1
|
Wang XB. General rogue waves in the AB system. APPLIED MATHEMATICS LETTERS 2023; 144:108725. [DOI: 10.1016/j.aml.2023.108725] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
|
2
|
Shao C, Yang L, Yan Y, Wu J, Zhu M, Li L. Periodic, n-soliton and variable separation solutions for an extended (3+1)-dimensional KP-Boussinesq equation. Sci Rep 2023; 13:15826. [PMID: 37739979 PMCID: PMC10517173 DOI: 10.1038/s41598-023-42845-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 09/15/2023] [Indexed: 09/24/2023] Open
Abstract
An extended (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq equation is studied in this paper to construct periodic solution, n-soliton solution and folded localized excitation. Firstly, with the help of the Hirota's bilinear method and ansatz, some periodic solutions have been derived. Secondly, taking Burgers equation as an auxiliary function, we have obtained n-soliton solution and n-shock wave. Lastly, we present a new variable separation method for (3+1)-dimensional and higher dimensional models, and use it to derive localized excitation solutions. To be specific, we have constructed various novel structures and discussed the interaction dynamics of folded solitary waves. Compared with the other methods, the variable separation solutions obtained in this paper not only directly give the analytical form of the solution u instead of its potential [Formula: see text], but also provide us a straightforward approach to construct localized excitation for higher order dimensional nonlinear partial differential equation.
Collapse
Affiliation(s)
- Chuanlin Shao
- School of Economics and Finance, Huaqiao University, Quanzhou, 362021, Fujian, People's Republic of China
| | - Lu Yang
- School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China
| | - Yongsheng Yan
- School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China
| | - Jingyu Wu
- School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China
| | - Minting Zhu
- School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China
| | - Lingfei Li
- School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China.
| |
Collapse
|
3
|
Huang Y, Gu S, Zeng Y, Zhou P, Li N. Spatiotemporal chaos induces extreme events in a three-element laterally coupled laser array. OPTICS LETTERS 2022; 47:4632-4635. [PMID: 36107050 DOI: 10.1364/ol.470524] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Accepted: 08/07/2022] [Indexed: 06/15/2023]
Abstract
Extreme events are observed in the spatiotemporal chaos dynamics of a three-element laterally coupled laser array. With the help of statistical and dynamical analyses, we confirm that spatiotemporal chaos induces extreme pulses that are high enough to be identified as extreme events and cannot be found in synchronization chaos. Interestingly, our results show that extreme events always preferentially appear in the middle laser as the laser separation ratio is decreased (i.e., upon increasing the coupling strength), and then in the two outer lasers. This thus reveals the importance of the middle laser in the transition between synchronization chaos and spatiotemporal chaos states. Additionally, we show the evolution of extreme events in the plane of the pump level and laser separation ratio by calculating the corresponding proportion. Our results build a relation between extreme events and the spatiotemporal dynamics, which makes it easy to understand the formation mechanism of extreme events.
Collapse
|
4
|
Kingston SL, Mishra A, Balcerzak M, Kapitaniak T, Dana SK. Instabilities in quasiperiodic motion lead to intermittent large-intensity events in Zeeman laser. Phys Rev E 2021; 104:034215. [PMID: 34654152 DOI: 10.1103/physreve.104.034215] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2021] [Accepted: 09/06/2021] [Indexed: 11/07/2022]
Abstract
We report intermittent large-intensity pulses that originate in Zeeman laser due to instabilities in quasiperiodic motion, one route follows torus-doubling to chaos and another goes via quasiperiodic intermittency in response to variation in system parameters. The quasiperiodic breakdown route to chaos via torus-doubling is well known; however, the laser model shows intermittent large-intensity pulses for parameter variation beyond the chaotic regime. During quasiperiodic intermittency, the temporal evolution of the laser shows intermittent chaotic bursting episodes intermediate to the quasiperiodic motion instead of periodic motion as usually seen during the Pomeau-Manneville intermittency. The intermittent bursting appears as occasional large-intensity events. In particular, this quasiperiodic intermittency has not been given much attention so far from the dynamical system perspective, in general. In both cases, the infrequent and recurrent large events show non-Gaussian probability distribution of event height extended beyond a significant threshold with a decaying probability confirming rare occurrence of large-intensity pulses.
