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Zhang Y, Qin Y, Zheng H, Ren H. Periodic evolution of the out-of-phase dipole and the single-charged vortex solitons in periodic photonic moiré lattice with saturable self-focusing nonlinearity media. OPTICS EXPRESS 2022; 30:28840-28852. [PMID: 36299072 DOI: 10.1364/oe.458708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 07/11/2022] [Indexed: 06/16/2023]
Abstract
We survey the propagation properties of the out-of-phase (OOP) dipole solitons and the single-charged vortex (SCV) soliton in a periodic photonic moiré lattice with θ=arctan(3/4) under self-focusing nonlinearity media. Since the rotation angle, periodic photonic moiré lattices have peculiar energy band structures, with highly flat bands and the bandgaps being much more extensive, which is very favorable for the realization and stability of the solitons. When exciting a single point on-site with the OOP dipole beam, its evolution shows a periodic rollover around the lattice axis. Whereas, when exciting a single point on-site with the SCV beam, it transmits counterclockwise rotating periodically. Both the OOP dipole solitons and the SVC soliton maintain the local state, but their phase exhibits different variations. The phase of the OOP dipole solitons is flipped, while that of the SCV is rotated counterclockwise. Our work further complements the exploration of solitons in photonic moiré lattice with nonlinearity.
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2
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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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3
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Al Khawaja U. Interaction forces among two-dimensional bright solitons and many-soliton molecules. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:056604. [PMID: 23004892 DOI: 10.1103/physreve.85.056604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2011] [Indexed: 06/01/2023]
Abstract
We consider two-dimensional bright matter-wave solitons in two-dimensional Bose-Einstein condensates. From the asymptotic form of their wave function, we derive an analytic expression for the force of interaction between solitons in the large separation limit, which turns out to decay with solitons separation Δ as F(Δ)∝exp(-Δ)/√Δ. Simulating the dynamics of two solitons using the relevant Gross-Pitaevskii equation, we obtain the force of the interaction for the full range of Δ, which turns out to be of molecular type. We show that many-soliton molecules can exist as a result of such a molecular-type of interaction. These include string-shaped, ring-shaped, or regular-lattice-shaped soliton molecules. By calculating their binding energy, we investigate the stability of these structures. Contrary to one-dimensional soliton molecules, which have no binding energy, two-dimensional molecules of a lattice of solitons with alternating phases are robust and have a negative binding energy. Lattices of size larger than 2 × 2 solitons have many discrete equilibrium values of the separation between two neighboring solitons.
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Affiliation(s)
- U Al Khawaja
- Department of Physics, United Arab Emirates University, Al-Ain, United Arab Emirates
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4
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Yakimenko AI, Prikhodko OO, Vilchynskyi SI. Bright vector solitons in cross-defocusing nonlinear media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:016605. [PMID: 20866753 DOI: 10.1103/physreve.82.016605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2010] [Indexed: 05/29/2023]
Abstract
We study two-dimensional soliton-soliton vector pairs in media with self-focusing nonlinearities and defocusing cross interactions. The general properties of the stationary states and their stability are investigated. The different scenarios of instability are observed using numerical simulations. The quasistable propagation regime of the high-power vector solitons is revealed.
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Affiliation(s)
- A I Yakimenko
- Department of Physics, Taras Shevchenko National University, Kiev, Ukraine
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5
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Xu Z, Smyth NF, Minzoni AA, Kivshar YS. Vector vortex solitons in nematic liquid crystals. OPTICS LETTERS 2009; 34:1414-1416. [PMID: 19412290 DOI: 10.1364/ol.34.001414] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response can dramatically enhance the field coupling leading to the stabilization of the vortex beam when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically.
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Affiliation(s)
- Zhiyong Xu
- Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia.
