1
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Yang Y, Shen M. Modulation instability in nonlinear media with sine-oscillatory nonlocal response function and pure quartic diffraction. Sci Rep 2024; 14:8961. [PMID: 38637682 PMCID: PMC11026490 DOI: 10.1038/s41598-024-59722-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Accepted: 04/15/2024] [Indexed: 04/20/2024] Open
Abstract
Modulation instability of one-dimensional plane wave is demonstrated in nonlinear Kerr media with sine-oscillatory nonlocal response function and pure quartic diffraction. The growth rate of modulation instability, which depends on the degree of nonlocality, coefficient of quartic diffraction, type of the nonlinearity and the power of plane wave, is analytically obtained with linear-stability analysis. Different from other nonlocal response functions, the maximum of the growth rate in media with sine-oscillatory nonlocal response function occurs always at a particular wave number. Theoretical results of modulation instability are confirmed numerically with split-step Fourier transform. Modulation instability can be controlled flexibly by adjusting the degree of nonlocality and quartic diffraction.
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Affiliation(s)
- Yuwen Yang
- Institute for Quantum Science and Technology, Department of Physics, Shanghai University, Shanghai, 200444, China
| | - Ming Shen
- Institute for Quantum Science and Technology, Department of Physics, Shanghai University, Shanghai, 200444, China.
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2
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Tabi CB, Tagwo H, Kofané TC. Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity. Phys Rev E 2022; 106:054201. [PMID: 36559471 DOI: 10.1103/physreve.106.054201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Accepted: 10/10/2022] [Indexed: 11/06/2022]
Abstract
The modulational instability (MI) phenomenon is addressed in a nonlocal medium under controllable saturation. The linear stability analysis of a plane-wave solution is used to derive an expression for the growth rate of MI that is exploited to parametrically discuss the possibility for the plane wave to disintegrate into nonlinear localized light patterns. The influence of the nonlocal parameter, the saturation coefficient, and the saturation index are mainly explored in the context of a Gaussian nonlocal response. It is pointed out that the instability spectrum, which tends to be quenched by the high nonlocality parameter, gets amplified under the right choices of the saturation parameters, especially the saturation index. Via direct numerical simulations, confirmations of analytical predictions are given, where competing nonlocal and saturable nonlinearities enable the emergence of trains of patterns as manifestations of MI. The comprehensive parametric analysis carried out throughout the numerical experiment reveals the robustness of the obtained rogue waves of A- and B-type Akhmediev breathers, as the nonlinear signature of MI, providing the saturation index as a suitable tool to manipulate nonlinear waves in nonlocal media.
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Affiliation(s)
- Conrad Bertrand Tabi
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16 Palapye, Botswana
| | - Hippolyte Tagwo
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
| | - Timoléon Crépin Kofané
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16 Palapye, Botswana.,Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon.,Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaoundé I, Cameroon
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3
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Liang G, Shu F, Cheng W, Jiao L. Nonlinearity-mediated collimation of optical beams. OPTICS EXPRESS 2022; 30:10770-10778. [PMID: 35473036 DOI: 10.1364/oe.455935] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 03/07/2022] [Indexed: 06/14/2023]
Abstract
We investigated the evolutions of optical beams in an optical system composed of free spaces and nonlocal nonlinear media layers in a cascaded manner. From an application point of view, two kinds of evolution processes for Gaussian beams, nonlinearity-mediated collimation and switching from breathers to solitons, were discussed in details. By adjusting the input optical power, the collimating, the compressing and the expanding of optical beams are convenient to be controlled.
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4
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Kolodina K, Wyller J, Oleynik A, Sørensen MP. Pattern formation in a 2-population homogenized neuronal network model. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2021; 11:9. [PMID: 34173912 PMCID: PMC8236021 DOI: 10.1186/s13408-021-00107-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/22/2020] [Accepted: 06/09/2021] [Indexed: 06/13/2023]
Abstract
We study pattern formation in a 2-population homogenized neural field model of the Hopfield type in one spatial dimension with periodic microstructure. The connectivity functions are periodically modulated in both the synaptic footprint and in the spatial scale. It is shown that the nonlocal synaptic interactions promote a finite band width instability. The stability method relies on a sequence of wave-number dependent invariants of [Formula: see text]-stability matrices representing the sequence of Fourier-transformed linearized evolution equations for the perturbation imposed on the homogeneous background. The generic picture of the instability structure consists of a finite set of well-separated gain bands. In the shallow firing rate regime the nonlinear development of the instability is determined by means of the translational invariant model with connectivity kernels replaced with the corresponding period averaged connectivity functions. In the steep firing rate regime the pattern formation process depends sensitively on the spatial localization of the connectivity kernels: For strongly localized kernels this process is determined by the translational invariant model with period averaged connectivity kernels, whereas in the complementary regime of weak and moderate localization requires the homogenized model as a starting point for the analysis. We follow the development of the instability numerically into the nonlinear regime for both steep and shallow firing rate functions when the connectivity kernels are modeled by means of an exponentially decaying function. We also study the pattern forming process numerically as a function of the heterogeneity parameters in four different regimes ranging from the weakly modulated case to the strongly heterogeneous case. For the weakly modulated regime, we observe that stable spatial oscillations are formed in the steep firing rate regime, whereas we get spatiotemporal oscillations in the shallow regime of the firing rate functions.
