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Lashkin VM. Dynamics of multidimensional fundamental and vortex solitons in random media. Phys Rev E 2024; 109:064216. [PMID: 39020928 DOI: 10.1103/physreve.109.064216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2023] [Accepted: 06/14/2024] [Indexed: 07/20/2024]
Abstract
We study the dynamics of fundamental and vortex solitons in the framework of the nonlinear Schrödinger equation with the spatial dimension D⩾2 with a multiplicative random term depending on the time and space coordinates. To this end, we develop a new technique for calculating the even moments of the Nth order. The proposed formalism does not use closure procedures for the nonlinear term, as well as the smallness of the random term and the use of perturbation theory. The essential point is the quadratic form of the autocorrelation function of the random field and the special stochastic change of variables. Using variational analysis to determine the field of structures in the deterministic case, we analytically calculate a number of statistical characteristics describing the dynamics of fundamental and vortex solitons in random medium, such as the mean intensities, the variance of the intensity, the centroid, and spread of the structures, the spatial mutual coherence function, etc. In particular, we show that, under the irreversible action of fluctuations, the solitons spread out, i.e., no collapse occurs.
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Sun ZY, Yu X. Nonlinear Schrödinger waves in a disordered potential: Branched flow, spectrum diffusion, and rogue waves. CHAOS (WOODBURY, N.Y.) 2022; 32:023108. [PMID: 35232051 DOI: 10.1063/5.0077794] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2021] [Accepted: 01/19/2022] [Indexed: 06/14/2023]
Abstract
The problem of nonlinear Schrödinger (NLS) waves in a disordered potential arises in many physical occasions, such as hydrodynamics, optics, and cold atoms. It provides a paradigm for studying the interaction between nonlinearity and random effect, but the current results are far from perfect. In this paper, we systematically simulate the turbulent waves for the focusing NLS equation with dynamical (time-dependent) random potentials, where the enhanced branching structures evolve into branched soliton flows as the nonlinearity increases. In this process, the occurrence of rogue waves for short times results from the interplay of linear random focusing and modulation instability. While the nonlinear spectral analysis reveals that for longer times, it is due to a self-organization of larger solitons competing with breakup of intermediate solitons. On the other hand, we found that the strong nonlinearity can significantly increase the width of the linear (Fourier) spectrum for several time scales, but its spreading rate becomes suppressed, which has a dependence on the correlation length of the potential. We hope that our findings will facilitate a deeper understanding of the nonlinear waves interacting with disordered media.
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Affiliation(s)
- Zhi-Yuan Sun
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
| | - Xin Yu
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
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Cisternas J, Cartes C, Descalzi O, Albers T, Radons G. Random walks of trains of dissipative solitons. CHAOS (WOODBURY, N.Y.) 2020; 30:073134. [PMID: 32752625 DOI: 10.1063/5.0006091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Accepted: 07/04/2020] [Indexed: 06/11/2023]
Abstract
The propagation of light pulses in dual-core nonlinear optical fibers is studied using a model proposed by Sakaguchi and Malomed. The system consists of a supercritical complex Ginzburg-Landau equation coupled to a linear equation. Our analysis includes single standing and walking solitons as well as walking trains of 3, 5, 6, and 12 solitons. For the characterization of the different scenarios, we used ensemble-averaged square displacement of the soliton trajectories and time-averaged power spectrum of the background waves. Power law spectra, indicative of turbulence, were found to be associated with random walks. The number of solitons (or their separations) can trigger anomalous random walks or totally suppress the background waves.
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Affiliation(s)
- Jaime Cisternas
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Monseñor Alvaro del Portillo 12455, Las Condes, Santiago, Chile
| | - Carlos Cartes
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Monseñor Alvaro del Portillo 12455, Las Condes, Santiago, Chile
| | - Orazio Descalzi
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Monseñor Alvaro del Portillo 12455, Las Condes, Santiago, Chile
| | - Tony Albers
- Institute of Physics, Technische Universität Chemnitz, 09107 Chemnitz, Germany
| | - Günter Radons
- Institute of Physics, Technische Universität Chemnitz, 09107 Chemnitz, Germany
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Sun ZY, Yu X. Anomalous diffusion of discrete solitons driven by evolving disorder. Phys Rev E 2020; 101:062211. [PMID: 32688546 DOI: 10.1103/physreve.101.062211] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 06/02/2020] [Indexed: 06/11/2023]
Abstract
Anomalous diffusion is simulated in this paper by studying the transport of discrete solitons in a lattice with evolving disorder. We find a Richardson-type diffusion for the small solitons and a regime of transient diffusion for larger solitons within the ensemble-averaged description. As a comparison, the time-averaged observables present a ballistic scaling for both cases. However, distribution of these observables changes remarkably with the soliton size. Our results suggest violation of ergodicity for the solitons' diffusive processes, which are expected to shed light on further understanding of the discreteness-disorder-nonlinearity interaction.
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Affiliation(s)
- Zhi-Yuan Sun
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
- International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China
| | - Xin Yu
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
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Sun ZY, Yu X. Transient diffusion and two-regime localization of discrete breatherlike excitations in nonlinear Schrödinger lattice with disorder. Phys Rev E 2019; 100:022202. [PMID: 31574744 DOI: 10.1103/physreve.100.022202] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2019] [Indexed: 11/07/2022]
Abstract
We systematically simulate and analyze the motion of discrete breatherlike excitations (DBEs) in the nonlinear Schrödinger lattice with random potentials. A universal transient diffusion of the DBEs is observed for short timescales (t≲10^{3}). For longer timescales (t up to 10^{5}), the DBEs become localized. Such localization, depending on the DBE powers, has two different regimes: Regime I is the Anderson-like localization induced by the disorder, while Regime II is an enhanced localization attributed to both the disorder and discreteness. Our study is expected to shed light on understanding the interplay between disorder and strong nonlinearity, from the diffusive transport and localization properties of nonlinear localized excitations in random media.
