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Mithun T, Fritsch AR, Spielman IB, Kevrekidis PG. Dynamical instability of 3D stationary and traveling planar dark solitons. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 51:014004. [PMID: 36317280 DOI: 10.1088/1361-648x/ac9e36] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2022] [Accepted: 10/27/2022] [Indexed: 06/16/2023]
Abstract
Here we revisit the topic of stationary and propagating solitonic excitations in self-repulsive three-dimensional (3D) Bose-Einstein condensates by quantitatively comparing theoretical analysis and associated numerical computations with our experimental results. Motivated by numerous experimental efforts, including our own herein, we use fully 3D numerical simulations to explore the existence, stability, and evolution dynamics of planar dark solitons. This also allows us to examine their instability-induced decay products including solitonic vortices and vortex rings. In the trapped case and with no adjustable parameters, our numerical findings are in correspondence with experimentally observed coherent structures. Without a longitudinal trap, we identify numerically exact traveling solutions and quantify how their transverse destabilization threshold changes as a function of the solitary wave speed.
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Affiliation(s)
- T Mithun
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, United States of America
| | - A R Fritsch
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
| | - I B Spielman
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, United States of America
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Koutsokostas GN, Theocharis G, Horikis TP, Kevrekidis PG, Frantzeskakis DJ. Transverse instability and dynamics of nonlocal bright solitons. Phys Rev E 2022; 104:064205. [PMID: 35030933 DOI: 10.1103/physreve.104.064205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2021] [Accepted: 11/22/2021] [Indexed: 11/07/2022]
Abstract
We study the transverse instability and dynamics of bright soliton stripes in two-dimensional nonlocal nonlinear media. Using a multiscale perturbation method, we derive analytically the first-order correction to the soliton shape, which features an exponential growth in time-a signature of the transverse instability. The soliton's characteristic timescale associated with its exponential growth is found to depend on the square root of the nonlocality parameter. This, in turn, highlights the nonlocality-induced suppression of the transverse instability. Our analytical predictions are corroborated by direct numerical simulations, with the analytical results being in good agreement with the numerical ones.
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Affiliation(s)
- G N Koutsokostas
- Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
| | - G Theocharis
- LAUM, CNRS, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans, France
| | - T P Horikis
- Department of Mathematics, University of Ioannina, Ioannina 45110, Greece
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
| | - D J Frantzeskakis
- Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
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Abstract
The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.
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Aleksanyan A, Louis H, Henninot JF, Louvergneaux E. Experimental focusing shocklike dynamics in a nonlocal optical stochastic Kerr medium. Phys Rev E 2021; 103:022701. [PMID: 33736110 DOI: 10.1103/physreve.103.022701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Accepted: 01/08/2021] [Indexed: 11/07/2022]
Abstract
We experimentally study the propagating of an optical intensity jump discontinuity in a nonlocal stochastic Kerr focusing nematic liquid crystal cell. We show both theoretically and experimentally that nonlocality opens a route towards beam steering in our system. Indeed, the discontinuity trajectory follows a curve that bends with the injected power. Despite the stochastic nature of the medium and the constant presence of transverse instabilities, the development of a focusing shocklike dynamics is shown to survive. The distance Z_{s} for the focusing shock to occur follows a power law with the beam power P according to Z_{s}∝P^{χ}, with χ=-4/3, as for shock dynamics in self-defocusing media.
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Affiliation(s)
- A Aleksanyan
- Universite Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - H Louis
- Universite Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - J F Henninot
- Universite Artois, CNRS, UMR 8181 - UCCS - Unite de Catalyse et de Chimie du Solide, F-62307 Lens Cedex, France
| | - E Louvergneaux
- Universite Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France
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Koutsokostas GN, Horikis TP, Frantzeskakis DJ. Soliton pairs in two-dimensional nonlocal media. Phys Rev E 2020; 101:042208. [PMID: 32422842 DOI: 10.1103/physreve.101.042208] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 03/20/2020] [Indexed: 11/07/2022]
Abstract
We study the interaction of optical beams of different wavelengths, described by a two-component, two-dimensional (2D) nonlocal nonlinear Schrödinger (NLS) model. Using a multiscale expansion method the NLS model is asymptotically reduced to the completely integrable 2D Mel'nikov system, the soliton solutions of which are used to construct approximate dark-bright and antidark-bright soliton solutions of the original NLS model; the latter being unique to the nonlocal NLS system with no relevant counterparts in the local case. Direct numerical simulations show that, for sufficiently small amplitudes, both these types of soliton stripes do exist and propagate undistorted, in excellent agreement with the analytical predictions. Larger amplitude of these soliton stripes, when perturbed along the transverse direction, disintegrate either to filled vortex structures (the dark-bright solitons) or to radiation (the antidark-bright solitons).
