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Suret P, Randoux S, Gelash A, Agafontsev D, Doyon B, El G. Soliton gas: Theory, numerics, and experiments. Phys Rev E 2024; 109:061001. [PMID: 39020870 DOI: 10.1103/physreve.109.061001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Indexed: 07/19/2024]
Abstract
The concept of soliton gas was introduced in 1971 by Zakharov as an infinite collection of weakly interacting solitons in the framework of Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted (rarefied) soliton gas, solitons with random amplitude and phase parameters are almost nonoverlapping. More recently, the concept has been extended to dense gases in which solitons strongly and continuously interact. The notion of soliton gas is inherently associated with integrable wave systems described by nonlinear partial differential equations like the KdV equation or the one-dimensional nonlinear Schrödinger equation that can be solved using the inverse scattering transform. Over the last few years, the field of soliton gases has received a rapidly growing interest from both the theoretical and experimental points of view. In particular, it has been realized that the soliton gas dynamics underlies some fundamental nonlinear wave phenomena such as spontaneous modulation instability and the formation of rogue waves. The recently discovered deep connections of soliton gas theory with generalized hydrodynamics have broadened the field and opened new fundamental questions related to the soliton gas statistics and thermodynamics. We review the main recent theoretical and experimental results in the field of soliton gas. The key conceptual tools of the field, such as the inverse scattering transform, the thermodynamic limit of finite-gap potentials, and generalized Gibbs ensembles are introduced and various open questions and future challenges are discussed.
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2
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Congy T, El GA, Roberti G, Tovbis A, Randoux S, Suret P. Statistics of Extreme Events in Integrable Turbulence. PHYSICAL REVIEW LETTERS 2024; 132:207201. [PMID: 38829059 DOI: 10.1103/physrevlett.132.207201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Accepted: 12/21/2023] [Indexed: 06/05/2024]
Abstract
We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schrödinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result to two fundamental scenarios of the generation of integrable turbulence: (i) the asymptotic development of the spontaneous modulational instability of a plane wave, and (ii) the long-time evolution of strongly nonlinear, partially coherent waves. In both cases, involving the bound state soliton gas dynamics, the analytically obtained values of the kurtosis are in perfect agreement with those inferred from direct numerical simulations of the fNLSE, providing the long-awaited theoretical explanation of the respective rogue wave statistics. Additionally, the evolution of a particular nonbound state gas is considered, providing important insights related to the validity of the so-called virial theorem.
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Affiliation(s)
- T Congy
- Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom
| | - G A El
- Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom
| | - G Roberti
- Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom
| | - A Tovbis
- Department of Mathematics, University of Central Florida, Orlando, Florida 32816, USA
| | - S Randoux
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - P Suret
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
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3
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Fache L, Bonnefoy F, Ducrozet G, Copie F, Novkoski F, Ricard G, Roberti G, Falcon E, Suret P, El G, Randoux S. Interaction of soliton gases in deep-water surface gravity waves. Phys Rev E 2024; 109:034207. [PMID: 38632798 DOI: 10.1103/physreve.109.034207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Accepted: 12/21/2023] [Indexed: 04/19/2024]
Abstract
Soliton gases represent large random soliton ensembles in physical systems that display integrable dynamics at leading order. We report hydrodynamic experiments in which we investigate the interaction between two beams or jets of soliton gases having nearly identical amplitudes but opposite velocities of the same magnitude. The space-time evolution of the two interacting soliton gas jets is recorded in a 140-m-long water tank where the dynamics is described at leading order by the focusing one-dimensional nonlinear Schrödinger equation. Varying the relative initial velocity of the two species of soliton gas, we change their interaction strength and we measure the macroscopic soliton gas density and velocity changes due to the interaction. Our experimental results are found to be in good quantitative agreement with predictions of the spectral kinetic theory of soliton gas despite the presence of perturbative higher-order effects that break the integrability of the wave dynamics.