Collapse
Affiliation(s)
- S Leo Kingston
- Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland
| | - Arindam Mishra
- Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland
| | - Marek Balcerzak
- Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland
| | - Syamal K Dana
- Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland.,National Institute of Technology, Durgapur 713209, India
| |
Collapse
|
5
|
Zhang G, Ling L, Yan Z, Konotop VV. Parity-time-symmetric rational vector rogue waves of the n-component nonlinear Schrödinger equation. CHAOS (WOODBURY, N.Y.) 2021; 31:063120. [PMID: 34241286 DOI: 10.1063/5.0048922] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 05/31/2021] [Indexed: 06/13/2023]
Abstract
Extreme events are investigated in the integrable n-component nonlinear Schrödinger (NLS) equation with focusing nonlinearity. We report novel multi-parametric families of rational vector rogue wave (RW) solutions featuring the parity-time ( PT) symmetry, which are characterized by non-identical boundary conditions for the components that are consistent with the degeneracy of n branches of Benjamin-Feir instability. Explicit examples of PT-symmetric rational vector RWs are presented. Subject to the specific choice of the parameters, high-amplitude RWs are generated. The effect of a small non-integrable deformation of the 3-NLS equation on the excitation of vector RWs is discussed. The reported results can be useful for the design of experiments for observation of high-amplitude RWs in multi-component nonlinear physical systems.
Collapse
Affiliation(s)
- Guoqiang Zhang
- Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
| | - Liming Ling
- School of Mathematics, South China University of Technology, Guangzhou 510640, China
| | - Zhenya Yan
- Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
| | - Vladimir V Konotop
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, Lisboa 1749-016, Portugal
| |
Collapse
|
6
|
Bonatto C, Prado SD, Metz FL, Schoffen JR, Correia RRB, Hickmann JM. Super rogue wave generation in the linear regime. Phys Rev E 2020; 102:052219. [PMID: 33327069 DOI: 10.1103/physreve.102.052219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2019] [Accepted: 11/08/2020] [Indexed: 06/12/2023]
Abstract
Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been considered a necessary ingredient to generate super rogue waves, i.e., an enhanced wave amplification, where the wave amplitudes exceed by far those of ordinary rogue waves. Here we show, experimentally and theoretically, that optical super rogue waves emerge in the simple case of linear light diffraction in one transverse dimension. The underlying physics is a long-range correlation on the random initial phases of the light waves. When subgroups of random phases appear recurrently along the spatial phase distribution, a more ordered phase structure greatly increases the probability of constructive interference to generate super rogue events (non-Gaussian statistics with superlong tails). Our results consist in a significant advance in the understanding of extreme waves formation by linear superposition of random waves, with applications in a large variety of wave systems.
Collapse
Affiliation(s)
- Cristian Bonatto
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| | - Sandra D Prado
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| | - Fernando L Metz
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
- Departamento de Física, Universidade Federal de Santa Maria, 97105-900 Santa Maria, Brazil
- London Mathematical Laboratory, 14 Buckingham Street, London WC2N 6DF, United Kingdom
| | - Júlio R Schoffen
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| | - Ricardo R B Correia
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| | - Jandir M Hickmann
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| |
Collapse
|
7
|
Suresh R, Chandrasekar VK. Parametric excitation induced extreme events in MEMS and Liénard oscillator. CHAOS (WOODBURY, N.Y.) 2020; 30:083141. [PMID: 32872813 DOI: 10.1063/5.0012322] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Accepted: 08/01/2020] [Indexed: 06/11/2023]
Abstract
Two paradigmatic nonlinear oscillatory models with parametric excitation are studied. The authors provide theoretical evidence for the appearance of extreme events (EEs) in those systems. First, the authors consider a well-known Liénard type oscillator that shows the emergence of EEs via two bifurcation routes: intermittency and period-doubling routes for two different critical values of the excitation frequency. The authors also calculate the return time of two successive EEs, defined as inter-event intervals that follow Poisson-like distribution, confirming the rarity of the events. Further, the total energy of the Liénard oscillator is estimated to explain the mechanism for the development of EEs. Next, the authors confirmed the emergence of EEs in a parametrically excited microelectromechanical system. In this model, EEs occur due to the appearance of a stick-slip bifurcation near the discontinuous boundary of the system. Since the parametric excitation is encountered in several real-world engineering models, like macro- and micromechanical oscillators, the implications of the results presented in this paper are perhaps beneficial to understand the development of EEs in such oscillatory systems.