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6
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Clougherty DP. Polarons and solitons in Jahn–Teller systems. J Mol Struct 2007. [DOI: 10.1016/j.molstruc.2006.12.037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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7
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Kartashov YV, Torner L, Vysloukh VA, Mihalache D. Multipole vector solitons in nonlocal nonlinear media. OPTICS LETTERS 2006; 31:1483-5. [PMID: 16642146 DOI: 10.1364/ol.31.001483] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive index profile. We found that stabilization of the otherwise highly unstable multipoles occurs below certain maximum energy flow. Such a threshold is determined by the nonlocality degree.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, Castelldefels (Barcelona), Spain.
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8
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Schröder J, Jander P, Denz C, Richter T, Motzek K, Kaiser F. Counterpropagating dipole-mode vector soliton. OPTICS LETTERS 2005; 30:1042-4. [PMID: 15906997 DOI: 10.1364/ol.30.001042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
We experimentally observed a counterpropagating dipole-mode vector soliton in a photorefractive SBN:60Ce crystal. We investigated the transient formation dynamics and show that the formation process differs significantly from the copropagating geometry. The experimental results are compared with fully anisotropic numerical simulations and show good qualitative agreement.
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Affiliation(s)
- Jochen Schröder
- Institute of Applied Physics, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany.
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9
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Montesinos GD, Pérez-García VM, Michinel H, Salgueiro JR. Stabilized vortices in layered Kerr media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036624. [PMID: 15903622 DOI: 10.1103/physreve.71.036624] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2004] [Revised: 12/20/2004] [Indexed: 05/02/2023]
Abstract
In this paper, we demonstrate the possibility of stabilizing beams with angular momentum propagating in Kerr media against filamentation and collapse. Very long propagation distances can be achieved by combining the choice of an appropriate layered medium with alternating focusing and defocusing nonlinearities with the presence of an incoherent guiding beam which is itself stabilized in this medium. The applicability of the results to the field of matter waves is also discussed.
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Affiliation(s)
- Gaspar D Montesinos
- Departamento de Matemáticas, Escuela Técnica Superior de Ingenieros Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain
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10
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Desyatnikov AS, Mihalache D, Mazilu D, Malomed BA, Denz C, Lederer F. Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:026615. [PMID: 15783449 DOI: 10.1103/physreve.71.026615] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2004] [Indexed: 05/24/2023]
Abstract
We demonstrate that two-dimensional two-component bright solitons of an annular shape, carrying vorticities (m,+/-m) in the components, may be stable in media with the cubic-quintic nonlinearity, including the hidden-vorticity (HV) solitons of the type (m,-m) , whose net vorticity is zero. Stability regions for the vortices of both (m,+/-m) types are identified for m=1 , 2, and 3, by dint of the calculation of stability eigenvalues, and in direct simulations. In addition to the well-known symmetry-breaking (external) instability, which splits the ring soliton into a set of fragments flying away in tangential directions, we report two new scenarios of the development of weak instabilities specific to the HV solitons. One features charge flipping, with the two components exchanging angular momentum and periodically reversing the sign of their spins. The composite soliton does not directly split in this case; therefore, we identify such instability as an intrinsic one. Eventually, the soliton splits, as weak radiation loss drives it across the border of the ordinary strong (external) instability. Another scenario proceeds through separation of the vortex cores in the two components, each individual core moving toward the outer edge of the annular soliton. After expulsion of the cores, there remains a zero-vorticity breather with persistent internal vibrations.
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Affiliation(s)
- A S Desyatnikov
- Nonlinear Physics Centre and Centre for Ultra-high bandwidth Devices for Optical Systems (CUDOS), Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
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11
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Motzek K, Kaiser F, Salgueiro JR, Kivshar Y, Denz C. Incoherent vector vortex-mode solitons in self-focusing nonlinear media. OPTICS LETTERS 2004; 29:2285-2287. [PMID: 15524382 DOI: 10.1364/ol.29.002285] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We suggest a novel type of composite spatial optical soliton created by a coherent vortex beam guiding a partially incoherent light beam in a self-focusing nonlinear medium. We show that the incoherence of the guided mode may enhance, rather than suppress, the vortex azimuthal instability, and we also demonstrate strong destabilization of dipole-mode solitons by partially incoherent light.