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Affiliation(s)
- Loic Fache
- Physique des Lasers Atomes et Molécules, UMR No. 8523, CNRS, Université de Lille, 59000 Lille, France
| | - Félicien Bonnefoy
- Nantes Université, École Centrale Nantes, CNRS, LHEEA, UMR 6598, F-44000 Nantes, France
| | - Guillaume Ducrozet
- Nantes Université, École Centrale Nantes, CNRS, LHEEA, UMR 6598, F-44000 Nantes, France
| | - François Copie
- Physique des Lasers Atomes et Molécules, UMR No. 8523, CNRS, Université de Lille, 59000 Lille, France
| | - Filip Novkoski
- Université Paris Cité, CNRS, MSC, UMR 7057, F-75013 Paris, France
| | - Guillaume Ricard
- Université Paris Cité, CNRS, MSC, UMR 7057, F-75013 Paris, France
| | - Giacomo Roberti
- Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom
| | - Eric Falcon
- Université Paris Cité, CNRS, MSC, UMR 7057, F-75013 Paris, France
| | - Pierre Suret
- Physique des Lasers Atomes et Molécules, UMR No. 8523, CNRS, Université de Lille, 59000 Lille, France
| | - Gennady El
- Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom
| | - Stéphane Randoux
- Physique des Lasers Atomes et Molécules, UMR No. 8523, CNRS, Université de Lille, 59000 Lille, France
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Pierangeli D, Perini G, Palmieri V, Grecco I, Friggeri G, De Spirito M, Papi M, DelRe E, Conti C. Extreme transport of light in spheroids of tumor cells. Nat Commun 2023; 14:4662. [PMID: 37537177 PMCID: PMC10400595 DOI: 10.1038/s41467-023-40379-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Accepted: 07/14/2023] [Indexed: 08/05/2023] Open
Abstract
Extreme waves are intense and unexpected wavepackets ubiquitous in complex systems. In optics, these rogue waves are promising as robust and noise-resistant beams for probing and manipulating the underlying material. Localizing large optical power is crucial especially in biomedical systems, where, however, extremely intense beams have not yet been observed. We here discover that tumor-cell spheroids manifest optical rogue waves when illuminated by randomly modulated laser beams. The intensity of light transmitted through bio-printed three-dimensional tumor models follows a signature Weibull statistical distribution, where extreme events correspond to spatially-localized optical modes propagating within the cell network. Experiments varying the input beam power and size indicate that the rogue waves have a nonlinear origin. We show that these nonlinear optical filaments form high-transmission channels with enhanced transmission. They deliver large optical power through the tumor spheroid, and can be exploited to achieve a local temperature increase controlled by the input wave shape. Our findings shed light on optical propagation in biological aggregates and demonstrate how nonlinear extreme event formation allows light concentration in deep tissues, paving the way to using rogue waves in biomedical applications, such as light-activated therapies.
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Affiliation(s)
- Davide Pierangeli
- Institute for Complex Systems, National Research Council, Rome, 00185, Italy.
- Physics Department, Sapienza University of Rome, Rome, 00185, Italy.
| | - Giordano Perini
- Neuroscience Department, University Cattolica del Sacro Cuore, Rome, 00168, Italy
- IRCSS, Fondazione Policlinico Universitario Agostino Gemelli, Rome, 00168, Italy
| | - Valentina Palmieri
- Institute for Complex Systems, National Research Council, Rome, 00185, Italy
- Neuroscience Department, University Cattolica del Sacro Cuore, Rome, 00168, Italy
| | - Ivana Grecco
- Physics Department, Sapienza University of Rome, Rome, 00185, Italy
| | - Ginevra Friggeri
- Neuroscience Department, University Cattolica del Sacro Cuore, Rome, 00168, Italy
- IRCSS, Fondazione Policlinico Universitario Agostino Gemelli, Rome, 00168, Italy
| | - Marco De Spirito
- Neuroscience Department, University Cattolica del Sacro Cuore, Rome, 00168, Italy
- IRCSS, Fondazione Policlinico Universitario Agostino Gemelli, Rome, 00168, Italy
| | - Massimiliano Papi
- Neuroscience Department, University Cattolica del Sacro Cuore, Rome, 00168, Italy.