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Affiliation(s)
- Georgios N Koutsokostas
- Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
| | | | - Dimitrios J Frantzeskakis
- Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
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Horikis TP, Frantzeskakis DJ, Antar N, Bakirtaş I, Smyth NF. Self-similar evolution in nonlocal nonlinear media. OPTICS LETTERS 2019; 44:3701-3704. [PMID: 31368947 DOI: 10.1364/ol.44.003701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2019] [Accepted: 06/24/2019] [Indexed: 06/10/2023]
Abstract
The self-similar propagation of optical beams in a broad class of nonlocal, nonlinear optical media is studied utilizing a generic system of coupled equations with linear gain. This system describes, for instance, beam propagation in nematic liquid crystals and optical thermal media. It is found, both numerically and analytically, that the nonlocal response has a focusing effect on the beam, concentrating its power around its center during propagation. In particular, the beam narrows in width and grows in amplitude faster than in local media, with the resulting beam shape being parabolic. Finally, a general initial localized beam evolves to a common shape.
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Zeng L, Zeng J, Kartashov YV, Malomed BA. Purely Kerr nonlinear model admitting flat-top solitons. OPTICS LETTERS 2019; 44:1206-1209. [PMID: 30821749 DOI: 10.1364/ol.44.001206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2018] [Accepted: 01/28/2019] [Indexed: 06/09/2023]
Abstract
We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including fundamental ones, 1D multipoles, and 2D vortices. Previously, solitons of this type were only produced by models with competing nonlinearities. The present setting may be implemented in optics and Bose-Einstein condensates. The 1D version gives rise to an exact analytical solution for stable flat-top solitons, and generic families may be predicted by means of the Thomas-Fermi approximation. Stability of the obtained flat-top solitons is analyzed by means of the linear-stability analysis and direct simulations. Fundamental solitons and 1D multipoles with k=1 and 2 nodes, as well as vortices with winding number m=1, are completely stable. For multipoles with k≥3 and vortices with m≥2, alternating stripes of stability and instability are identified in their parameter spaces.
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Laudyn UA, Piccardi A, Kwasny M, Klus B, Karpierz MA, Assanto G. Interplay of Thermo-Optic and Reorientational Responses in Nematicon Generation. MATERIALS 2018; 11:ma11101837. [PMID: 30261684 PMCID: PMC6212951 DOI: 10.3390/ma11101837] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/31/2018] [Revised: 09/21/2018] [Accepted: 09/25/2018] [Indexed: 11/16/2022]
Abstract
Employing several nematic liquid crystal mixtures, we investigate how the thermo-optic response of nonlinear birefringent soft-matter affects the propagation of light beams and the features of self-induced waveguides. We address the formation of optical spatial solitons and the control of their trajectories versus temperature, comparing the measurements with the expectations based on a simplified model, showing an excellent agreement. Moreover, in a guest⁻host mixture with an absorbing dye dopant, we study the competition between reorientational and thermal nonlinearities, demonstrating that the two processes can be adjusted independently in order to tune the soliton properties, i.e., trajectory and confinement strength. Our results are an important contribution to better comprehend the role played by material properties on linear and nonlinear beam propagation, as well as their exploitation for signal processing and addressing.