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Affiliation(s)
- Kristian Motzek
- Institute of Applied Physics, Darmstadt University of Technology, Darmstadt, Germany
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12
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Kizner Z, Khvoles R. The tripole vortex: Experimental evidence and explicit solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:016307. [PMID: 15324169 DOI: 10.1103/physreve.70.016307] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2003] [Indexed: 05/24/2023]
Abstract
Based on experimental evidence, explicit vorticity-distributed solutions to the Euler equations in two dimensions are constructed describing the tripole vortex. The vortex form and the solution outside the region of nonzero vorticity are derived analytically, while the interior is solved numerically. The continuous-vorticity solution reproduces the main features of the tripoles observed in laboratory experiments and numerical simulations-their shape, flow pattern, and the form of the nonlinear vorticity vs streamfunction relation. The approach followed in the construction of a tripole proves to be beneficial in the search for higher-order multipoles, an example being a smooth quadrupole solution.
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Affiliation(s)
- Ziv Kizner
- Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel.
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13
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Motzek K, Jander P, Desyatnikov A, Belić M, Denz C, Kaiser F. Dynamic counterpropagating vector solitons in saturable self-focusing media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:066611. [PMID: 14754340 DOI: 10.1103/physreve.68.066611] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2003] [Indexed: 05/24/2023]
Abstract
We display rich spatial and temporal dynamics of light fields counterpropagating in a saturable self-focusing medium numerically, and analyze instabilities that counterpropagating solitons experience. An expression for the maximum length that the medium must not exceed for the solitons to be stable is derived and connected to the coupling strength of beam interaction. The instability can lead to periodic or irregular temporal dynamics of the light beams. By considering mutually incoherent counterpropagating beams, we show that differences to the copropagating case are due to the different boundary conditions.
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Affiliation(s)
- K Motzek
- Institute of Applied Physics, Darmstadt University of Technology, Hochschulstrasse 4a, 64289 Darmstadt, Germany
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14
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Krolikowski W, McCarthy G, Kivshar YS, Weilnau C, Denz C, García-Ripoll JJ, Pérez-García VM. Scattering of dipole-mode vector solitons: theory and experiment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:016612. [PMID: 12935275 DOI: 10.1103/physreve.68.016612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2003] [Indexed: 05/24/2023]
Abstract
We study, both theoretically and experimentally, the scattering properties of optical dipole-mode vector solitons-radially asymmetric composite self-trapped optical beams. First, we analyze the soliton collisions in an isotropic two-component model with a saturable nonlinearity, and demonstrate that in many cases the scattering dynamics of the dipole-mode solitons allows us to classify them as "molecules of light"-extremely robust spatially localized objects which survive a wide range of interactions and display many properties of composite states with a rotational degree of freedom. Next, we study the composite solitons in an anisotropic nonlinear model that describes photorefractive nonlinearities, and also present a number of experimental verifications of our analysis.
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Affiliation(s)
- Wieslaw Krolikowski
- Laser Physics Center, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, ACT 0200, Australia
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15
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Bishop AR, Kalosakas G, Rasmussen KO, Kevrekidis PG. Localization in physical systems described by discrete nonlinear Schrodinger-type equations. CHAOS (WOODBURY, N.Y.) 2003; 13:588-595. [PMID: 12777124 DOI: 10.1063/1.1567651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Following a short introduction on localized modes in a model system, namely the discrete nonlinear Schrodinger equation, we present explicit results pertaining to three different physical systems described by similar equations. The applications range from the Raman scattering spectra of a complex electronic material through intrinsic localized vibrational modes, to the manifestation of an abrupt and irreversible delocalizing transition of Bose-Einstein condensates trapped in two-dimensional optical lattices, and to the instabilities of localized modes in coupled arrays of optical waveguides.
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Affiliation(s)
- A R Bishop
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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16
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Pérez-García VM, Vekslerchik V. Soliton molecules in trapped vector nonlinear Schrödinger systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:061804. [PMID: 16241251 DOI: 10.1103/physreve.67.061804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2002] [Indexed: 05/04/2023]
Abstract
We propose a method to build a great variety of stable multisoliton "molecules" with coupled light beams in Kerr graded index (GRIN) media or atomic mixtures of Bose-Einstein condensates. We present a general theory and discuss several specific cases, including two-, three-, and four-atom molecules made up of Gaussian modes or vortices. A three-dimensional example is also presented.