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Affiliation(s)
- Karina Kolodina
- Faculty of Science and Technology, Norwegian University of Life Sciences, P.O. Box 5003, N-1432, Ås, Norway
| | - John Wyller
- Faculty of Science and Technology, Norwegian University of Life Sciences, P.O. Box 5003, N-1432, Ås, Norway.
| | - Anna Oleynik
- Department of Mathematics, University of Bergen, P.O. Box 7803, N-5020, Bergen, Norway
| | - Mads Peter Sørensen
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800, Kongens Lyngby, Denmark
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5
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Li H, Peng X, Shi Z. Vector solitons in nonlocal optical media with pseudo spin-orbit-coupling. Phys Rev E 2021; 103:022205. [PMID: 33736013 DOI: 10.1103/physreve.103.022205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2020] [Accepted: 01/15/2021] [Indexed: 11/07/2022]
Abstract
We numerically investigate the existence and stability of nonlocal vector solitons with pseudo spin-orbit-coupling (SOC). The pseudo SOC is realized by a framework based on the spatial-domain copropagation of two beams with mutually orthogonal polarizations and opposite transverse components of the carrier wave vectors in nonlocal optical media. The numerical results show that there are two kinds of solutions for vector solitons, one is central symmetric, and the other is noncentral symmetric. The solitons may exist below a certain threshold value of the effective SOC strength in the system.
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Affiliation(s)
- Huagang Li
- School of Photoelectric Engineering, Guangdong Polytechnic Normal University, Guangzhou 510665, China
| | - Xi Peng
- School of Photoelectric Engineering, Guangdong Polytechnic Normal University, Guangzhou 510665, China
| | - Zhiwei Shi
- School of Electro-mechanical Engineering, Guangdong University of Technology, Guangzhou 510006, China
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6
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Dragonas K, Kominis Y. Solitary wave formation under the interplay between spatial inhomogeneity and nonlocality. Phys Rev E 2019; 100:052209. [PMID: 31870039 DOI: 10.1103/physreve.100.052209] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Indexed: 11/07/2022]
Abstract
The presence of spatial inhomogeneity in a nonlinear medium restricts the formation of solitary waves (SW) on a discrete set of positions, whereas a nonlocal nonlinearity tends to smooth the medium response by averaging over neighboring points. The interplay of these antagonistic effects is studied in terms of SW formation and propagation. Formation dynamics is analyzed under a phase-space approach and analytical conditions for the existence of either discrete families of bright SW or continuous families of kink SW are obtained in terms of Melinikov's method. Propagation dynamics are studied numerically and cases of stable and oscillatory propagation as well as dynamical transformation between different types of SW are shown. The existence of different types and families of SW in the same configuration, under appropriate relations between their spatial width and power with the inhomogeneity and the nonlocality parameters, suggests an advanced functionality of such structures that is quite promising for applications.
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Affiliation(s)
- Konstantinos Dragonas
- School of Applied Mathematical and Physical Science, National Technical University of Athens, Zographou GR-15773, Greece
| | - Yannis Kominis
- School of Applied Mathematical and Physical Science, National Technical University of Athens, Zographou GR-15773, Greece
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7
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Song L, Yang Z, Zhang S, Li X. Dynamics of rotating Laguerre-Gaussian soliton arrays. OPTICS EXPRESS 2019; 27:26331-26345. [PMID: 31674517 DOI: 10.1364/oe.27.026331] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Accepted: 08/11/2019] [Indexed: 06/10/2023]
Abstract
Trajectory control of spatial solitons is an important subject in optical transmission field. Here we investigate the propagation dynamics of Laguerre-Gaussian soliton arrays in nonlinear media with a strong nonlocality and introduce two parameters, which we refer to as initial tangential velocity and displacement, to control the propagation path. The general analytical expression for the evolution of the soliton array is derived and the propagation properties, such as the intensity distribution, the propagation trajectory, the center distance, and the angular velocity are analyzed. It is found that the initial tangential velocity and displacement make the solitons sinusoidally oscillate in the x and y directions, and each constituent soliton undergoes elliptically or circularly spiral trajectory during propagation. A series of numerical examples is exhibited to graphically illustrate these typical propagation properties. Our results may provide a new perspective and stimulate further active investigations of multisoliton interaction and may be applied in optical communication and particle control.
