approximation of the laser nonlinearity by a cubic term is only valid for small field intensities, it qualitatively reproduces results for dissipative solitons obtained in models with a more complex nonlinearity in the whole parameter region where the solitons exist. The analysis is focused on two-dimensional stripe-shaped and vortex solitons. An analytical expression for the stripe solitons is obtained from the known one-dimensional soliton solution, and its relation with vortex solitons is highlighted. The radius of the vortices increases linearly with their topological charge m, therefore the stripe-shaped soliton may be interpreted as the vortex with m=∞, and, conversely, vortex solitons can be realized as unstable stripes bent into stable rings. The results for the vortices are applicable for a broad class of physical systems.
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Affiliation(s)
- P V Paulau
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07071 Palma de Mallorca, Spain
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17
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Borovkova OV, Lobanov VE, Kartashov YV, Torner L. Rotating vortex solitons supported by localized gain. OPTICS LETTERS 2011; 36:1936-1938. [PMID: 21593941 DOI: 10.1364/ol.36.001936] [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
We show that ringlike localized gain landscapes imprinted in focusing cubic (Kerr) nonlinear media with strong two-photon absorption support new types of stable higher-order vortex solitons containing multiple phase singularities nested inside a single core. The phase singularities are found to rotate around the center of the gain landscape, with the rotation period being determined by the strength of the gain and the nonlinear absorption.
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Affiliation(s)
- Olga V Borovkova
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, 08860, Castelldefels, Barcelona, Spain.
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Lobanov VE, Kartashov YV, Vysloukh VA, Torner L. Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain. OPTICS LETTERS 2011; 36:85-87. [PMID: 21209695 DOI: 10.1364/ol.36.000085] [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
We discover that a spatially localized gain supports stable vortex solitons in media with cubic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying rings results in the suppression of otherwise ubiquitous azimuthal modulation instabilities of radially symmetric vortex solitons. We find that the topology of the gain profile imposes restrictions on the maximal possible charge of vortex solitons. Symmetry breaking occurs at high gain levels, resulting in the formation of necklace vortex solitons composed of asymmetric bright spots.
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Affiliation(s)
- Valery E Lobanov
- ICFO-Institut de Ciencies Fotoniques and Universitat Politecnica de Catalunya, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
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Skarka V, Aleksić NB, Leblond H, Malomed BA, Mihalache D. Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses. PHYSICAL REVIEW LETTERS 2010; 105:213901. [PMID: 21231306 DOI: 10.1103/physrevlett.105.213901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2010] [Indexed: 05/30/2023]
Abstract
Using a combination of the variation approximation and direct simulations, we consider the model of the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous loss provides for the hitherto elusive stabilization of vortex solitons, in a large zone of the parameter space. Adjacent to it, stability domains are found for several novel kinds of localized vortices, including spinning elliptically shaped ones, eccentric elliptic vortices which feature double rotation, spinning crescents, and breathing vortices.
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Affiliation(s)
- V Skarka
- Laboratoire de Photonique d'Angers, EA 4464, Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers Cedex 01, France
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Kartashov YV, Konotop VV, Vysloukh VA, Torner L. Vortex lattice solitons supported by localized gain. OPTICS LETTERS 2010; 35:3177-3179. [PMID: 20890325 DOI: 10.1364/ol.35.003177] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We show that localized gain supports the existence of dissipative vortex solitons in periodic Kerr media with strong two-photon absorption. Vortex solitons exist in both focusing and defocusing media, with their propagation constants emerging from semi-infinite or finite gaps in the lattice spectrum. Coincidence of the discrete rotational symmetries of the gain landscape and refractive index distribution is a necessary condition for exciting vortex solitons, which otherwise transform into stable dissipative multipoles.
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Affiliation(s)
- Yaroslav V Kartashov
- Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
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21
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Liu B, He YJ, Malomed BA, Wang XS, Kevrekidis PG, Wang TB, Leng FC, Qiu ZR, Wang HZ. Continuous generation of soliton patterns in two-dimensional dissipative media by razor, dagger, and needle potentials. OPTICS LETTERS 2010; 35:1974-1976. [PMID: 20548357 DOI: 10.1364/ol.35.001974] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We report dynamic regimes supported by a sharp quasi-one-dimensional (1D) ("razor"), pyramid-shaped ("dagger"), and conical ("needle") potentials in the 2D complex Ginzburg-Landau (CGL) equation with cubic-quintic nonlinearity. This is a model of an active optical medium with respective expanding antiwaveguiding structures. If the potentials are strong enough, they give rise to continuous generation of expanding soliton patterns by a 2D soliton initially placed at the center. In the case of the pyramidal potential with M edges, the generated patterns are sets of M jets for M < or = 5, or expanding polygonal chains of solitons for M > or = 6. In the conical geometry, these are concentric waves expanding in the radial direction.
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Affiliation(s)
- Bin Liu
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-Sen University, 510275, Guangzhou, China
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22
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Genevet P, Barland S, Giudici M, Tredicce JR. Bistable and addressable localized vortices in semiconductor lasers. PHYSICAL REVIEW LETTERS 2010; 104:223902. [PMID: 20867170 DOI: 10.1103/physrevlett.104.223902] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2009] [Indexed: 05/09/2023]
Abstract
We demonstrate experimentally that localized emission states in coupled broad-area semiconductor lasers can carry a finite orbital angular momentum. The resulting structures therefore possess the chirality of optical vortices together with the properties of localized structures in dissipative systems, namely, the coexistence with a low intensity homogeneous emission and the mutual independence. These results open the way to the realization of arrays of optically addressable and bistable chiral laser pixels.