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Affiliation(s)
- Víctor M Pérez-García
- Departamento de Matemáticas, Escuela Técnica Superior de Ingenieros Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain.
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17
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Hudock J, Kevrekidis PG, Malomed BA, Christodoulides DN. Discrete vector solitons in two-dimensional nonlinear waveguide arrays: solutions, stability, and dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:056618. [PMID: 12786307 DOI: 10.1103/physreve.67.056618] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2001] [Revised: 01/23/2003] [Indexed: 05/24/2023]
Abstract
We identify and investigate bimodal (vector) solitons in models of square-lattice arrays of nonlinear optical waveguides. These vector self-localized states are, in fact, self-induced channels in a nonlinear photonic-crystal matrix. Such two-dimensional discrete vector solitons are possible in waveguide arrays in which each element carries two light beams that are either orthogonally polarized or have different carrier wavelengths. Estimates of the physical parameters necessary to support such soliton solutions in waveguide arrays are given. Using Newton relaxation methods, we obtain stationary vector-soliton solutions, and examine their stability through the computation of linearized eigenvalues for small perturbations. Our results may also be applicable to other systems such as two-component Bose-Einstein condensates trapped in a two-dimensional optical lattice.
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Affiliation(s)
- J Hudock
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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18
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Yang J, Pelinovsky DE. Stable vortex and dipole vector solitons in a saturable nonlinear medium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:016608. [PMID: 12636626 DOI: 10.1103/physreve.67.016608] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2002] [Indexed: 05/24/2023]
Abstract
We study both analytically and numerically the existence, uniqueness, and stability of vortex and dipole vector solitons in a saturable nonlinear medium in (2+1) dimensions. We construct perturbation series expansions for the vortex and dipole vector solitons near the bifurcation point, where the vortex and dipole components are small. We show that both solutions uniquely bifurcate from the same bifurcation point. We also prove that both vortex and dipole vector solitons are linearly stable in the neighborhood of the bifurcation point. Far from the bifurcation point, the family of vortex solitons becomes linearly unstable via oscillatory instabilities, while the family of dipole solitons remains stable in the entire domain of existence. In addition, we show that an unstable vortex soliton breaks up either into a rotating dipole soliton or into two rotating fundamental solitons.
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Affiliation(s)
- Jianke Yang
- Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA
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19
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Saito H, Ueda M. Split instability of a vortex in an attractive Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2002; 89:190402. [PMID: 12443103 DOI: 10.1103/physrevlett.89.190402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2002] [Indexed: 05/24/2023]
Abstract
An attractive Bose-Einstein condensate with a vortex splits into two pieces via the quadrupole dynamical instability, which arises at a weaker strength of interaction than the monopole and the dipole instabilities. The split pieces subsequently unite to restore the original vortex or collapse.
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Affiliation(s)
- Hiroki Saito
- Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan
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20
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Skryabin DV, McSloy JM, Firth WJ. Stability of spiralling solitary waves in Hamiltonian systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:055602. [PMID: 12513549 DOI: 10.1103/physreve.66.055602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2002] [Indexed: 05/24/2023]
Abstract
We present a rigorous criterion for stability of spiralling solitary structures in Hamiltonian systems incorporating the angular momentum integral and demonstrate its applicability to the spiralling of two mutually incoherent optical beams propagating in a photorefractive material.
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Affiliation(s)
- Dmitry V Skryabin
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
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21
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Bigelow MS, Park QH, Boyd RW. Stabilization of the propagation of spatial solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:046631. [PMID: 12443373 DOI: 10.1103/physreve.66.046631] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2002] [Revised: 08/26/2002] [Indexed: 05/24/2023]
Abstract
We investigate a class of vector ring spatial solitons that carry no net angular momentum. Specifically, we show analytically and numerically that the dominant low-frequency perturbations that typically disrupt ring solitons are suppressed for these solitons. By comparing our analytical and numerical results, we show that our simple analysis gives good qualitative predictions on the regions of stability for these beams.
