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Wang Q, Mihalache D, Belić MR, Lin J. Mode conversion of various solitons in parabolic and cross-phase potential wells. OPTICS LETTERS 2024; 49:1607-1610. [PMID: 38489462 DOI: 10.1364/ol.520451] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Accepted: 02/25/2024] [Indexed: 03/17/2024]
Abstract
We numerically establish the controllable conversion between Laguerre-Gaussian and Hermite-Gaussian solitons in nonlinear media featuring parabolic and cross-phase potential wells. The parabolic potential maintains the stability of Laguerre-Gaussian and Hermite-Gaussian beams, while the actual conversion between the two modes is facilitated by the cross-phase potential, which induces an additional phase shift. By flexibly engineering the range of the cross-phase potential well, various higher-mode solitons can be generated at desired distances. Beams carrying orbital angular momentum can also be efficiently controlled by this method. In addition, other types of beams, such as sine complex-various-function Gaussian and hypergeometric-Gaussian vortex beams, can be periodically transformed and manipulated in a similar manner. Our approach allows the intricate internal relationships between different modes of beams to be conveniently revealed.
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Wang Q, Mihalache D, Belić MR, Zeng L, Lin J. Soliton transformation between different potential wells. OPTICS LETTERS 2023; 48:747-750. [PMID: 36723579 DOI: 10.1364/ol.481216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Accepted: 12/31/2022] [Indexed: 06/18/2023]
Abstract
This paper presents a novel, to the best of our knowledge, method for realizing soliton transformation between different potential wells by gradually manipulating their depths in the propagation direction. The only requirements for such a transformation are that the gradient of the manipulated depth is smooth enough and the solitons in different potential wells are both in the regions of stability. The comparison of transformed solitons with the iterative ones obtained by the accelerated imaginary-time evolution method proves that our method is efficient and reliable. An interesting consequence is that in some complex potential wells in which it is difficult to find solitons by iterative numerical methods, stable solitons can be obtained by the transformation method. The controllable soliton transformation provides an excellent opportunity for all-optical switching, optical information processing, and other applications.
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Wang Q, Belić MR, Mihalache D, Zeng L, Zhang L, Lin J. Vortex chaoticons in thermal nonlocal nonlinear media. Phys Rev E 2022; 106:054214. [PMID: 36559458 DOI: 10.1103/physreve.106.054214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2022] [Accepted: 11/03/2022] [Indexed: 06/17/2023]
Abstract
This paper numerically investigates the propagation of Laguerre-Gaussian vortex beams launched in nonlocal nonlinear media, such as lead glass. Our results show that the propagation properties depend on the selection of beam parameters m and p, which represent the azimuthal and radial mode numbers. When p=0, these profiles can be stable solitons for m≤2, or break up and then form a set of single-hump profiles for m≥3, which are unbounded states with scattered remnants of the energy. However, for p≥1, the broken beams can evolve into vortex chaoticons, which exhibit both chaotic and solitonlike properties. The chaotic properties are determined by the positive Lyapunov exponents and spatial decoherence, while the solitonlike properties are demonstrated by the invariance of beam width and the interaction of beams in the form of quasielastic collisions. In addition, the power and orbital angular momentum of unbounded beam states both decay in propagation, while those of the chaoticons maintain their values well.
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Affiliation(s)
- Qing Wang
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China
- College of Science, JiuJiang University, Jiujiang 334000, China
| | | | - Dumitru Mihalache
- Horia Hulubei National Institute of Physics and Nuclear Engineering, Magurele, Bucharest, RO-077125, Romania
| | - Liangwei Zeng
- College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Lingling Zhang
- College of Science, JiuJiang University, Jiujiang 334000, China
| | - Ji Lin
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China
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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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Meng L, Liu J, Zhang H, Yang W. Symmetrical superfission of optical solitons in a well-type nonlocal system. APPLIED OPTICS 2021; 60:5854-5859. [PMID: 34263805 DOI: 10.1364/ao.423993] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
The dynamical properties of fundamental and dipolar mode solitons, in the process of propagating in the well-type nonlocal system, are provided. During propagating in a deep well-type nonlocal system with a moderate width, a fundamental mode soliton splits into a pair of symmetrical sub-beams, and a dipolar mode soliton can divide into two pairs of symmetrical sub-beams. Furthermore, the propagation directions of these sub-beams can be effectively controlled by adjusting system parameters that include the well depth and well width. These properties could be applied to optical routing, all-optical switching, signal processing, and ultrafast optical communications.
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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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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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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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Wang Q, Li J, Zhang L, Xie W. Hermite-Gaussian–like soliton in the nonlocal nonlinear fractional Schrödinger equation. ACTA ACUST UNITED AC 2018. [DOI: 10.1209/0295-5075/122/64001] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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