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Affiliation(s)
- Urszula A Laudyn
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland.
| | - Armando Piccardi
- NooEL-Nonlinear Optics and OptoElectronics Lab, University Roma Tre, I-00146 Rome, Italy.
| | - Michal Kwasny
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland.
| | - Bartlomiej Klus
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland.
| | - Miroslaw A Karpierz
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland.
| | - Gaetano Assanto
- NooEL-Nonlinear Optics and OptoElectronics Lab, University Roma Tre, I-00146 Rome, Italy.
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Laudyn UA, Piccardi A, Kwasny M, Karpierz MA, Assanto G. Thermo-optic soliton routing in nematic liquid crystals. OPTICS LETTERS 2018; 43:2296-2299. [PMID: 29762576 DOI: 10.1364/ol.43.002296] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Accepted: 04/16/2018] [Indexed: 06/08/2023]
Abstract
We demonstrate thermo-optic control on the propagation of optical spatial solitons in nematic liquid crystals. By varying the sample temperature, both linear and nonlinear optical properties of the reorientational material are modulated by acting on the refractive indices, the birefringence, and the elastic response. As a result, both the trajectory and transverse confinement of spatial solitons can be adjusted, demonstrating an effective means to tune and readdress self-induced optical waveguides.
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Alberucci A, Laudyn UA, Piccardi A, Kwasny M, Klus B, Karpierz MA, Assanto G. Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects. Phys Rev E 2018; 96:012703. [PMID: 29347250 DOI: 10.1103/physreve.96.012703] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Indexed: 11/07/2022]
Abstract
We investigate nonlinear optical propagation of continuous-wave (CW) beams in bulk nematic liquid crystals. We thoroughly analyze the competing roles of reorientational and thermal nonlinearity with reference to self-focusing/defocusing and, eventually, the formation of nonlinear diffraction-free wavepackets, the so-called spatial optical solitons. To this extent we refer to dye-doped nematic liquid crystals in planar cells excited by a single CW beam in the highly nonlocal limit. To adjust the relative weight between the two nonlinear responses, we employ two distinct wavelengths, inside and outside the absorption band of the dye, respectively. Different concentrations of the dye are considered in order to enhance the thermal effect. The theoretical analysis is complemented by numerical simulations in the highly nonlocal approximation based on a semi-analytic approach. Theoretical results are finally compared to experimental results in the Nematic Liquid Crystals (NLC) 4-trans-4'-n-hexylcyclohexylisothiocyanatobenzene (6CHBT) doped with Sudan Blue dye.
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Affiliation(s)
- Alessandro Alberucci
- Photonics Laboratory, Tampere University of Technology, FI-33101 Tampere, Finland
| | - Urszula A Laudyn
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland
| | - Armando Piccardi
- NooEL-Nonlinear Optics and OptoElectronics Lab, University "Roma Tre," I-00146 Rome, Italy
| | - Michał Kwasny
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland
| | - Bartlomiej Klus
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland
| | - Mirosław A Karpierz
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland
| | - Gaetano Assanto
- Photonics Laboratory, Tampere University of Technology, FI-33101 Tampere, Finland.,NooEL-Nonlinear Optics and OptoElectronics Lab, University "Roma Tre," I-00146 Rome, Italy
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Zeng J, Malomed BA. Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity. Phys Rev E 2017; 95:052214. [PMID: 28618638 DOI: 10.1103/physreve.95.052214] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2016] [Indexed: 11/07/2022]
Abstract
Recent studies have demonstrated that defocusing cubic nonlinearity with local strength growing from the center to the periphery faster than r^{D}, in space of dimension D with radial coordinate r, supports a vast variety of robust bright solitons. In the framework of the same model, but with a weaker spatial-growth rate ∼r^{α} with α≤D, we test here the possibility to create stable localized continuous waves (LCWs) in one-dimensional (1D) and 2D geometries, localized dark solitons (LDSs) in one dimension, and localized dark vortices (LDVs) in two dimensions, which are all realized as loosely confined states with a divergent norm. Asymptotic tails of the solutions, which determine the divergence of the norm, are constructed in a universal analytical form by means of the Thomas-Fermi approximation (TFA). Global approximations for the LCWs, LDSs, and LDVs are constructed on the basis of interpolations between analytical approximations available far from (TFA) and close to the center. In particular, the interpolations for the 1D LDS, as well as for the 2D LDVs, are based on a deformed-tanh expression, which is suggested by the usual 1D dark-soliton solution. The analytical interpolations produce very accurate results, in comparison with numerical findings, for the 1D and 2D LCWs, 1D LDSs, and 2D LDVs with vorticity S=1. In addition to the 1D fundamental LDSs with the single notch and 2D vortices with S=1, higher-order LDSs with multiple notches are found too, as well as double LDVs, with S=2. Stability regions for the modes under consideration are identified by means of systematic simulations, the LCWs being completely stable in one and two dimensions, as they are ground states in the corresponding settings. Basic evolution scenarios are identified for those vortices that are unstable. The settings considered in this work may be implemented in nonlinear optics and in Bose-Einstein condensates.