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22
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Yang J. Internal oscillations and instability characteristics of (2+1)-dimensional solitons in a saturable nonlinear medium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:026601. [PMID: 12241305 DOI: 10.1103/physreve.66.026601] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2002] [Indexed: 11/07/2022]
Abstract
Two related problems on scalar (2+1)-dimensional solitons in a saturable nonlinear medium are investigated. The first one is the internal oscillations of fundamental (single-hump) solitons. Internal modes which cause these oscillations, both with and without angular dependence, are discovered. The visual effect of angle-dependent internal modes on the soliton can be a rotation or spatially uneven breathing of the perturbed soliton. These internal oscillations are very robust and persist for a very long distance. The second problem is the instability of double-hump and radially symmetric solitons. Unstable eigenmodes of these solitons are presented. Contrary to intuition, the instability growth rates decrease to zero when the soliton power becomes high. Thus the instability is strongly suppressed at high powers. This phenomenon is corroborated by our direct numerical simulations.
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Affiliation(s)
- Jianke Yang
- Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA
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23
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Belić MR, Vujić D, Stepken A, Kaiser F, Calvo GF, Agulló-López F, Carrascosa M. Isotropic versus anisotropic modeling of photorefractive solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:066610. [PMID: 12188854 DOI: 10.1103/physreve.65.066610] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2001] [Indexed: 05/23/2023]
Abstract
The question of the isotropic versus anisotropic modeling of incoherent spatial screening solitons in photorefractive crystals is addressed by a careful theoretical and numerical analysis. Isotropic, or local, models allow for an extended spiraling of two interacting scalar solitons, and for a prolonged propagation of vortex vector solitons, whereas anisotropic, nonlocal, models prevent such phenomena. In the context of Kukhtarev's material equations, the difference in behavior is traced to the continuity equation for the current density. We further show that neither an indefinite spiraling of two solitons nor stable propagation of vortex vector solitons is generally possible in both isotropic and anisotropic models. Such systems do not conserve angular momentum, even in the case of an isotropic change in the index of refraction.
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Affiliation(s)
- M R Belić
- Institute of Physics, P.O. Box 57, 11001 Belgrade, Yugoslavia
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24
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Desyatnikov AS, Kivshar YS, Motzek K, Kaiser F, Weilnau C, Denz C. Multicomponent dipole-mode spatial solitons. OPTICS LETTERS 2002; 27:634-636. [PMID: 18007886 DOI: 10.1364/ol.27.000634] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We study (2+1) -dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents and demonstrate that these solitary waves exhibit a symmetry-breaking instability, provided their total topological charge is nonzero. We describe a novel type of stable multicomponent dipole-mode solitons with intriguing swinging dynamics.
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25
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Desyatnikov AS, Kivshar YS. Rotating optical soliton clusters. PHYSICAL REVIEW LETTERS 2002; 88:053901. [PMID: 11863725 DOI: 10.1103/physrevlett.88.053901] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2001] [Indexed: 05/23/2023]
Abstract
We introduce the concept of soliton clusters--multisoliton bound states in a homogeneous bulk optical medium--and reveal a key physical mechanism for their stabilization associated with a staircaselike phase distribution that induces a net angular momentum and leads to cluster rotation. The ringlike soliton clusters provide a nontrivial generalization of the concepts of two-soliton spiraling, optical vortex solitons, and necklace-type optical beams.
