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Kartashov YV, Malomed BA, Torner L. Metastability of Quantum Droplet Clusters. PHYSICAL REVIEW LETTERS 2019; 122:193902. [PMID: 31144921 DOI: 10.1103/physrevlett.122.193902] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Revised: 03/25/2019] [Indexed: 06/09/2023]
Abstract
We show that metastable ring-shaped clusters can be constructed from two-dimensional quantum droplets in systems described by the Gross-Pitaevskii equations augmented with Lee-Huang-Yang quantum corrections. The clusters exhibit dynamical behavior ranging from contraction to rotation with simultaneous periodic pulsations, or expansion, depending on the initial radius of the necklace pattern and phase shift between adjacent quantum droplets. We show that, using an energy-minimization analysis, one can predict equilibrium values of the cluster radius that correspond to rotation without radial pulsations. In such a regime, the clusters evolve as metastable states, withstanding abrupt variations in the underlying scattering lengths and keeping their azimuthal symmetry in the course of evolution, even in the presence of considerable perturbations.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 108840, Russia
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Centre for Light-Matter Interaction, Tel Aviv University, P. O. Box 39040 Tel Aviv, Israel
| | - Lluis Torner
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Universitat Politecnica de Catalunya, 08034 Barcelona, Spain
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Dynamics of necklace beams in nonlinear colloidal suspensions. Sci Rep 2017; 7:11709. [PMID: 28916768 PMCID: PMC5601962 DOI: 10.1038/s41598-017-12169-x] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2017] [Accepted: 08/30/2017] [Indexed: 11/08/2022] Open
Abstract
Recently, we have predicted that the modulation instability of optical vortex solitons propagating in nonlinear colloidal suspensions with exponential saturable nonlinearity leads to formation of necklace beams (NBs). Here, we investigate the dynamics of NB formation and propagation, and demonstrate a variety of optical beam structures emerging upon vortex beam propagation in engineered nonlinear colloidal medium. In particular, we show that the distance at which the NB is formed depends on the input power of the vortex beam. Moreover, we show that the NB trajectories are not necessarily tangent to the initial vortex ring, and that their velocities have components stemming both from the beam diffraction and from the beam orbital angular momentum. We also demonstrate the generation of elliptical rotating solitons and analyze the influence of losses on their propagation. Finally, we investigate the conservation of the orbital angular momentum in necklace and elliptical rotating beams. Our studies, performed in ideal lossless media and in realistic colloidal suspensions with losses, provide a detailed description of NB dynamics, and may be useful in analysis of light propagation in highly scattering colloids and biological samples.
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Silahli SZ, Walasik W, Litchinitser NM. Necklace beam generation in nonlinear colloidal engineered media. OPTICS LETTERS 2015; 40:5714-5717. [PMID: 26670494 DOI: 10.1364/ol.40.005714] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes as supercontinuum generation, light filamentation, rogue waves, and ring (or necklace) beam formation. To date, a majority of studies of these phenomena have focused on light-matter interactions in self-focusing Kerr media existing in nature. However, a large and tunable nonlinear response of a colloidal suspension can be tailored at will by judiciously engineering the optical polarizability. Here, we analytically and numerically show the possibility of necklace beam generation originating from spatial modulational instability of vortex beams in engineered soft-matter nonlinear media with different types of exponential nonlinearity.
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Zhang Y, Wu Z, Yuan C, Yao X, Lu K, Belić M, Zhang Y. Optical vortices induced in nonlinear multilevel atomic vapors. OPTICS LETTERS 2012; 37:4507-4509. [PMID: 23114345 DOI: 10.1364/ol.37.004507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
In a numerical investigation, we demonstrate the existence and curious evolution of vortices in a ladder-type three-level nonlinear atomic vapor with linear, cubic, and quintic susceptibilities considered simultaneously with the dressing effect. We find that the number of beads and topological charge of the incident beam, as well as its size, greatly affect the formation and evolution of vortices. To determine the number of induced vortices and the corresponding rotation direction, we give common rules associated with the initial conditions coming from various incident beams.
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Affiliation(s)
- Yiqi Zhang
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi'an Jiaotong University, Xi'an, China.
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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, Li SJ. Phase controlling of collisions between solitons in the two-dimensional complex Ginzburg-Landau equation without viscosity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:056607. [PMID: 22181536 DOI: 10.1103/physreve.84.056607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2011] [Revised: 10/23/2011] [Indexed: 05/31/2023]
Abstract
We present a systematic analysis of the outcome of soliton collisions upon variation of the relative phase φ of the solitons, in the two-dimensional cubic-quintic complex Ginzburg-Landau equation in the absence of viscosity. Three generic outcomes are identified: merger of the solitons into a single one, creation of an extra soliton, and quasielastic interaction. The velocities of the merger soliton and the extra soliton can be effectively controlled by φ. In addition, the range of the outcome of creating an extra soliton decreases to zero with the reduction of gain or the increasing of loss. The above features have potential applications in optical switching and logic gates based on interaction of optical solitons.
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Affiliation(s)
- Bin Liu
- Key Laboratory of Nondestructive Test (Ministry of Education), Nanchang Hangkong University, Nanchang, People's Republic of China.
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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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Zhang Y, Nie Z, Zhao Y, Li C, Wang R, Si J, Xiao M. Modulated vortex solitons of four-wave mixing. OPTICS EXPRESS 2010; 18:10963-10972. [PMID: 20588952 DOI: 10.1364/oe.18.010963] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We experimentally demonstrate the vortex solitons of four-wave mixing (FWM) in multi-level atomic media created by the interference patterns with superposing three or more waves. The modulation effect of the vortex solitons is induced by the cross-Kerr nonlinear dispersion due to atomic coherence in the multi-level atomic system. These FWM vortex patterns are explained via the three-, four- and five-wave interference topologies.
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Affiliation(s)
- Yanpeng Zhang
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China.
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Liu B, He YJ, Qiu ZR, Wang HZ. Annularly and radially phase-modulated spatiotemporal necklace-ring patterns in the Ginzburg-Landau and Swift-Hohenberg equations. OPTICS EXPRESS 2009; 17:12203-12209. [PMID: 19654622 DOI: 10.1364/oe.17.012203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Annularly and radially phase-modulated spatiotemporal necklace-shaped patterns (SNPs) in the complex Ginzburg-Landau (CGL) and complex Swift-Hohenberg (CSH) equations are theoretically studied. It is shown that the annularly phase-modulated SNPs, with a small initial radius of the necklace and modulation parameters, can evolve into stable fundamental or vortex solitons. To the radially phase-modulated SNPs, the modulated "beads" on the necklace rapidly vanish under strong dissipation in transmission, which may have potential application for optical switching in signal processing. A prediction that the SNPs with large initial radii keep necklace-ring shapes upon propagation is demonstrated by use of balance equations for energy and momentum. Differences between both models for the evolution of solitons are revealed.
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Affiliation(s)
- Bin Liu
- State Key Laboratory of Optoelectronic Materials and Technologies, Zhongshan (Sun Yat-Sen) University, Guangzhou 510275, China
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