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8
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Kumar M, Nithyanandan K, Porsezian K. Influence of spatial delay on the modulational instability in a composite system with a controllable nonlinearity. Phys Rev E 2018; 97:062208. [PMID: 30011578 DOI: 10.1103/physreve.97.062208] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Indexed: 11/07/2022]
Abstract
A theoretical investigation of the modulational instability (MI) in a composite system with a nonlocal response function is presented. A composite system of silver nanoparticles in acetone is chosen, whose nonlinearity can be delicately varied by controlling the volume fraction of the constituents, thus enabling the possibility of nonlinearity management. A pump-probe counterpropagation configuration has been assumed, and the interplay between the competing nonlinearities and the nonlocalities in the MI dynamics is systematically explored. A different class of nonlocalities have been considered, and the study reveals that the nonlocality critically depends on the kind of nonlocal function. However, the general behavior is that the strength of nonlocality suppresses the MI gain, while for a rectangular function it assists the emergence of new spectral windows. We also show that the cross coupling effects are significant in enhancing MI, especially in the defocusing nonlinearity. We also emphasize the impact of the relative strength of the nonlinearities in the MI dynamics at different settings of competing nonlinearities. Thus, we emphasize the importance of the different class of nonlocal response in the MI dynamics and explore the interplay between the higher order nonlinear effects and nonlocalities in the counterpropagating configurations.
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Affiliation(s)
- Monisha Kumar
- Department of Physics, School of Physical, Chemical and Applied Sciences, Pondicherry University, Pondicherry 605014, India
| | - K Nithyanandan
- Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS, Université de Bourgogne, 9 avenue A. Savary, BP 47870, Dijon Cedex F-21078, France.,CNRS/Universite Joseph Fourier, Laboratoire Interdisciplinaire de Physique (LIPHY), F-38400 Grenoble, France
| | - K Porsezian
- Department of Physics, School of Physical, Chemical and Applied Sciences, Pondicherry University, Pondicherry 605014, India
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9
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Liang G, Dai Z. Spiraling elliptic Hermite-Gaussian solitons in nonlocal nonlinear media without anisotropy. Sci Rep 2017; 7:3234. [PMID: 28607465 PMCID: PMC5468243 DOI: 10.1038/s41598-017-03669-x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2017] [Accepted: 05/03/2017] [Indexed: 11/09/2022] Open
Abstract
We introduce a kind of the spiraling elliptic Hermite-Gaussian solitons in nonlocal nonlinear media without anisotropy, which carries the orbital angular momentum and can rotate in the transverse. The n-th mode of the spiraling elliptic Hermite-Gaussian solitons has n holes nested in the elliptic profile. The analytical spiraling elliptic Hermite-Gaussian solitons solutions are obtained based on the variational approach, which agree well with the numerical simulations. It is found that the critical power and the critical angular velocity for the spiraling elliptic Hermite-Gaussian solitons are the same as the counterpart of the ground mode.
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Affiliation(s)
- Guo Liang
- School of Electrical & Electronic Engineering, Shangqiu Normal University, Shangqiu, 476000, China
| | - Zhiping Dai
- College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, 421002, China.
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10
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Pokam Nguewawe C, Fewo SI, Yemélé D. Higher-order effects on the properties of the optical compact bright pulse: Collective variable approach. Phys Rev E 2017; 95:012215. [PMID: 28208352 DOI: 10.1103/physreve.95.012215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2016] [Indexed: 06/06/2023]
Abstract
The effects of higher-order (HO) terms on the properties of the compact bright (CB) pulse described by the dispersionless nonlocal nonlinear Schrödinger (DNNLS) equation are investigated. These effects include third-order dispersion (TOD), the Raman term, and the time derivative of the pulse envelope. By means of the collective variable method, the dynamical behavior of the pulse amplitude, width, frequency, velocity, phase, and chirp during propagation is pointed out. The results indicate that the CB pulse experiences a self-frequency shift and self-steepening, respectively, in the presence of an isolated Raman term and the time derivative of the pulse envelope and acquires a velocity as the result of the TOD effect. In addition, TOD may also induce the breathing mode inside the variation of the pulse parameters when the width of the input pulse is slightly less than that of the unperturbed CB pulse. The combination of these terms, indispensable for describing ultrashort pulses, reproduces all these phenomena in the CB pulse behavior. Further, other properties are observed, namely, the pulse decay, the breathing mode even when the unperturbed CB pulse is taken as the input signal, and the attenuated pulse. These results are in good agreement with the results of the direct numerical simulations of the DNNLS equation with HO terms.
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Affiliation(s)
- Chancelor Pokam Nguewawe
- Laboratory of Mechanics and Modeling of Physics Systems, Faculty of Science, University of Dschang, P.O. Box 067, Dschang, Cameroon
| | - Serge I Fewo
- Laboratory of Mechanics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
| | - David Yemélé
- Laboratory of Mechanics and Modeling of Physics Systems, Faculty of Science, University of Dschang, P.O. Box 067, Dschang, Cameroon
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11
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Liang G, Guo Q, Cheng W, Yin N, Wu P, Cao H. Spiraling elliptic beam in nonlocal nonlinear media. OPTICS EXPRESS 2015; 23:24612-24625. [PMID: 26406663 DOI: 10.1364/oe.23.024612] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Analytically discussed is the dynamical properties of the spiraling elliptic beams in nonlocal nonlinear media. This class of spiraling elliptic beams carry the orbital angular momentum (OAM), and can rotate on the cross section perpendicular to the propagation direction during the propagations. The optical intensity, the beam width, and specially the angular velocity are both analytically and numerically discussed in details. We shown that both the deviations from the critical power and the deviations from the critical OAM can make the spiraling elliptic beams breathe. The decrease (increase) of the OAM or the increase (decrease) of the power can both make the spiraling elliptic breathers contract (diffract), however, there still exist differences between them. The rotating speed can be changed by the input optical power or the input OAM, which may have potential applications in the controlling of the optical beams.