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Affiliation(s)
- Anton S Desyatnikov
- Nonlinear Physics Group, Research School of Physical Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia
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Kevrekidis PG, Nistazakis HE, Frantzeskakis DJ, Malomed BA, Bishop AR. Ring solitons on vortices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:066611. [PMID: 11736300 DOI: 10.1103/physreve.64.066611] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2001] [Indexed: 05/23/2023]
Abstract
Interaction of a ring dark or antidark soliton (RDS and RADS, respectively) with a vortex is considered in the defocusing nonlinear Schrödinger equation with cubic (for RDS) or saturable (for RADS) nonlinearities. By means of direct simulations, it is found that the interaction gives rise to either an almost isotropic or a spiral-like pattern. A transition between them occurs at a critical value of the RDS or RADS amplitude, the spiral pattern appearing if the amplitude exceeds the critical value. An initial ring soliton created on top of the vortex splits into a pair of rings moving inward and outward. In the subcritical case, the inbound ring reverses its polarity, bouncing from the vortex core, without conspicuous effect on the core. In the transcritical case, the bounced ring soliton suffers a spiral deformation, while the vortex changes its position and structure and also loses its axial symmetry. Through a variational-type approach to the system's Hamiltonian, we additionally find that the vortex-RDS and vortex-RADS interactions are, respectively, attractive and repulsive. Simulations with the vortex placed eccentrically with respect to the RDS or RADS reveal the generation of strongly localized multispot dark and/or antidark coherent structures. The occurrence of spiral-like patterns in many numerical experiments prompted an attempt to generate a spiral dark soliton, but the latter is found to suffer a core instability that converts it into a rotating dipole emitting waves in the outward direction.
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Affiliation(s)
- P G Kevrekidis
- Program in Applied and Computational Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544, USA
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27
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Weilnau C, Denz C, Ahles M, Stepken A, Motzek K, Kaiser F. Generation of higher-order optical (2+1)-dimensional spatial vector solitons in a nonlinear anisotropic medium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:056601. [PMID: 11736110 DOI: 10.1103/physreve.64.056601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2001] [Indexed: 05/23/2023]
Abstract
We investigate the generation of higher-order optical vector solitons in two transverse dimensions in anisotropic nonlinear media consisting of an incoherent superposition of a Gaussian beam and a higher-order laser mode with a complex internal modal structure. We demonstrate both numerically and experimentally various examples of these stable self-trapped light structures and show that vortex modes carrying topological charge always decay into multiple-humped structures that remain self trapped during propagation. Furthermore, we demonstrate the mutual stabilization of a triple- and a double-humped transverse light structure leading to the formation of a two-dimensional vector soliton without a stabilizing fundamental Gaussian mode.
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Affiliation(s)
- C Weilnau
- Institute of Applied Physics, Westfälische Wilhelms-Universität Münster, Corrensstrasse 2-4, D-48149 Münster, Germany.
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28
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Kolossovski KY, Buryak AV, Skryabin DV, Sammut RA. Nonlinear dynamics of higher-order solitons near the oscillatory instability threshold. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:056612. [PMID: 11736121 DOI: 10.1103/physreve.64.056612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2001] [Indexed: 05/23/2023]
Abstract
Nonlinear theory describing the dynamics of solitons in the vicinity of oscillatory instability threshold with a low frequency offset is developed. The theory is tested on the example of parametric degenerate four-wave mixing. All major predictions of our theory are in agreement with the results of direct numerical modeling. This includes the position of oscillatory instability threshold, instability rates, and various instability development scenarios.
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Affiliation(s)
- K Y Kolossovski
- School of Mathematics and Statistics, University of New South Wales, Australian Defence Force Academy, Canberra 2600, Australia
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29
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Pigier C, Uzdin R, Carmon T, Segev M, Nepomnyaschchy A, Musslimani ZH. Collisions between (2+1)D rotating propeller solitons. OPTICS LETTERS 2001; 26:1577-1579. [PMID: 18049668 DOI: 10.1364/ol.26.001577] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We study theoretically the collisions between (2+1)D rotating-dipole-type bimodal solitons and find that such interactions exhibit many interesting exchanges of angular momentum.