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Affiliation(s)
- Jianhua Zeng
- State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics of CAS, Xi'an 710119, China
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.,Laboratory of Nonlinear-Optical Informatics, ITMO University, St. Petersburg 197101, Russia
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Dai Z, Yang Z, Ling X, Zhang S, Pang Z, Li X, Wang Y. Tripole-mode and quadrupole-mode solitons in (1 + 1)-dimensional nonlinear media with a spatial exponential-decay nonlocality. Sci Rep 2017; 7:122. [PMID: 28273924 PMCID: PMC5427903 DOI: 10.1038/s41598-017-00197-6] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2016] [Accepted: 02/14/2017] [Indexed: 11/18/2022] Open
Abstract
The approximate analytical expressions of tripole-mode and quadrupole-mode solitons in (1 + 1)-dimensional nematic liquid crystals are obtained by applying the variational approach. It is found that the soliton powers for the two types of solitons are not equal with the same parameters, which is much different from their counterparts in the Snyder-Mitchell model (an ideal and typical strongly nolocal nonlinear model). The numerical simulations show that for the strongly nonlocal case, by expanding the response function to the second order, the approximate soliton solutions are in good agreement with the numerical results. Furthermore, by expanding the respond function to the higher orders, the accuracy and the validity range of the approximate soliton solutions increase. If the response function is expanded to the tenth order, the approximate solutions are still valid for the general nonlocal case.
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Affiliation(s)
- Zhiping Dai
- College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, 421002, China
| | - Zhenjun Yang
- College of Physics and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang, 050024, China.
| | - Xiaohui Ling
- College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, 421002, China
| | - Shumin Zhang
- College of Physics and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang, 050024, China
| | - Zhaoguang Pang
- College of Physics and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang, 050024, China
| | - Xingliang Li
- College of Physics and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang, 050024, China
| | - Youwen Wang
- College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, 421002, China
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El GA, Smyth NF. Radiating dispersive shock waves in non-local optical media. Proc Math Phys Eng Sci 2016; 472:20150633. [PMID: 27118911 PMCID: PMC4841477 DOI: 10.1098/rspa.2015.0633] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2015] [Accepted: 02/04/2016] [Indexed: 11/12/2022] Open
Abstract
We consider the step Riemann problem for the system of equations describing the propagation of a coherent light beam in nematic liquid crystals, which is a general system describing nonlinear wave propagation in a number of different physical applications. While the equation governing the light beam is of defocusing nonlinear Schrödinger (NLS) equation type, the dispersive shock wave (DSW) generated from this initial condition has major differences from the standard DSW solution of the defocusing NLS equation. In particular, it is found that the DSW has positive polarity and generates resonant radiation which propagates ahead of it. Remarkably, the velocity of the lead soliton of the DSW is determined by the classical shock velocity. The solution for the radiative wavetrain is obtained using the Wentzel-Kramers-Brillouin approximation. It is shown that for sufficiently small initial jumps the nematic DSW is asymptotically governed by a Korteweg-de Vries equation with the fifth-order dispersion, which explicitly shows the resonance generating the radiation ahead of the DSW. The constructed asymptotic theory is shown to be in good agreement with the results of direct numerical simulations.