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12
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Zhang B, Chen Z. Dynamics of polarized vortex solitons in nonlocal media with Bessel optical lattices. OPTICS EXPRESS 2015; 23:24265-24273. [PMID: 26406632 DOI: 10.1364/oe.23.024265] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We investigate the formation of polarized vortex solitons in nonlocal media with Bessel optical lattices and show the various dynamics of these solitons. Particularly, the stable high-order polarized vortex solitons, which are not found in local media with Bessel optical lattices, are found in nonlocal media. It is found that the nonlocal nonlinearity plays an important role in the stability of these solitons which is similar to that of phase vortex solitons. However, we show that the dynamics of these polarized vortex solitons are quite different from the phase vortex solitons.
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13
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Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media. Sci Rep 2015; 5:9814. [PMID: 25900878 PMCID: PMC4405770 DOI: 10.1038/srep09814] [Citation(s) in RCA: 65] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2014] [Accepted: 03/13/2015] [Indexed: 11/08/2022] Open
Abstract
We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media.
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14
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Colet P, Matías MA, Gelens L, Gomila D. Formation of localized structures in bistable systems through nonlocal spatial coupling. I. General framework. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012914. [PMID: 24580304 DOI: 10.1103/physreve.89.012914] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2013] [Indexed: 05/23/2023]
Abstract
The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in one-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear dependence on the field. Leveraging spatial dynamics we provide a general framework to understand the effect of the nonlocality on the shape of the fronts connecting two stable states. In particular we show that nonlocal terms can induce spatial oscillations in the front tails, allowing for the creation of localized structures, that emerge from pinning between two fronts. In parameter space the region where fronts are oscillatory is limited by three transitions: the modulational instability of the homogeneous state, the Belyakov-Devaney transition in which monotonic fronts acquire spatial oscillations with infinite wavelength, and a crossover in which monotonically decaying fronts develop spatial oscillations with a finite wavelength. We show how these transitions are organized by codimension 2 and 3 points and illustrate how by changing the parameters of the nonlocal coupling it is possible to bring the system into the region where localized structures can be formed.
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Affiliation(s)
- Pere Colet
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Manuel A Matías
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Lendert Gelens
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain and Applied Physics Research Group (APHY), Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium
| | - Damià Gomila
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
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15
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Gelens L, Matías MA, Gomila D, Dorissen T, Colet P. Formation of localized structures in bistable systems through nonlocal spatial coupling. II. The nonlocal Ginzburg-Landau equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012915. [PMID: 24580305 DOI: 10.1103/physreve.89.012915] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2013] [Indexed: 05/23/2023]
Abstract
We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-dimensional real Ginzburg-Landau equation. While for local coupling the fronts are always monotonic and therefore the dynamical behavior leads to coarsening and the annihilation of pairs of fronts, nonlocal terms can induce spatial oscillations in the front, allowing for the creation of localized structures, emerging from pinning between two fronts. We show this for three different nonlocal influence kernels. The first two, mod-exponential and Gaussian, are positive definite and decay exponentially or faster, while the third one, a Mexican-hat kernel, is not positive definite.
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Affiliation(s)
- Lendert Gelens
- Applied Physics Research Group (APHY), Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium and IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Manuel A Matías
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Damià Gomila
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Tom Dorissen
- Applied Physics Research Group (APHY), Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
| | - Pere Colet
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
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16
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Kenmogne F, Yemélé D. Bright and peaklike pulse solitary waves and analogy with modulational instability in an extended nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:043204. [PMID: 24229297 DOI: 10.1103/physreve.88.043204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2013] [Revised: 09/16/2013] [Indexed: 06/02/2023]
Abstract
The modulational instability (MI) phenomenon in the nonlinear Schrödinger equation (NLSE) extended by two different nonlinear dispersion terms and the gradient term is investigated. We find that the possibility of instability of plane waves depends on the sign of the nonlinear dispersion parameters with regard to the linear dispersion coefficient. In contrast to the basic NLSE, the system may exhibit instability in the defocusing media for amplitude exceeding a critical value depending on the magnitude of the nonlinear dispersion. An additional feature, namely the higher order or the infinite gain band, absent in the NLSE case, may appear and in which MI induces the birth of the nonlinear localized wave (NLW) of different carrier wave numbers. The result of the qualitative investigations of the system's dynamics indicates the existence of the NLW, such as peak, bright, dark, and compact dark solitary waves which can be well predicted by the MI criteria. In addition the nonlinear dispersion induces the existence of a pair of bright-dark solitary waves which is usually exhibited by the coupled NLSEs only, and the pairs of peak-dark and compact dark-bright solitary waves.