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30
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Carmon T, Uzdin R, Pigier C, Musslimani ZH, Segev M, Nepomnyashchy A. Rotating propeller solitons. PHYSICAL REVIEW LETTERS 2001; 87:143901. [PMID: 11580651 DOI: 10.1103/physrevlett.87.143901] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2000] [Indexed: 05/23/2023]
Abstract
We demonstrate experimentally and theoretically (both analytically and numerically) a new type of spatial soliton: a rotating "propeller" soliton. This is a composite soliton made of a rotating dipole component jointly trapped with a bell-shaped component. We observe as much as 239 degrees of rotation over 13 mm of propagation (6.5 diffraction lengths).
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Affiliation(s)
- T Carmon
- Technion-Israel Institute of Technology, Haifa 32000, Israel
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31
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Neshev D, Krolikowski W, Pelinovsky DE, McCarthy G, Kivshar YS. Transverse instability of vector solitons and generation of dipole arrays. PHYSICAL REVIEW LETTERS 2001; 87:103903. [PMID: 11531480 DOI: 10.1103/physrevlett.87.103903] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2001] [Indexed: 05/23/2023]
Abstract
We develop a theory of modulational instability of multiparameter solitary waves and analyze the transverse instability of composite (or vector) optical solitons in a saturable nonlinear medium. We demonstrate theoretically and experimentally that a soliton stripe breaks up into an array of ( 2+1)-dimensional dipole-mode vector solitons, thus confirming the robust nature of those solitons as fundamental composite structures of incoherently coupled fields.
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Affiliation(s)
- D Neshev
- Nonlinear Physics Group, Research School of Physical Sciences and Engineering, The Institute of Advanced Studies, The Australian National University, Canberra ACT 0200, Australia
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32
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Neshev D, McCarthy G, Krolikowski W, Ostrovskaya EA, Kivshar YS, Calvo GF, Agullo-Lopez F. Dipole-mode vector solitons in anisotropic nonlocal self-focusing media. OPTICS LETTERS 2001; 26:1185-1187. [PMID: 18049557 DOI: 10.1364/ol.26.001185] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We demonstrate, theoretically and experimentally, that dipole-mode vector solitons created in biased photorefractive media possess a number of anisotropy-driven properties, such as stability of a selected orientation, wobbling, and incomplete rotation, owing to the anisotropic nonlocal response of the photorefractive non-linearity. Such features are found for higher-order (multipole) vector solitons, and they are carefully verified in an experiment.
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33
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Picozzi A. Three-dimensional hybrid solitary waves: transverse vortex solitons stabilized by longitudinal parametric solitary waves. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:016614. [PMID: 11461435 DOI: 10.1103/physreve.64.016614] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2001] [Revised: 03/15/2001] [Indexed: 05/23/2023]
Abstract
We show that the parametric process in quadratic nonlinear media supports three-dimensional (3D) hybrid solitary wave solution in which a transverse vortex solitons embedded in an infinite plane-wave background is sustained by a longitudinal parametric solitary wave. The structure of the parametric solitary wave results from the interplay of the quadratic nonlinearity and the temporal walk off (i.e., the velocity mismatch) between the interacting waves. The 3D hybrid solitary wave proved to be robust with respect to modulational instability, a feature that contrasts with previous studies on quadratic vortex solitons that revealed them to be always modulationally unstable. We show that the mechanism of stabilization of the vortex background lies on the temporal walkoff between the interacting waves that is able to drift the modulational instability out of the temporally localized structure that constitutes the 3D hybrid solitary wave.
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Affiliation(s)
- A Picozzi
- Laboratoire de Physique de la Matière Condensée, CNRS-UMR 6622, Université de Nice Sophia-Antipolis, Parc Valrose, F-06108 Nice Cedex, France
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Musslimani ZH, Soljacić M, Segev M, Christodoulides DN. Interactions between two-dimensional composite vector solitons carrying topological charges. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:066608. [PMID: 11415243 DOI: 10.1103/physreve.63.066608] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2000] [Indexed: 05/23/2023]
Abstract
We present a comprehensive study of interactions (collisions) between two-dimensional composite vector solitons carrying topological charges in isotropic saturable nonlinear media. We numerically study interactions between such composite solitons for different regimes of collision angle and report numerous effects which are caused solely by the "spin" (topological charge) carried by the second excited mode. The most intriguing phenomenon we find is the delayed-action interaction between interacting composite solitons carrying opposite spins. In this case, two colliding solitons undergo a fusion process and form a metastable bound state that decays after long propagation distances into two or three new solitons. Another noticeable effect is spin-orbit coupling in which angular momentum is being transferred from "spin" to orbital angular momentum. This phenomenon occurs at angles below the critical angle, including the case when the initial soliton trajectories are in parallel to one another and lie in the same plane. Finally, we report on shape transformation of vortex component into a rotating dipole-mode solitons that occurs at large collision angles, i.e., at angles for which scalar solitons of all types simply go through one another unaffected.