Collapse
Affiliation(s)
- R Suresh
- Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, India
| | - V K Chandrasekar
- Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, India
| |
Collapse
|
8
|
Panajotov K, Tlidi M, Song Y, Zhang H. Control of dissipative rogue waves in nonlinear cavity optics: Optical injection and time-delayed feedback. CHAOS (WOODBURY, N.Y.) 2020; 30:053103. [PMID: 32491873 DOI: 10.1063/5.0003225] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Accepted: 04/13/2020] [Indexed: 06/11/2023]
Abstract
We investigate and review the formation of two-dimensional dissipative rogue waves in cavity nonlinear optics with transverse effects. Two spatially extended systems are considered for this purpose: the driven Kerr optical cavities subjected to optical injection and the broad-area surface-emitting lasers with a saturable absorber. We also consider a quasi-two-dimensional system (the two dimensions being space and time) of a fiber laser describing the complex cubic-quintic Ginzburg-Landau equation. We show that rogue waves are controllable by means of time-delayed feedback and optical injection. We show that without delayed feedback, transverse structures are stationary or oscillating. However, when the strength of the delayed feedback is increased, all the systems generate giant two-dimensional pulses that appear with low probability and suddenly appear and disappear. We characterize their formation by computing the probability distribution, which shows a long tail. Besides, we have computed the significant wave height, which measures the mean wave height of the highest third of the waves. We show that for all systems, the distribution tails expand beyond two times the significant wave height. Furthermore, we also show that optical injection may suppress the rogue wave formation in a semiconductor laser with a saturable absorber.
Collapse
Affiliation(s)
- Krassimir Panajotov
- Department of Applied Physics and Photonics (IR-TONA), Vrije Universiteit Brussels, Pleinlaan 2, B-1050 Brussels, Belgium
| | - Mustapha Tlidi
- Faculté des Sciences, Optique Nonlinéaire Thérorique, Université libre de Bruxelles (U.L.B.), C.P. 231, Campus Plaine, B-1050 Bruxelles, Belgium
| | - Yufeng Song
- Shenzhen Engineering Laboratory of Phosphorene and Optoelectronics, Collaborative Innovation Center for Optoelectronic Science and Technology, Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen 518060, China
| | - Han Zhang
- Shenzhen Engineering Laboratory of Phosphorene and Optoelectronics, Collaborative Innovation Center for Optoelectronic Science and Technology, Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen 518060, China
| |
Collapse
|
9
|
Statistical Properties and Predictability of Extreme Epileptic Events. Sci Rep 2019; 9:7243. [PMID: 31076609 PMCID: PMC6510789 DOI: 10.1038/s41598-019-43619-3] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2018] [Accepted: 04/26/2019] [Indexed: 01/03/2023] Open
Abstract
The use of extreme events theory for the analysis of spontaneous epileptic brain activity is a relevant multidisciplinary problem. It allows deeper understanding of pathological brain functioning and unraveling mechanisms underlying the epileptic seizure emergence along with its predictability. The latter is a desired goal in epileptology which might open the way for new therapies to control and prevent epileptic attacks. With this goal in mind, we applied the extreme event theory for studying statistical properties of electroencephalographic (EEG) recordings of WAG/Rij rats with genetic predisposition to absence epilepsy. Our approach allowed us to reveal extreme events inherent in this pathological spiking activity, highly pronounced in a particular frequency range. The return interval analysis showed that the epileptic seizures exhibit a highly-structural behavior during the active phase of the spiking activity. Obtained results evidenced a possibility for early (up to 7 s) prediction of epileptic seizures based on consideration of EEG statistical properties.