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Affiliation(s)
- Fabien Kenmogne
- Laboratory of Modelling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
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17
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Ghofraniha N, Gentilini S, Folli V, Delre E, Conti C. Shock waves in disordered media. PHYSICAL REVIEW LETTERS 2012; 109:243902. [PMID: 23368319 DOI: 10.1103/physrevlett.109.243902] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2012] [Indexed: 06/01/2023]
Abstract
We experimentally investigate the interplay between spatial shock waves and the degree of disorder during nonlinear optical propagation in a thermal defocusing medium. We characterize the way the shock point is affected by the amount of disorder and scales with wave amplitude. Evidence for the existence of a phase diagram in terms of nonlinearity and amount of randomness is reported. The results are in quantitative agreement with a theoretical approach based on the hydrodynamic approximation.
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Affiliation(s)
- N Ghofraniha
- IPCF-CNR, Dipartimento di Fisica-Università La Sapienza, PA. Moro 2, 00185 Roma, Italy.
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18
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Ghofraniha N, Amato LS, Folli V, Trillo S, DelRe E, Conti C. Measurement of scaling laws for shock waves in thermal nonlocal media. OPTICS LETTERS 2012; 37:2325-2327. [PMID: 22739896 DOI: 10.1364/ol.37.002325] [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 are able to detect the details of spatial optical collisionless wave breaking through the high aperture imaging of a beam suffering shock in a fluorescent nonlinear nonlocal thermal medium. This allows us to directly measure how nonlocality and nonlinearity affect the point of shock formation and compare results with numerical simulations.
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Affiliation(s)
- N Ghofraniha
- Istituto dei Processi Chimico Fisici (IPCF)-Consiglio Nazionale delle Ricerche (CNR), UOS Roma Kerberos, Università La Sapienza, P. le A. Moro 2, I-00185 Roma, Italy.
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19
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Jia J, Lin J. Solitons in nonlocal nonlinear Kerr media with exponential response function. OPTICS EXPRESS 2012; 20:7469-7479. [PMID: 22453426 DOI: 10.1364/oe.20.007469] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
In this paper, we find some exact analytical solutions including bright soliton solution, dipole-mode soliton solution, double soliton solution and periodic solution when a slit laser beam propagates in Kerr-type nonlinear, nonlocal media with exponential response function. Furthermore, we address the energy flow is a monotonically growing function of d₂ and the Hamiltonian decreases while the energy flow increases. And we also obtain an Airy-like soliton by numerical method.
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Affiliation(s)
- Jian Jia
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China
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20
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Bekenstein R, Segev M. Self-accelerating optical beams in highly nonlocal nonlinear media. OPTICS EXPRESS 2011; 19:23706-23715. [PMID: 22109397 DOI: 10.1364/oe.19.023706] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We find self-accelerating beams in highly nonlocal nonlinear optical media, and show that their propagation dynamics is strongly affected by boundary conditions. Specifically for the thermal optical nonlinearity, the boundary conditions have a strong impact on the beam trajectory: they can increase the acceleration during propagation, or even cause beam bending in a direction opposite to the initial trajectory. Under strong self-focusing, the accelerating beam decomposes into a localized self-trapped beam propagating on an oscillatory trajectory and a second beam which accelerates in a different direction. We augment this study by investigating the effects caused by a finite aperture and by a nonlinear range of a finite extent.
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Affiliation(s)
- Rivka Bekenstein
- Physics Department and Solid State Institute, Technion, 32000 Haifa, Israel
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21
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Sevinçli S, Henkel N, Ates C, Pohl T. Nonlocal nonlinear optics in cold Rydberg gases. PHYSICAL REVIEW LETTERS 2011; 107:153001. [PMID: 22107290 DOI: 10.1103/physrevlett.107.153001] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2011] [Indexed: 05/31/2023]
Abstract
We present an analytical theory for the nonlinear optical response of a strongly interacting Rydberg gas under conditions of electromagnetically induced transparency. Simple formulas for the third-order optical susceptibility are derived and shown to be in excellent agreement with recent experiments. The obtained expressions reveal strong nonlinearities, which in addition are of highly nonlocal character. This property together with the enormous strength of the Rydberg-induced nonlinearities is shown to yield a unique laboratory platform for nonlinear wave phenomena, such as collapse-arrested modulational instabilities in a self-defocusing medium.
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Affiliation(s)
- S Sevinçli
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
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22
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Ghofraniha N, Conti C, Ruocco G, Trillo S. Shocks in nonlocal media. PHYSICAL REVIEW LETTERS 2007; 99:043903. [PMID: 17678367 DOI: 10.1103/physrevlett.99.043903] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2007] [Indexed: 05/16/2023]
Abstract
We investigate the formation of collisionless shocks along the spatial profile of a Gaussian laser beam propagating in nonlocal nonlinear media. For defocusing nonlinearity the shock survives the smoothing effect of the nonlocal response, though its dynamics is qualitatively affected by the latter, whereas for focusing nonlinearity it dominates over filamentation. The patterns observed in a thermal defocusing medium are interpreted in the framework of our theory.
