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Xu X, Zhao F, Huang J, He H, Zhang L, Chen Z, Nie Z, Malomed BA, Li Y. Semidiscrete optical vortex droplets in quasi-phase-matched photonic crystals. OPTICS EXPRESS 2023; 31:38343-38354. [PMID: 38017942 DOI: 10.1364/oe.506130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 10/18/2023] [Indexed: 11/30/2023]
Abstract
What we believe is a new scheme for producing semidiscrete self-trapped vortices ("swirling photon droplets") in photonic crystals with competing quadratic (χ(2)) and self-defocusing cubic (χ(3)) nonlinearities is proposed. The photonic crystal is designed with a striped structure, in the form of spatially periodic modulation of the χ(2) susceptibility, which is imposed by the quasi-phase-matching technique. Unlike previous realizations of semidiscrete optical modes in composite media, built as combinations of continuous and arrayed discrete waveguides, the semidiscrete vortex "droplets" are produced here in the fully continuous medium. This work reveals that the system supports two types of semidiscrete vortex droplets, viz., onsite- and intersite-centered ones, which feature, respectively, odd and even numbers of stripes, N. Stability areas for the states with different values of N are identified in the system's parameter space. Some stability areas overlap with each other, giving rise to the multistability of states with different N. The coexisting states are mutually degenerate, featuring equal values of the Hamiltonian and propagation constant. An experimental scheme to realize the droplets is outlined, suggesting new possibilities for the long-distance transmission of nontrivial vortex beams in nonlinear media.
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Zhang H, Chen M, Yang L, Tian B, Chen C, Guo Q, Shou Q, Hu W. Higher-charge vortex solitons and vector vortex solitons in strongly nonlocal media. OPTICS LETTERS 2019; 44:3098-3101. [PMID: 31199390 DOI: 10.1364/ol.44.003098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2019] [Accepted: 05/16/2019] [Indexed: 06/09/2023]
Abstract
We report, to the best of our knowledge, the first experimental observation of higher-charge vortex solitons and vector vortex solitons in lead glass with strongly thermal nonlocal nonlinearity. A higher-charge vortex soliton with a topological charge of l=4 and a vector vortex soliton consisting of two orthogonally polarized vortex components, with charges l1=1 and l2=4, were observed at several times of diffraction length. We show that the ring profiles and the carried topological charges of the two incoherently coupled vortex components can be preserved. We also numerically find that the stability of the higher-charge vortex can be enhanced by co-propagating a stable, single-charge vortex.
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Feijoo D, Ordóñez I, Paredes A, Michinel H. Drag force in bimodal cubic-quintic nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033204. [PMID: 25314556 DOI: 10.1103/physreve.90.033204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Indexed: 06/04/2023]
Abstract
We consider a system of two cubic-quintic nonlinear Schrödinger equations in two dimensions, coupled by repulsive cubic terms. We analyze situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and analyze their interaction. We find a realization of D'Alembert's paradox for small velocities and nontrivial drag forces for larger ones. We present numerical analysis including the search of static and traveling form-preserving solutions along with simulations of the dynamical evolution in some representative examples.
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Affiliation(s)
- David Feijoo
- Área de Óptica, Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
| | - Ismael Ordóñez
- Área de Óptica, Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
| | - Angel Paredes
- Área de Óptica, Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
| | - Humberto Michinel
- Área de Óptica, Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
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Izdebskaya YV, Rebling J, Desyatnikov AS, Kivshar YS. Observation of vector solitons with hidden vorticity. OPTICS LETTERS 2012; 37:767-769. [PMID: 22378387 DOI: 10.1364/ol.37.000767] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
This letter reports the first experimental observation, to our knowledge, of optical vector solitons composed of two incoherently coupled vortex components. We employ nematic liquid crystal to generate stable vector solitons with counterrotating vortices and hidden vorticity. In contrast, the solitons with explicit vorticity and corotating vortex components show azimuthal splitting.