- IRCSS, Fondazione Policlinico Universitario Agostino Gemelli, Rome, 00168, Italy.
| | - Eugenio DelRe
- Physics Department, Sapienza University of Rome, Rome, 00185, Italy
| | - Claudio Conti
- Physics Department, Sapienza University of Rome, Rome, 00185, Italy
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5
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The piston Riemann problem in a photon superfluid. Nat Commun 2022; 13:3137. [PMID: 35668094 PMCID: PMC9170689 DOI: 10.1038/s41467-022-30734-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Accepted: 05/12/2022] [Indexed: 11/24/2022] Open
Abstract
Light flow in nonlinear media can exhibit quantum hydrodynamical features which are profoundly different from those of classical fluids. Here, we show that a rather extreme regime of quantum hydrodynamics can be accessed by exploring the piston problem (a paradigm in gas dynamics) for light, and its generalization, named after the celebrated mathematician Riemann, where the piston acts on a concomitant abrupt change of photon density. Our experiment reveals regimes featuring optical rarefaction (retracting piston) or shock (pushing piston) wave pairs, and most importantly the transition to a peculiar type of flow, occurring above a precise critical piston velocity, where the light shocks are smoothly interconnected by a large contrast, periodic, fully nonlinear wave. The transition to such extreme hydrodynamic state is generic for superfluids, but to date remained elusive to any other quantum fluid system. Our full-fiber setup used to observe this phenomenon in temporal domain proves to be a versatile alternative to other platforms currently employed to investigate the hydrodynamical properties of quantum fluids of light. The flow of light in nonlinear media can be considered as superfluid flow and described with quantum hydrodynamics. Here the authors demonstrate superfluid flow, optical rarefaction (retracting piston) and shock (pushing piston) wave pairs and characterize associated phase transitions by using fiber-based platform.
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Bongiovanni D, Jukić D, Hu Z, Lunić F, Hu Y, Song D, Morandotti R, Chen Z, Buljan H. Dynamically Emerging Topological Phase Transitions in Nonlinear Interacting Soliton Lattices. PHYSICAL REVIEW LETTERS 2021; 127:184101. [PMID: 34767391 DOI: 10.1103/physrevlett.127.184101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 09/13/2021] [Indexed: 06/13/2023]
Abstract
We demonstrate dynamical topological phase transitions in evolving Su-Schrieffer-Heeger lattices made of interacting soliton arrays, which are entirely driven by nonlinearity and thereby exemplify an emergent nonlinear topological phenomenon. The phase transitions occur from the topologically trivial-to-nontrivial phase in periodic succession with crossovers from the topologically nontrivial-to-trivial regime. The signature of phase transition is the gap-closing and reopening point, where two extended states are pulled from the bands into the gap to become localized topological edge states. Crossovers occur via decoupling of the edge states from the bulk of the lattice.
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Affiliation(s)
- Domenico Bongiovanni
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, Quebec J3X 1S2, Canada
| | - Dario Jukić
- Faculty of Civil Engineering, University of Zagreb, A. Kačića Miošića 26, 10000 Zagreb, Croatia
| | - Zhichan Hu
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Frane Lunić
- Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000 Zagreb, Croatia
| | - Yi Hu
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Daohong Song
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Roberto Morandotti
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, Quebec J3X 1S2, Canada
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
| | - Zhigang Chen
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Hrvoje Buljan
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000 Zagreb, Croatia
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7
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Gomel A, Chabchoub A, Brunetti M, Trillo S, Kasparian J, Armaroli A. Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation. PHYSICAL REVIEW LETTERS 2021; 126:174501. [PMID: 33988389 DOI: 10.1103/physrevlett.126.174501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Revised: 02/23/2021] [Accepted: 04/01/2021] [Indexed: 06/12/2023]
Abstract
We introduce a dynamic stabilization scheme universally applicable to unidirectional nonlinear coherent waves. By abruptly changing the waveguiding properties, the breathing of wave packets subject to modulation instability can be stabilized as a result of the abrupt expansion a homoclinic orbit and its fall into an elliptic fixed point (center). We apply this concept to the nonlinear Schrödinger equation framework and show that an Akhmediev breather envelope, which is at the core of Fermi-Pasta-Ulam-Tsingou recurrence and extreme wave events, can be frozen into a steady periodic (dnoidal) wave by a suitable variation of a single external physical parameter. We experimentally demonstrate this general approach in the particular case of surface gravity water waves propagating in a wave flume with an abrupt bathymetry change. Our results highlight the influence of topography and waveguide properties on the lifetime of nonlinear waves and confirm the possibility to control them.