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Affiliation(s)
- Neda Ghofraniha
- Research Center SMC INFM-CNR, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
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23
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Minovich A, Neshev DN, Dreischuh A, Krolikowski W, Kivshar YS. Experimental reconstruction of nonlocal response of thermal nonlinear optical media. OPTICS LETTERS 2007; 32:1599-601. [PMID: 17572718 DOI: 10.1364/ol.32.001599] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
We study experimentally and theoretically the nonlocal response of a medium with thermal nonlinearity and show that despite its inherently infinite range it can be accurately characterized by a well-defined nonlocal response function. We retrieve the shape of this function and analyze its transformation with the change of boundaries.
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Affiliation(s)
- Alexander Minovich
- Nonlinear Physics Centre, Australian National University, Canberra, ACT 0200, Australia.
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24
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Buccoliero D, Desyatnikov AS, Krolikowski W, Kivshar YS. Laguerre and Hermite soliton clusters in nonlocal nonlinear media. PHYSICAL REVIEW LETTERS 2007; 98:053901. [PMID: 17358858 DOI: 10.1103/physrevlett.98.053901] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2006] [Indexed: 05/14/2023]
Abstract
We introduce novel classes of higher-order spatial optical solitons in analogy with Laguerre-Gaussian and Hermite-Gaussian linear eigenmodes. We reveal that stable higher-order optical solitons can exist in nonlocal nonlinear media in the various forms of soliton necklaces and soliton matrices. Modulational instability can lead to nontrivial transformations between energetically close solitons with different symmetries through the intermediate states resembling generalized Hermite-Laguerre-Gaussian modes.
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Affiliation(s)
- Daniel Buccoliero
- Nonlinear Physics Center, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia
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25
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Fischer R, Neshev DN, Krolikowski W, Kivshar YS, Iturbe-Castillo D, Chavez-Cerda S, Meneghetti MR, Caetano DP, Hickman JM. Oblique interaction of spatial dark-soliton stripes in nonlocal media. OPTICS LETTERS 2006; 31:3010-2. [PMID: 17001383 DOI: 10.1364/ol.31.003010] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
We report what we believe to be the first experimental observation of a large spatial lateral shift in the interaction of obliquely oriented spatial dark-soliton stripes. We demonstrate by numerical simulations that this new effect can be attributed to the specific features of optical media with a nonlocal nonlinear response.
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Affiliation(s)
- Robert Fischer
- Nonlinear Physics Center, Research School of Physical Sciences and Engineering, Australian National University, Canberra, Australia
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26
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Conti C, Ghofraniha N, Ruocco G, Trillo S. Laser beam filamentation in fractal aggregates. PHYSICAL REVIEW LETTERS 2006; 97:123903. [PMID: 17025967 DOI: 10.1103/physrevlett.97.123903] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2006] [Indexed: 05/12/2023]
Abstract
We investigate filamentation of a cw laser beam in soft matter such as colloidal suspensions and fractal gels. The process, driven by electrostriction, is strongly affected by material properties, which are taken into account via the static structure factor, and have impact on the statistics of the light filaments.
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Affiliation(s)
- Claudio Conti
- Research Center Enrico Fermi, Via Panisperna 89/A, 00184 Rome, Italy.
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27
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Ouyang S, Guo Q, Hu W. Perturbative analysis of generally nonlocal spatial optical solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:036622. [PMID: 17025779 DOI: 10.1103/physreve.74.036622] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2006] [Indexed: 05/12/2023]
Abstract
In analogy to a perturbed harmonic oscillator, we calculate the fundamental and some other higher order soliton solutions of the nonlocal nonlinear Schödinger equation (NNLSE) in the second approximation in the generally nonlocal case. Comparing with numerical simulations we show that soliton solutions in the second approximation can describe the generally nonlocal soliton states of the NNLSE more exactly than that in the zeroth approximation. We show that for the nonlocal case of an exponential-decay type nonlocal response the Gaussian-function-like soliton solutions cannot describe the nonlocal soliton states exactly even in the strongly nonlocal case. The properties of such nonlocal solitons are investigated. In the strongly nonlocal limit, the soliton's power and phase constant are both in inverse proportion to the fourth power of its beam width for the nonlocal case of a Gaussian function type nonlocal response, and are both in inverse proportion to the third power of its beam width for the nonlocal case of an exponential-decay type nonlocal response.
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Affiliation(s)
- Shigen Ouyang
- Laboratory of Photonic Information Technology, South China Normal University Guangzhou, 510631, Peoples Republic of China
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28
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Conti C, Peccianti M, Assanto G. Complex dynamics and configurational entropy of spatial optical solitons in nonlocal media. OPTICS LETTERS 2006; 31:2030-2. [PMID: 16770422 DOI: 10.1364/ol.31.002030] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Intense light propagating in a nonlinear medium can generate an ensemble of interacting filaments of light, or spatial solitons. Using nematic liquid crystals, we demonstrate that the filaments exhibit collective behavior typical of complex systems, including the formation of clusters and soundlike vibrations, as well as the reduction of the configurational entropy, controlled by the degree of nonlocality of the medium.