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Affiliation(s)
- Z H Musslimani
- Department of Applied Mathematics, University of Colorado, Campus Box 526, Boulder, Colorado 80309-0526, USA
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35
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Towers I, Buryak AV, Sammut RA, Malomed BA. Stable localized vortex solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:055601. [PMID: 11414954 DOI: 10.1103/physreve.63.055601] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2000] [Indexed: 05/23/2023]
Abstract
We demonstrate that parametric interaction of a fundamental beam with its second harmonic in bulk media, in the presence of self-defocusing third-order nonlinearity, gives rise to the first ever examples of completely stable localized ring-shaped solitons with intrinsic vorticity n=1 and n=2. The stability is demonstrated both in direct simulations and by computing eigenvalues of the corresponding linearized equations. A potential application of the (2+1)-dimensional ring solitons in optics is a possibility to design a reconfigurable multichannel system guiding signal beams.
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Affiliation(s)
- I Towers
- School of Mathematics and Statistics, Australian Defence Force Academy, Canberra, ACT 2600, Australia
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36
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Desyatnikov AS, Neshev D, Ostrovskaya EA, Kivshar YS, Krolikowski W, Luther-Davies B, García-Ripoll JJ, Pérez-García VM. Multipole spatial vector solitons. OPTICS LETTERS 2001; 26:435-437. [PMID: 18040345 DOI: 10.1364/ol.26.000435] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We introduce the concept of multipole spatial optical vector solitons associated with higher-order guided modes trapped by a soliton-induced waveguide in a bulk medium. Such stationary localized waves include previously predicted vortex- and dipole-mode vector solitons and also describe new higher-order vector solitons and necklace-type beams. We present the theoretical and experimental results of the structure, formation, and instability development of the quadrupole vector solitons.
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37
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Musslimani ZH, Soljacić M, Segev M, Christodoulides DN. Delayed-action interaction and spin-orbit coupling between solitons. PHYSICAL REVIEW LETTERS 2001; 86:799-802. [PMID: 11177943 DOI: 10.1103/physrevlett.86.799] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2000] [Revised: 08/15/2000] [Indexed: 05/23/2023]
Abstract
We report on new fundamental phenomena in soliton interactions: delayed-action interaction and "spin"-orbit coupling upon collision between two-dimensional composite solitons carrying topological charges.
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Affiliation(s)
- Z H Musslimani
- Department of Mathematics, Technion--Israel Institute of Technology, Haifa
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38
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Krolikowski W, Ostrovskaya EA, Weilnau C, Geisser M, McCarthy G, Kivshar YS, Denz C, Luther-Davies B. Observation of dipole-mode vector solitons. PHYSICAL REVIEW LETTERS 2000; 85:1424-1427. [PMID: 10970520 DOI: 10.1103/physrevlett.85.1424] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2000] [Indexed: 05/23/2023]
Abstract
We report on the first experimental observation of a novel type of optical vector soliton, a dipole-mode soliton, recently predicted theoretically. We show that these vector solitons can be generated in a photorefractive medium employing two different processes: a phase imprinting, and a symmetry-breaking instability of a vortex-mode vector soliton. The experimental results display remarkable agreement with the theory, and confirm the robust nature of these radially asymmetric two-component solitary waves.
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Affiliation(s)
- W Krolikowski
- Laser Physics Centre, The Australian National University, Canberra ACT 0200, Australia
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