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Affiliation(s)
- Alexis Gomel
- GAP, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland
- Institute for Environmental Sciences, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
| | - Amin Chabchoub
- Hakubi Center for Advanced Research, Kyoto University, Yoshida-Honmachi, Kyoto 606-8501, Japan
- Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto 611-0011, Japan
- Centre for Wind, Waves and Water, School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
| | - Maura Brunetti
- GAP, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland
- Institute for Environmental Sciences, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
| | - Stefano Trillo
- Department of Engineering, University of Ferrara, via Saragat 1, 44122 Ferrara, Italy
| | - Jérôme Kasparian
- GAP, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland
- Institute for Environmental Sciences, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
| | - Andrea Armaroli
- GAP, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland
- Institute for Environmental Sciences, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
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8
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Lebel A, Tikan A, Randoux S, Suret P, Copie F. Single-shot observation of breathers from noise-induced modulation instability using heterodyne temporal imaging. OPTICS LETTERS 2021; 46:298-301. [PMID: 33449014 DOI: 10.1364/ol.408730] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 12/08/2020] [Indexed: 06/12/2023]
Abstract
We report phase and amplitude measurements of large coherent structures originating from the noise-induced modulation instability in optical fibers. By using a specifically designed time-lens system (SEAHORSE) in which aberrations are compensated, the complex field is recorded in single-shot over long durations of 200 ps with sub-picosecond resolution. Signatures of Akhmediev breather-like patterns are identified in the ultrafast temporal dynamics in very good agreement with numerical predictions based on the nonlinear Schrödinger equation.
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9
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Suret P, Tikan A, Bonnefoy F, Copie F, Ducrozet G, Gelash A, Prabhudesai G, Michel G, Cazaubiel A, Falcon E, El G, Randoux S. Nonlinear Spectral Synthesis of Soliton Gas in Deep-Water Surface Gravity Waves. PHYSICAL REVIEW LETTERS 2020; 125:264101. [PMID: 33449735 DOI: 10.1103/physrevlett.125.264101] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Accepted: 11/30/2020] [Indexed: 06/12/2023]
Abstract
Soliton gases represent large random soliton ensembles in physical systems that exhibit integrable dynamics at the leading order. Despite significant theoretical developments and observational evidence of ubiquity of soliton gases in fluids and optical media, their controlled experimental realization has been missing. We report a controlled synthesis of a dense soliton gas in deep-water surface gravity waves using the tools of nonlinear spectral theory [inverse scattering transform (IST)] for the one-dimensional focusing nonlinear Schrödinger equation. The soliton gas is experimentally generated in a one-dimensional water tank where we demonstrate that we can control and measure the density of states, i.e., the probability density function parametrizing the soliton gas in the IST spectral phase space. Nonlinear spectral analysis of the generated hydrodynamic soliton gas reveals that the density of states slowly changes under the influence of perturbative higher-order effects that break the integrability of the wave dynamics.
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Affiliation(s)
- Pierre Suret
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59 000 Lille, France
| | - Alexey Tikan
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59 000 Lille, France
| | - Félicien Bonnefoy
- École Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44 321 Nantes, France
| | - François Copie
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59 000 Lille, France
| | | | - Andrey Gelash
- Institute of Automation and Electrometry SB RAS, Novosibirsk 630090, Russia
- Skolkovo Institute of Science and Technology, Moscow 121205, Russia
| | - Gaurav Prabhudesai
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, 75005 Paris, France
| | - Guillaume Michel
- Sorbonne Université, CNRS, UMR 7190, Institut Jean Le Rond dAlembert, F-75 005 Paris, France
| | - Annette Cazaubiel
- Université de Paris, Université Paris Diderot, MSC, UMR 7057 CNRS, F-75 013 Paris, France
| | - Eric Falcon
- Université de Paris, Université Paris Diderot, MSC, UMR 7057 CNRS, F-75 013 Paris, France
| | - Gennady El
- Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne, NE1 8ST, United Kingdom
| | - Stéphane Randoux
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59 000 Lille, France
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10
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Marcucci G, Hu X, Cala P, Man W, Pierangeli D, Conti C, Chen Z. Anisotropic Optical Shock Waves in Isotropic Media with Giant Nonlocal Nonlinearity. PHYSICAL REVIEW LETTERS 2020; 125:243902. [PMID: 33412069 DOI: 10.1103/physrevlett.125.243902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Revised: 09/05/2020] [Accepted: 10/27/2020] [Indexed: 06/12/2023]
Abstract