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Affiliation(s)
- P Genevet
- Université de Nice Sophia Antipolis, Institut Non-Linéaire de Nice, UMR 6618, 06560 Valbonne, France
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23
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Paulau PV, Gomila D, Colet P, Loiko NA, Rosanov NN, Ackemann T, Firth WJ. Vortex solitons in lasers with feedback. OPTICS EXPRESS 2010; 18:8859-66. [PMID: 20588731 DOI: 10.1364/oe.18.008859] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
We report on the existence, stability and dynamical properties of two-dimensional self-localized vortices with azimuthal numbers up to 4 in a simple model for lasers with frequency-selective feedback.We build the full bifurcation diagram for vortex solutions and characterize the different dynamical regimes. The mathematical model used, which consists of a laser rate equation coupled to a linear equation for the feedback field, can describe the spatiotemporal dynamics of broad area vertical cavity surface emitting lasers with external frequency selective feedback in the limit of zero delay.
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Affiliation(s)
- P V Paulau
- IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain.
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24
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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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25
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Mihalache D, Mazilu D, Lederer F, Leblond H, Malomed BA. Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:056601. [PMID: 19113227 DOI: 10.1103/physreve.78.056601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2008] [Indexed: 05/27/2023]
Abstract
We report results of collisions between coaxial vortex solitons with topological charges +/-S in the complex cubic-quintic Ginzburg-Landau equation. With the increase of the collision momentum, merger of the vortices into one or two dipole or quadrupole clusters of fundamental solitons (for S=1 and 2, respectively) is followed by the appearance of pairs of counter-rotating "unfinished vortices," in combination with a soliton cluster or without it. Finally, the collisions become elastic. The clusters generated by the collisions are very robust, while the "unfinished vortices," eventually split into soliton pairs.
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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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26
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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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27
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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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28
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He YJ, Fan HH, Dong JW, Wang HZ. Self-trapped spatiotemporal necklace-ring solitons in the Ginzburg-Landau equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:016611. [PMID: 16907208 DOI: 10.1103/physreve.74.016611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2005] [Revised: 05/05/2006] [Indexed: 05/11/2023]
Abstract
We consider a class of self-trapped spatiotemporal solitons: spatiotemporal necklace-ring solitons, whose intensities are azimuthally periodically modulated. We reveal numerically that the spatiotemporal necklace-ring solitons carrying zero, integer, and even fractional angular momentum can be self-trapped over a huge propagation distance in the three-dimensional cubic-quintic complex Ginzburg-Landau equation, even in the presence of random perturbations.
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Affiliation(s)
- Y J He
- State Key Laboratory of Optoelectronic Materials and Technologies, Zhongshan (Sun Yat-Sen) University, Guangzhou 510275, China
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29
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Skarka V, Aleksić NB. Stability criterion for dissipative soliton solutions of the one-, two-, and three-dimensional complex cubic-quintic Ginzburg-Landau equations. PHYSICAL REVIEW LETTERS 2006; 96:013903. [PMID: 16486455 DOI: 10.1103/physrevlett.96.013903] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2005] [Indexed: 05/06/2023]
Abstract
The generation and nonlinear dynamics of multidimensional optical dissipative solitonic pulses are examined. The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the (D + 1)-dimensional complex cubic-quintic Ginzburg-Landau equation (D = 1, 2, 3). A stability criterion is established fixing a domain of dissipative parameters for stable steady state solutions. Following numerical simulations, evolution of any input pulse from this domain leads to stable dissipative solitons.
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Affiliation(s)
- V Skarka
- Laboratoire POMA, UMR 6136 CNRS, Université d'Angers, 2, boulevard Lavoisier, 49045 Angers, Cedex 1, France
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32
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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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33
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Taranenko VB, Slekys G, Weiss CO. Spatial resonator solitons. CHAOS (WOODBURY, N.Y.) 2003; 13:777-790. [PMID: 12777142 DOI: 10.1063/1.1576971] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Spatial solitons can exist in various kinds of nonlinear optical resonators with and without amplification. In the past years different types of these localized structures such as vortices, bright, dark solitons, and phase solitons have been experimentally shown to exist. Many links appear to exist to fields different from optics, such as fluids, phase transitions, or particle physics. These spatial resonator solitons are bistable and due to their mobility suggest schemes of information processing not possible with the fixed bistable elements forming the basic ingredient of traditional electronic processing. The recent demonstration of existence and manipulation of spatial solitons in semiconductor microresonators represents a step in the direction of such optical parallel processing applications. We review some proof of principle soliton experiments on slow systems, and describe in more detail the experiments on semiconductor resonator solitons which are aimed at applications.
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Affiliation(s)
- V B Taranenko
- Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
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34
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Efremidis NK, Christodoulides DN. Discrete Ginzburg-Landau solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:026606. [PMID: 12636840 DOI: 10.1103/physreve.67.026606] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2002] [Indexed: 05/24/2023]
Abstract
We demonstrate that discrete solitons are possible in Ginzburg-Landau lattices. As a result of discreteness, we find that this system exhibits a host of features that have no counterpart whatsoever in either the continuous limit or in other conservative discrete models.
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Affiliation(s)
- Nikolaos K Efremidis
- School of Optics/CREOL, University of Central Florida, Orlando, FL 32816-2700, USA
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35
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Sakaguchi H. Domain-size control by global feedback in bistable systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:047101. [PMID: 11690175 DOI: 10.1103/physreve.64.047101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2001] [Indexed: 05/23/2023]
Abstract
We study domain structures in bistable systems such as the Ginzburg-Landau equation. The size of domains can be controlled by a global negative feedback. The domain-size control is applied for a localized spiral pattern.
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Affiliation(s)
- H 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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