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Affiliation(s)
- Yana V Izdebskaya
- Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia.
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Baizakov BB, Bouketir A, Messikh A, Umarov BA. Modulational instability in two-component discrete media with cubic-quintic nonlinearity. Phys Rev E 2009; 79:046605. [PMID: 19518369 DOI: 10.1103/physreve.79.046605] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2008] [Revised: 01/04/2009] [Indexed: 11/07/2022]
Abstract
The effect of cubic-quintic nonlinearity and associated intercomponent couplings on the modulational instability (MI) of plane-wave solutions of the two-component discrete nonlinear Schrödinger (DNLS) equation is considered. Conditions for the onset of MI are revealed and the growth rate of small perturbations is analytically derived. For the same set of initial parameters as equal amplitudes of plane waves and intercomponent coupling coefficients, the effect of quintic nonlinearity on MI is found to be essentially stronger than the effect of cubic nonlinearity. Analytical predictions are supported by numerical simulations of the underlying coupled cubic-quintic DNLS equation. Relevance of obtained results to dense Bose-Einstein condensates (BECs) in deep optical lattices, when three-body processes are essential, is discussed. In particular, the phase separation under the effect of MI in a two-component repulsive BEC loaded in a deep optical lattice is predicted and found in numerical simulations. Bimodal light propagation in waveguide arrays fabricated from optical materials with non-Kerr nonlinearity is discussed as another possible physical realization for the considered model.
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Affiliation(s)
- B B Baizakov
- Physical-Technical Institute, Uzbek Academy of Sciences, 100084 Tashkent, Uzbekistan
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Prytula V, Vekslerchik V, Pérez-García VM. Eigenvalue cutoff in the cubic-quintic nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:027601. [PMID: 18850979 DOI: 10.1103/physreve.78.027601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2008] [Indexed: 05/26/2023]
Abstract
Using theoretical arguments, we prove the numerically well-known fact that the eigenvalues of all localized stationary solutions of the cubic-quintic (2+1) -dimensional nonlinear Schrödinger equation exhibit an upper cutoff value. The existence of the cutoff is inferred using Gagliardo-Nirenberg and Hölder inequalities together with Pohozaev identities. We also show that, in the limit of eigenvalues close to zero, the eigenstates of the cubic-quintic nonlinear Schrödinger equation behave similarly to those of the cubic nonlinear Schrödinger equation.
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Affiliation(s)
- Vladyslav Prytula
- Departamento de Matemáticas, E.T.S. Ingenieros Industriales and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería, Universidad de Castilla-La Mancha, Avenida Camilo José Cela 3, Ciudad Real, 13071 Spain
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Bezryadina A, Neshev DN, Desyatnikov A, Young J, Chen Z, Kivshar YS. Observation of topological transformations of optical vortices in two-dimensional photonic lattices. OPTICS EXPRESS 2006; 14:8317-8327. [PMID: 19529208 DOI: 10.1364/oe.14.008317] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We study interaction of a discrete vortex with a supporting photonic lattice and analyze how the combined action of the lattice periodicity and the medium nonlinearity can modify the vortex structure. In particular, we describe theoretically and observe in experiment, for the first time to our knowledge, the nontrivial topological transformations of the discrete vortex including the flipping of vortex charge and inversion of its orbital angular momentum. We also demonstrate the stabilizing effect of the interaction with the so-called "mixed" optically-induced photonic lattices on the vortex propagation and topological structure.
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He YJ, Fan HH, Dong JW, Wang HZ. Self-trapped spatiotemporal necklace-ring solitons in the Ginzburg-Landau equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:016611. [PMID: 16907208 DOI: 10.1103/physreve.74.016611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2005] [Revised: 05/05/2006] [Indexed: 05/11/2023]
Abstract
We consider a class of self-trapped spatiotemporal solitons: spatiotemporal necklace-ring solitons, whose intensities are azimuthally periodically modulated. We reveal numerically that the spatiotemporal necklace-ring solitons carrying zero, integer, and even fractional angular momentum can be self-trapped over a huge propagation distance in the three-dimensional cubic-quintic complex Ginzburg-Landau equation, even in the presence of random perturbations.