Dispersive shock waves in thermal optical media are nonlinear phenomena whose intrinsic irreversibility is described by time asymmetric quantum mechanics. Recent studies demonstrated that the nonlocal wave breaking evolves in an exponentially decaying dynamics ruled by the reversed harmonic oscillator, namely, the simplest irreversible quantum system in the rigged Hilbert spaces. The generalization of this theory to more complex scenarios is still an open question. In this work, we use a thermal third-order medium with an unprecedented giant Kerr coefficient, the m-cresol/nylon mixed solution, to access an extremely nonlinear, highly nonlocal regime and realize anisotropic shock waves with internal gaps. We compare our experimental observations to results obtained under similar conditions but in hemoglobin solutions from human red blood cells, and found that the gap formation strongly depends on the nonlinearity strength. We prove that a superposition of Gamow vectors in an ad hoc rigged Hilbert space, that is, a tensorial product between the reversed and the standard harmonic oscillators spaces, describes the beam propagation beyond the shock point. The anisotropy turns out from the interaction of trapping and antitrapping potentials. Our work furnishes the description of novel intriguing shock phenomena mediated by extreme nonlinearities.
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Affiliation(s)
- Giulia Marcucci
- Department of Physics, Sapienza University, P.le Aldo Moro 2, 00185 Rome, Italy
- Institute for Complex Systems, Via dei Taurini 19, 00185 Rome, Italy
| | - Xubo Hu
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
- College of Electronics Engineering, South China Agricultural University, Guangzhou 510642, China
| | - Phillip Cala
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Weining Man
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Davide Pierangeli
- Department of Physics, Sapienza University, P.le Aldo Moro 2, 00185 Rome, Italy
- Institute for Complex Systems, Via dei Taurini 19, 00185 Rome, Italy
| | - Claudio Conti
- Department of Physics, Sapienza University, P.le Aldo Moro 2, 00185 Rome, Italy
- Institute for Complex Systems, Via dei Taurini 19, 00185 Rome, Italy
- TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Zhigang Chen
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
- TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
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11
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Ivanov SK, Suchorski JE, Kamchatnov AM, Isoard M, Pavloff N. Formation of dispersive shock waves in a saturable nonlinear medium. Phys Rev E 2020; 102:032215. [PMID: 33075994 DOI: 10.1103/physreve.102.032215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Accepted: 08/25/2020] [Indexed: 06/11/2023]
Abstract
We use the Gurevich-Pitaevskii approach based on the Whitham averaging method for studying the formation of dispersive shock waves in an intense light pulse propagating through a saturable nonlinear medium. Although the Whitham modulation equations cannot be diagonalized in this case, the main characteristics of the dispersive shock can be derived by means of an analysis of the properties of these equations at the boundaries of the shock. Our approach generalizes a previous analysis of steplike initial intensity distributions to a more realistic type of initial light pulse and makes it possible to determine, in a setting of experimental interest, the value of measurable quantities such as the wave-breaking time or the position and light intensity of the shock edges.
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Affiliation(s)
- Sergey K Ivanov
- Moscow Institute of Physics and Technology, Institutsky Lane 9, Dolgoprudny, Moscow Region 141700, Russia
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 108840, Russia
| | - Jules-Elémir Suchorski
- Université Paris-Saclay, Centre National de la Recherche Scientifique, LPTMS, 91405 Orsay, France
| | - Anatoly M Kamchatnov
- Moscow Institute of Physics and Technology, Institutsky Lane 9, Dolgoprudny, Moscow Region 141700, Russia
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 108840, Russia
| | - Mathieu Isoard
- Université Paris-Saclay, Centre National de la Recherche Scientifique, LPTMS, 91405 Orsay, France
| | - Nicolas Pavloff
- Université Paris-Saclay, Centre National de la Recherche Scientifique, LPTMS, 91405 Orsay, France
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12
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Marcucci G, Pierangeli D, Conti C. Theory of Neuromorphic Computing by Waves: Machine Learning by Rogue Waves, Dispersive Shocks, and Solitons. PHYSICAL REVIEW LETTERS 2020; 125:093901. [PMID: 32915624 DOI: 10.1103/physrevlett.125.093901] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Revised: 04/14/2020] [Accepted: 07/09/2020] [Indexed: 06/11/2023]
Abstract
We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layered model, with an encoding input layer, a wave layer, and a decoding readout, behaves as a conventional neural network in approximating mathematical functions, real-world datasets, and universal Boolean gates. The rank of the transmission matrix has a fundamental role in assessing the learning abilities of the wave. For a given set of training points, a threshold nonlinearity for universal interpolation exists. When considering the nonlinear Schrödinger equation, the use of highly nonlinear regimes implies that solitons, rogue, and shock waves do have a leading role in training and computing. Our results may enable the realization of novel machine learning devices by using diverse physical systems, as nonlinear optics, hydrodynamics, polaritonics, and Bose-Einstein condensates. The application of these concepts to photonics opens the way to a large class of accelerators and new computational paradigms. In complex wave systems, as multimodal fibers, integrated optical circuits, random, topological devices, and metasurfaces, nonlinear waves can be employed to perform computation and solve complex combinatorial optimization.