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Affiliation(s)
- Zhi-Yuan Sun
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China.,International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China
| | - Xin Yu
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
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Alberucci A, Jisha CP, Bolis S, Beeckman J, Nolte S. Interplay between multiple scattering and optical nonlinearity in liquid crystals. OPTICS LETTERS 2018; 43:3461-3464. [PMID: 30067685 DOI: 10.1364/ol.43.003461] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2018] [Accepted: 06/13/2018] [Indexed: 06/08/2023]
Abstract
We discuss the role played by time-dependent scattering on light propagation in liquid crystals. In the linear regime, the effects of the molecular disorder accumulate in propagation, yielding a monotonic decrease in the beam spatial coherence. In the nonlinear case, despite the disorder-imposed Brownian-like motion to the self-guided waves, self-focusing increases the spatial coherence of the beam by inducing spatial localization. Eventually, a strong enhancement in the beam oscillations occurs when power is strong enough to induce self-steering, i.e., in the non-perturbative regime.
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Louis H, Tlidi M, Louvergneaux E. Experimental evidence of dynamical propagation for solitary waves in ultra slow stochastic non-local Kerr medium. OPTICS EXPRESS 2016; 24:16205-16210. [PMID: 27410886 DOI: 10.1364/oe.24.016205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We perform a statistical analysis of the optical solitary wave propagation in an ultra-slow stochastic non-local focusing Kerr medium such as liquid crystals. Our experimental results show that the localized beam trajectory presents a dynamical random walk whose beam position versus the propagation distance z depicts two different kind of evolutions A power law is found for the beam position standard deviation during the first stage of propagation. It obeys approximately z3/2 up to ten times the power threshold for solitary wave generation.
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Louis H, Tlidi M, Louvergneaux E. Experimental evidence of dynamical propagation for solitary waves in ultra slow stochastic non-local Kerr medium. OPTICS EXPRESS 2016; 24:16206-16211. [PMID: 27410887 DOI: 10.1364/oe.24.016206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We perform a statistical analysis of the optical solitary wave propagation in an ultra-slow stochastic non-local focusing Kerr medium such as liquid crystals. Our experimental results show that the localized beam trajectory presents a dynamical random walk whose beam position versus the propagation distance z depicts two different kind of evolutions A power law is found for the beam position standard deviation during the first stage of propagation. It obeys approximately z3/2 up to ten times the power threshold for solitary wave generation.
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Folli V, Gallo K, Conti C. Purely nonlinear disorder-induced localizations and their parametric amplification. OPTICS LETTERS 2013; 38:5276-5279. [PMID: 24322236 DOI: 10.1364/ol.38.005276] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We investigate spatial localization in a quadratic nonlinear medium in the presence of randomness. By means of numerical simulations and theoretical analyses we show that, in the down conversion regime, the transverse random modulation of the nonlinear susceptibility generates localizations of the fundamental wave that grow exponentially in propagation. The localization length is optically controlled by the pump intensity that determines the amplification rate. The results also apply to cubic nonlinearities.
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Ghofraniha N, Viola I, Zacheo A, Arima V, Gigli G, Conti C. Transition from nonresonant to resonant random lasers by the geometrical confinement of disorder. OPTICS LETTERS 2013; 38:5043-5046. [PMID: 24281505 DOI: 10.1364/ol.38.005043] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We report on a transition in random lasers that is induced by the geometrical confinement of the emitting material. Different dye doped paper devices with controlled geometry are fabricated by soft lithography and show two distinguished behaviors in the stimulated emission: in the absence of boundary constraints, the energy threshold decreases for larger laser volumes showing the typical trend of diffusive nonresonant random lasers, while when the same material is lithographed into channels, the walls act as cavity and the resonant behavior typical of standard lasers is observed. The experimental results are consistent with the general theories of random and standard lasers and a clear phase diagram of the transition is reported.
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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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Folli V, Conti C. Anderson localization in nonlocal nonlinear media. OPTICS LETTERS 2012; 37:332-334. [PMID: 22297343 DOI: 10.1364/ol.37.000332] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We theoretically and numerically investigate the effect of focusing and defocusing nonlinearities on Anderson localization in highly nonlocal media. A perturbative approach is developed to solve the nonlocal nonlinear Schrödinger equation in the presence of a random potential, showing that nonlocality stabilizes Anderson states.
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Affiliation(s)
- Viola Folli
- Department of Physics, University Sapienza, Rome, Italy.
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Folli V, Conti C. Self-induced transparency and the Anderson localization of light. OPTICS LETTERS 2011; 36:2830-2832. [PMID: 21808327 DOI: 10.1364/ol.36.002830] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Self-induced transparency pulses propagating in a random medium embedded in a two-level system can transfer energy to localized Anderson states. This allows the onset of two-level laserlike action.
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Affiliation(s)
- Viola Folli
- Department of Physics, University Sapienza, Piazzale Aldo Moro, 5, 00185 Rome, Italy
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Kartashov YV, Vysloukh VA, Torner L. Disorder-induced soliton transmission in nonlinear photonic lattices. OPTICS LETTERS 2011; 36:466-468. [PMID: 21326424 DOI: 10.1364/ol.36.000466] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We address soliton transmission and reflection in nonlinear photonic lattices embedded into uniform Kerr nonlinear media. We show that by introducing disorder into the guiding lattice channels, one may achieve soliton transmission even under conditions where regular lattices reflect the input beam completely. In contrast, in the parameter range in which the lattice is almost transparent for incoming solitons, disorder may induce a significant reflection.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Castelldefels (Barcelona), Spain.
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