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Affiliation(s)
- Y J He
- State Key Laboratory of Optoelectronic Materials and Technologies, Zhongshan (Sun Yat-Sen) University, Guangzhou 510275, China
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Abstract
We study discrete vortices in coupled discrete nonlinear Schrödinger equations. We focus on the vortex cross configuration that has been experimentally observed in photorefractive crystals. Stability of the single-component vortex cross in the anti-continuum limit of small coupling between lattice nodes is proved. In the vector case, we consider two coupled configurations of vortex crosses, namely the charge-one vortex in one component coupled in the other component to either the charge-one vortex (forming a double-charge vortex) or the charge-negative-one vortex (forming a, so-called, hidden-charge vortex). We show that both vortex configurations are stable in the anti-continuum limit, if the parameter for the inter-component coupling is small and both of them are unstable when the coupling parameter is large. In the marginal case of the discrete two-dimensional Manakov system, the double-charge vortex is stable while the hidden-charge vortex is linearly unstable. Analytical predictions are corroborated with numerical observations that show good agreement near the anti-continuum limit, but gradually deviate for larger couplings between the lattice nodes.
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Affiliation(s)
- P.G Kevrekidis
- Department of Mathematics, University of MassachusettsAmherst, MA 01003-4515, USA
| | - D.E Pelinovsky
- Department of Mathematics, McMaster UniversityHamilton, Ontario L8S 4K1, Canada
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Leblond H, Malomed BA, Mihalache D. Quasistable two-dimensional solitons with hidden and explicit vorticity in a medium with competing nonlinearities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036608. [PMID: 15903606 DOI: 10.1103/physreve.71.036608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2004] [Indexed: 05/02/2023]
Abstract
We consider basic types of two-dimensional (2D) vortex solitons in a three-wave model combining quadratic chi((2)) and self-defocusing cubic chi((3))(-) nonlinearities. The system involves two fundamental-frequency (FF) waves with orthogonal polarizations and a single second-harmonic (SH) one. The model makes it possible to introduce a 2D soliton, with hidden vorticity (HV). Its vorticities in the two FF components are S(1,2) = +/-1 , whereas the SH carries no vorticity, S(3) = 0 . We also consider an ordinary compound vortex, with 2S(1) = 2S(2) = S(3) = 2 . Without the chi((3))(-) terms, the HV soliton and the ordinary vortex are moderately unstable. Within the propagation distance z approximately 15 diffraction lengths, Z(diffr), the former one turns itself into a usual zero-vorticity (ZV) soliton, while the latter splits into three ZV solitons (the splinters form a necklace pattern, with its own intrinsic dynamics). To gain analytical insight into the azimuthal instability of the HV solitons, we also consider its one-dimensional counterpart, viz., the modulational instability (MI) of a one-dimensional CW (continuous-wave) state with "hidden momentum," i.e., opposite wave numbers in its two components, concluding that such wave numbers may partly suppress the MI. As concerns analytical results, we also find exact solutions for spreading localized vortices in the 2D linear model; in terms of quantum mechanics, these are coherent states with angular momentum (we need these solutions to accurately define the diffraction length of the true solitons). The addition of the chi((3))(-) interaction strongly stabilizes both the HV solitons and the ordinary vortices, helping them to persist over z up to 50 Z(diffr). In terms of the possible experiment, they are completely stable objects. After very long propagation, the HV soliton splits into two ZV solitons, while the vortex with S(3) = 2S(1,2) = 2 splits into a set of three or four ZV solitons.
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Affiliation(s)
- Hervé Leblond
- Laboratoire POMA, UMR 6136, Université d'Angers, France
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