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Affiliation(s)
- Giulia Marcucci
- Institute for Complex Systems, National Research Council (ISC-CNR), Via dei Taurini 19, 00185 Rome, Italy and Department of Physics, Sapienza University, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Davide Pierangeli
- Institute for Complex Systems, National Research Council (ISC-CNR), Via dei Taurini 19, 00185 Rome, Italy and Department of Physics, Sapienza University, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Claudio Conti
- Institute for Complex Systems, National Research Council (ISC-CNR), Via dei Taurini 19, 00185 Rome, Italy and Department of Physics, Sapienza University, Piazzale Aldo Moro 2, 00185 Rome, Italy
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El G, Tovbis A. Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation. Phys Rev E 2020; 101:052207. [PMID: 32575216 DOI: 10.1103/physreve.101.052207] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2019] [Accepted: 04/03/2020] [Indexed: 06/11/2023]
Abstract
Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles" of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and nonlinear optical media, these "integrable" gases present a fundamental interest for nonlinear physics. We develop an analytical theory of breather and soliton gases by considering a special, thermodynamic-type limit of the wave-number-frequency relations for multiphase (finite-gap) solutions of the focusing nonlinear Schrödinger equation. This limit is defined by the locus and the critical scaling of the band spectrum of the associated Zakharov-Shabat operator, and it yields the nonlinear dispersion relations for a spatially homogeneous breather or soliton gas, depending on the presence or absence of the "background" Stokes mode. The key quantity of interest is the density of states defining, in principle, all spectral and statistical properties of a soliton (breather) gas. The balance of terms in the nonlinear dispersion relations determines the nature of the gas: from an ideal gas of well separated, noninteracting breathers (solitons) to a special limiting state, which we term a breather (soliton) condensate, and whose properties are entirely determined by the pairwise interactions between breathers (solitons). For a nonhomogeneous breather gas, we derive a full set of kinetic equations describing the slow evolution of the density of states and of its carrier wave counterpart. The kinetic equation for soliton gas is recovered by collapsing the Stokes spectral band. A number of concrete examples of breather and soliton gases are considered, demonstrating the efficacy of the developed general theory with broad implications for nonlinear optics, superfluids, and oceanography. In particular, our work provides the theoretical underpinning for the recently observed remarkable connection of the soliton gas dynamics with the long-term evolution of spontaneous modulational instability.
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Affiliation(s)
- Gennady El
- Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom
| | - Alexander Tovbis
- Department of Mathematics, University of Central Florida, Orlando, Florida 32816, USA
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Finot C. Photonic generation of picosecond pulse doublets from the nonlinear splitting of super-Gaussian pulses. EPJ WEB OF CONFERENCES 2020. [DOI: 10.1051/epjconf/202023811012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We experimentally demonstrate the generation of temporal pulse doublets from the propagation of initial super-Gaussian waveforms in an optical fiber with anomalous dispersion. The nonlinear focusing dynamics leads to picosecond structures that are characterized both in amplitude and phase. Their close-to-Gaussian Fourier-transform limited shape is found in excellent agreement with numerical simulations. This single-stage reshaping scheme is energy efficient, can sustain GHz repetition rates and temporal compression factors around 10 are demonstrated.
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