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Affiliation(s)
- Gennady A. El
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK
| | - Noel F. Smyth
- School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, UK
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Horikis TP, Frantzeskakis DJ. Ring dark and antidark solitons in nonlocal media. OPTICS LETTERS 2016; 41:583-586. [PMID: 26907429 DOI: 10.1364/ol.41.000583] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Ring dark and antidark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable CW background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvili (aka Johnson's) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability properties.
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Laudyn UA, Kwasny M, Piccardi A, Karpierz MA, Dabrowski R, Chojnowska O, Alberucci A, Assanto G. Nonlinear competition in nematicon propagation. OPTICS LETTERS 2015; 40:5235-5238. [PMID: 26565843 DOI: 10.1364/ol.40.005235] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We investigate the role of competing nonlinear responses in the formation and propagation of bright spatial solitons. We use nematic liquid crystals (NLCs) exhibiting both thermo-optic and reorientational nonlinearities with continuous-wave beams. In a suitably prepared dye-doped sample and dual beam collinear geometry, thermal heating in the visible affects reorientational self-focusing in the near infrared, altering light propagation and self-trapping.
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Assanto G, MacNeil JML, Smyth NF. Diffraction-induced instability of coupled dark solitary waves. OPTICS LETTERS 2015; 40:1771-1774. [PMID: 25872070 DOI: 10.1364/ol.40.001771] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We report on a novel instability arising from the propagation of coupled dark solitary beams governed by coupled defocusing nonlinear Schrödinger equations. Considering dark notches on backgrounds with different wavelengths, hence different diffraction coefficients, we find that the vector dark soliton solution is unstable to radiation modes. Using perturbation theory and numerical integration, we demonstrate that the component undergoing stronger diffraction radiates away, leaving a single dark soliton in the other mode/wavelength.
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Chen W, Shen M, Kong Q, Shi J, Wang Q, Krolikowski W. Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities. OPTICS LETTERS 2014; 39:1764-1767. [PMID: 24686599 DOI: 10.1364/ol.39.001764] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We investigate analytically and numerically the interactions of dark solitons under competing nonlocal cubic and local quintic nonlinearities. It is shown that the self-defocusing quintic nonlinearity will strengthen the attractive interaction and decrease the relative distance between solitons, whereas the self-focusing quintic nonlinearity will enhance the repulsive interaction and increase soliton separation. We demonstrate these results by approximate variational approach and direct numerical simulation.
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Horikis TP, Frantzeskakis DJ. Dark solitons in the presence of higher-order effects. OPTICS LETTERS 2013; 38:5098-5101. [PMID: 24281519 DOI: 10.1364/ol.38.005098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Dark soliton propagation is studied in the presence of higher-order effects, including third-order dispersion, self-steepening, linear/nonlinear gain/loss, and Raman scattering. It is found that for certain values of the parameters a stable evolution can exist for both the soliton and the relative continuous-wave background. Using a newly developed perturbation theory we show that the perturbing effects give rise to a shelf that accompanies the soliton in its propagation. Although, the stable solitons are not affected by the shelf it remains an integral part of the dynamics otherwise not considered so far in studies of higher-order nonlinear Schrödinger models.
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Assanto G, Marchant TR, Minzoni AA, Smyth NF. Reorientational versus Kerr dark and gray solitary waves using modulation theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:066602. [PMID: 22304206 DOI: 10.1103/physreve.84.066602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2011] [Indexed: 05/31/2023]
Abstract
We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schrödinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations, which have no exact solitary wave solution. We find that the evolution of dark and gray NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive radiation, in contrast to the evolution of bright NLS solitons and bright nematicons. Moreover, the steady nematicon profile is nonmonotonic due to the long-range nonlocality associated with the perturbation of the optic axis. Excellent agreement is obtained with numerical solutions of both the defocusing NLS and nematicon equations. The comparisons for the nematicon solutions raise a number of subtle issues relating to the definition and measurement of the width of a dark or gray nematicon.
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Affiliation(s)
- Gaetano Assanto
- NooEL, Nonlinear Optics and OptoElectronics Lab, University of Rome Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
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