Collapse
|
10
|
Peysokhan M, Keeney J, Mafi A. Impact of spatial correlation in fluctuations of the refractive index on rogue wave generation probability. OPTICS LETTERS 2019; 44:2244-2247. [PMID: 31042194 DOI: 10.1364/ol.44.002244] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2019] [Accepted: 03/27/2019] [Indexed: 06/09/2023]
Abstract
The presence of refractive index fluctuations in an optical medium can result in the generation of optical rogue waves (RWs). Using numerical simulations and statistical analysis, we have shown that the probability of optical rogue waves increases in the presence of spatial correlations in the fluctuations of the refractive index. We have analyzed the impact of the magnitude and the spatial correlation length of these fluctuations on the probability of optical rogue wave generation.
Collapse
|
11
|
Akosman AE, Sander MY. Route towards extreme optical pulsation in linear cavity ultrafast fibre lasers. Sci Rep 2018; 8:13385. [PMID: 30190582 PMCID: PMC6127321 DOI: 10.1038/s41598-018-31725-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2018] [Accepted: 08/24/2018] [Indexed: 12/03/2022] Open
Abstract
Pathways towards the generation of extreme optical pulsation in a chaotic transition regime in a linear fibre laser cavity configuration are presented. In a thulium mode-locked fibre laser, extreme events that can be controllably induced by manipulating the cavity birefringence for pulse energies exceeding the single soliton pulse operating regime are studied in detail for the first time. While a solitonic pulsation structure at the fundamental repetition rate is maintained, additional energy is shed in a chaotic manner, leading to broader spectral generation and shorter pulse durations whose behaviour deviates significantly from a classical statistical distribution. These pulses display markedly different characteristics from any previously reported extreme events in fibre lasers associated with multiple solitons and pulse bunching, thus presenting a novel observation of extreme pulsation. Detailed noise studies indicate that significant enhancement of relaxation oscillations, modulation instability and the interplay with reabsorption mechanisms contribute in this transient chaotic regime. The extreme pulsation generated in a compact fibre laser without any additional nonlinear attractors can provide an attractive platform to accelerate the exploration of the underlying physics of the chaos observed in mode-locked laser systems and can lead to novel fibre laser cavity designs.
Collapse
Affiliation(s)
- Ahmet E Akosman
- Department of Electrical and Computer Engineering, Boston University, 8 St. Mary's Street, Boston, MA, 02115, USA.,Photonics Center, Boston University, 8 St. Mary's Street, Boston, MA, 02115, USA
| | - Michelle Y Sander
- Department of Electrical and Computer Engineering, Boston University, 8 St. Mary's Street, Boston, MA, 02115, USA. .,Photonics Center, Boston University, 8 St. Mary's Street, Boston, MA, 02115, USA. .,Division of Materials Science and Engineering, Boston University, 15 St. Mary's Street, Brookline, MA, 02446, USA.
| |
Collapse
|
12
|
Bonazzola C, Hnilo A, Kovalsky M, Tredicce J. Extreme events and single-pulse spatial patterns observed in a self-pulsing all-solid-state laser. Phys Rev E 2018; 97:032215. [PMID: 29776151 DOI: 10.1103/physreve.97.032215] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2017] [Indexed: 11/07/2022]
Abstract
The passively Q-switched, self-pulsing all-solid-state laser is a device of widespread use in many applications. Depending on the condition of saturation of the absorber, which is easy to adjust, different dynamical regimes are observed: continuous-wave emission, stable oscillations, period doubling bifurcations, chaos, and, within some chaotic regimes, extreme events (EEs) in the form of pulses of extraordinary intensity. These pulses are sometimes called "dissipative optical rogue waves." The mechanism of their formation in this laser is unknown. Previous observations suggest they are caused by the interaction of a few transverse modes. Here we report a direct observation of the pulse-to-pulse evolution of the transverse pattern. In the periodical regimes, sequences of intensities are correlated with sequences of patterns. In the chaotic ones, a few different patterns alternate, and the EEs are related with even fewer ones. In addition, the series of patterns and the pulse intensities before and after an EE are markedly repetitive. These observations demonstrate that EEs follow a deterministic evolution, and that they can appear even in a system with few interacting modes. This information plays a crucial role for the development of a mathematical description of EEs in this laser. This would allow managing the formation of EE through control of chaos, which is of both academic and practical interest (laser rangefinder).