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29
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Skupin S, Bang O, Edmundson D, Krolikowski W. Stability of two-dimensional spatial solitons in nonlocal nonlinear media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066603. [PMID: 16906993 DOI: 10.1103/physreve.73.066603] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2006] [Indexed: 05/11/2023]
Abstract
We discuss the existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose-Einstein condensates, may support a variety of stationary localized structures, including rotating dipole solitons. We also demonstrate that the stability of these structures critically depends on the spatial profile of the nonlocal response function.
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Affiliation(s)
- S Skupin
- Laser Physics Center, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia.
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30
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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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31
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Xu Z, Kartashov YV, Torner L. Stabilization of vector soliton complexes in nonlocal nonlinear media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:055601. [PMID: 16802990 DOI: 10.1103/physreve.73.055601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2005] [Indexed: 05/10/2023]
Abstract
We introduce vector soliton complexes in nonlocal Kerr-type nonlinear media. We discover that under proper conditions the combination of nonlocality and vectorial coupling has a remarkable stabilizing action on multihumped solitons. In particular, we find that stable bound states featuring several field oscillations in each soliton component do exist. This affords stabilization of vector soliton trains incorporating a large number of humps, a class of structures known to self-destroy via strong instabilities in scalar settings.
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Affiliation(s)
- Zhiyong Xu
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, Castelldefels (Barcelona), Spain
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32
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Shen M, Wang Q, Shi J, Hou P, Kong Q. Partially coherent accessible solitons in strongly nonlocal media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056602. [PMID: 16803052 DOI: 10.1103/physreve.73.056602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2005] [Indexed: 05/10/2023]
Abstract
We study the propagation of incoherent accessible solitons in strongly nonlocal media with arbitrary response function. Based on the linear propagation equation and the mutual coherence function approach, we obtain an exact analytical solution of such incoherent accessible solitons. The solitons radius is related to the total power as well as the coherence characteristics of the incoherent beam. We find that there is not a threshold for incoherent solitons exist in strongly nonlocal media because the model is linear. Evolution behaviors of the solitons width and the coherence radius are also described when the solitons undergo linear harmonic oscillation.
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Affiliation(s)
- Ming Shen
- Department of Physics, Shanghai University, PR China.
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33
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Lopez-Aguayo S, Desyatnikov AS, Kivshar YS, Skupin S, Krolikowski W, Bang O. Stable rotating dipole solitons in nonlocal optical media. OPTICS LETTERS 2006; 31:1100-2. [PMID: 16625916 DOI: 10.1364/ol.31.001100] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
We reveal that nonlocality can provide a simple physical mechanism for stabilization of multihump optical solitons and present what we believe to be the first example of stable rotating dipole solitons and soliton spiraling, which are known to be unstable in all types of realistic nonlinear media with a local response.
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Affiliation(s)
- Servando Lopez-Aguayo
- Nonlinear Physics Center, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia
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34
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Dreischuh A, Neshev DN, Petersen DE, Bang O, Krolikowski W. Observation of attraction between dark solitons. PHYSICAL REVIEW LETTERS 2006; 96:043901. [PMID: 16486823 DOI: 10.1103/physrevlett.96.043901] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2005] [Indexed: 05/06/2023]
Abstract
We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems, such as Bose-Einstein condensates with repulsive long-range interparticle interaction.
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Affiliation(s)
- Alexander Dreischuh
- Nonlinear Physics Centre, Research School of Physical Sciences and Engineering, Canberra ACT 0200, Australia
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35
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Rasmussen PD, Bang O, Królikowski W. Theory of nonlocal soliton interaction in nematic liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:066611. [PMID: 16486082 DOI: 10.1103/physreve.72.066611] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2005] [Indexed: 05/06/2023]
Abstract
We investigate interactions between spatial nonlocal bright solitons in nematic liquid crystals using an analytical ("effective particle") approach as well as direct numerical simulations. The model predicts attraction of out-of-phase solitons and the existence of their stable bound state. This nontrivial property is solely due to the nonlocal nature of the nonlinear response of the liquid crystals. We further predict and verify numerically the critical outwards angle and degree of nonlocality which determine the transition between attraction and repulsion of out-of-phase solitons.
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Affiliation(s)
- Per Dalgaard Rasmussen
- COM.DTU Department of Communications, Optics & Materials, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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36
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Shen M, Wang Q, Shi J, Chen Y, Wang X. Nonlocal incoherent white-light solitons in logarithmically nonlinear media. Phys Rev E 2005; 72:026604. [PMID: 16196732 DOI: 10.1103/physreve.72.026604] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2005] [Revised: 06/02/2005] [Indexed: 11/06/2022]
Abstract
The propagation properties of white-light solitons in spatially nonlocal media with a logarithmically nonlinearity are investigated theoretically. The existence curve of the stationary nonlocal incoherent soliton is obtained and the coherence characteristics of the soliton are also described. The evolution behaviors of the nonlocal white-light soliton are discussed in detail by both approximate analytical solution and numerical simulation when the solitons undergo periodic oscillation.
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Affiliation(s)
- Ming Shen
- Department of Physics, Shanghai University, 99 Shangda Road, Shanghai 200444, People's Republic of China.
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37
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Xu Z, Kartashov YV, Torner L. Soliton mobility in nonlocal optical lattices. PHYSICAL REVIEW LETTERS 2005; 95:113901. [PMID: 16197005 DOI: 10.1103/physrevlett.95.113901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2005] [Indexed: 05/04/2023]
Abstract
We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discover that the nonlocality of the nonlinear response can profoundly affect the soliton mobility, hence all the related phenomena. Such behavior manifests itself in significant reductions of the Peierls-Nabarro potential with an increase in the degree of nonlocality, a result that opens the rare possibility in nature of almost radiationless propagation of highly localized solitons across the lattice.
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Affiliation(s)
- Zhiyong Xu
- ICFO-Institut de Ciencies Fotoniques and Universitat Politecnica de Catalunya, Barcelona, Spain
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38
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Peccianti M, Assanto G. Observation of power-dependent walk-off via modulational instability in nematic liquid crystals. OPTICS LETTERS 2005; 30:2290-2. [PMID: 16190447 DOI: 10.1364/ol.30.002290] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
We investigate power-controlled angular steering of light filaments produced by transverse modulational instability in an anisotropic nematic liquid-crystal cell.
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Affiliation(s)
- Marco Peccianti
- Nonlinear Optics and OptoElectronics Lab, Istituto Nazionale per la Fisica della Materia and Department of Electronic Engineering, University Roma Tre, Rome, Italy
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39
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Briedis D, Petersen D, Edmundson D, Krolikowski W, Bang O. Ring vortex solitons in nonlocal nonlinear media. OPTICS EXPRESS 2005; 13:435-443. [PMID: 19488370 DOI: 10.1364/opex.13.000435] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction.
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40
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Królikowski W, Bang O, Wyller J. Nonlocal incoherent solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:036617. [PMID: 15524666 DOI: 10.1103/physreve.70.036617] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2004] [Indexed: 05/24/2023]
Abstract
We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons.
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Affiliation(s)
- Wiesław Królikowski
- Laser Physics Centre, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia
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41
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Królikowski W, Bang O, Nikolov NI, Neshev D, Wyller J, Rasmussen JJ, Edmundson D. Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media. ACTA ACUST UNITED AC 2004. [DOI: 10.1088/1464-4266/6/5/017] [Citation(s) in RCA: 323] [Impact Index Per Article: 16.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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42
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Nikolov NI, Neshev D, Królikowski W, Bang O, Rasmussen JJ, Christiansen PL. Attraction of nonlocal dark optical solitons. OPTICS LETTERS 2004; 29:286-288. [PMID: 14759053 DOI: 10.1364/ol.29.000286] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We study the formation and interaction of spatial dark optical solitons in materials with a nonlocal nonlinear response. We show that unlike in local materials, where dark solitons typically repel, the nonlocal nonlinearity leads to a long-range attraction and formation of stable bound states of dark solitons.
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Affiliation(s)
- Nikola I Nikolov
- Informatics and Mathematical Modelling, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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43
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Peccianti M, Conti C, Assanto G. Optical multisoliton generation in nematic liquid crystals. OPTICS LETTERS 2003; 28:2231-2233. [PMID: 14649951 DOI: 10.1364/ol.28.002231] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The nonlocal nonlinearity stemming from molecular reorientation in nematic liquid crystals supports the formation of multiple solitary waves, following the onset of spatial modulational instability from both wide and focused input beams. We report experimental observations of such phenomena at power levels of hundreds of milliwatts in planar cells with a voltage bias.
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Affiliation(s)
- Marco Peccianti
- Nonlinear Optics and OptoElectronics Laboratory, National Institute for the Physics of Matter (INFM), University Roma Tre, 00146 Rome, Italy
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44
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Nikolov NI, Neshev D, Bang O, Królikowski WZ. Quadratic solitons as nonlocal solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:036614. [PMID: 14524919 DOI: 10.1103/physreve.68.036614] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2003] [Indexed: 05/24/2023]
Abstract
We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical solutions and the prediction of bound states of quadratic solitons.
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Affiliation(s)
- Nikola I Nikolov
- Informatics and Mathematical Modelling, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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45
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Peccianti M, Conti C, Assanto G. Optical modulational instability in a nonlocal medium. ACTA ACUST UNITED AC 2003; 68:025602. [PMID: 14525042 DOI: 10.1103/physreve.68.025602] [Citation(s) in RCA: 89] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2003] [Indexed: 11/07/2022]
Abstract
We report the first observation of modulational instability in nematic liquid crystals encompassing a nonlocal behavior. The experimental results are quantitatively compared with the theory revealing the fundamental features associated to a nonlocal nonlinearity.
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Affiliation(s)
- Marco Peccianti
- NOOEL-Nonlinear Optics and Optoelectronics Laboratory, National Institute for the Physics of Matter, INFM-Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
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