Collapse
Affiliation(s)
- Carlos Bonazzola
- Centro de Investigaciones en Láseres y Aplicaciones (CEILAP), Instituto de Investigaciones Científicas y Técnicas para la Defensa (CITEDEF), Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), J. B. de La Salle 4397, (1603) Villa Martelli, Argentina
| | - Alejandro Hnilo
- Centro de Investigaciones en Láseres y Aplicaciones (CEILAP), Instituto de Investigaciones Científicas y Técnicas para la Defensa (CITEDEF), Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), J. B. de La Salle 4397, (1603) Villa Martelli, Argentina
| | - Marcelo Kovalsky
- Centro de Investigaciones en Láseres y Aplicaciones (CEILAP), Instituto de Investigaciones Científicas y Técnicas para la Defensa (CITEDEF), Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), J. B. de La Salle 4397, (1603) Villa Martelli, Argentina
| | - Jorge Tredicce
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Intendente Güiraldes 2160, Ciudad Autónoma de Buenos Aires, Argentina and Université de la Nouvelle Calédonie, ISEA, Boîte Postale R4, Noumea, Nouvelle Calédonie, France
| |
Collapse
|
13
|
El Koussaifi R, Tikan A, Toffoli A, Randoux S, Suret P, Onorato M. Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics. Phys Rev E 2018; 97:012208. [PMID: 29448489 DOI: 10.1103/physreve.97.012208] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Indexed: 06/08/2023]
Abstract
Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of a partially coherent wave field, i.e., a wave field characterized by a finite band spectrum with random Fourier phases. Their understanding is fundamental for the design of ships and offshore platforms. In many meteorological conditions waves in the ocean are characterized by the so-called Joint North Sea Wave Project (JONSWAP) spectrum. Here we compare two unique experimental results: the first one has been performed in a 270 m wave tank and the other in optical fibers. In both cases, waves characterized by a JONSWAP spectrum and random Fourier phases have been launched at the input of the experimental device. The quantitative comparison, based on an appropriate scaling of the two experiments, shows a very good agreement between the statistics in hydrodynamics and optics. Spontaneous emergence of heavy tails in the probability density function of the wave amplitude is observed in both systems. The results demonstrate the universal features of rogue waves and provide a fundamental and explicit bridge between two important fields of research. Numerical simulations are also compared with experimental results.
Collapse
Affiliation(s)
- R El Koussaifi
- Laboratoire de Physique des Lasers, Atomes et Molecules, Université de Lille, UMR-CNRS 8523, 59655 Villeneuve d'Ascq, France
- Centre d'Etudes et de Recherches Lasers et Applications (CERLA), 59655 Villeneuve d'Ascq, France
| | - A Tikan
- Laboratoire de Physique des Lasers, Atomes et Molecules, Université de Lille, UMR-CNRS 8523, 59655 Villeneuve d'Ascq, France
- Centre d'Etudes et de Recherches Lasers et Applications (CERLA), 59655 Villeneuve d'Ascq, France
| | - A Toffoli
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, VIC 3010, Australia
| | - S Randoux
- Laboratoire de Physique des Lasers, Atomes et Molecules, Université de Lille, UMR-CNRS 8523, 59655 Villeneuve d'Ascq, France
- Centre d'Etudes et de Recherches Lasers et Applications (CERLA), 59655 Villeneuve d'Ascq, France
| | - P Suret
- Laboratoire de Physique des Lasers, Atomes et Molecules, Université de Lille, UMR-CNRS 8523, 59655 Villeneuve d'Ascq, France
- Centre d'Etudes et de Recherches Lasers et Applications (CERLA), 59655 Villeneuve d'Ascq, France
| | - M Onorato
- Dipartimento di Fisica, Università degli Studi di Torino, 10125 Torino, Italy
- Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, 10125 Torino, Italy
| |
Collapse
|
14
|
Liu J, Hang C, Huang G. Weak-light vector rogue waves, breathers, and their Stern-Gerlach deflection via electromagnetically induced transparency. OPTICS EXPRESS 2017; 25:23408-23423. [PMID: 29041642 DOI: 10.1364/oe.25.023408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2017] [Accepted: 07/23/2017] [Indexed: 06/07/2023]
Abstract
We propose a scheme for generating and manipulating vector (or two-component) optical rogue waves using Akhmediev and Kuznetsov-Ma breathers in a coherent atomic system with an M-type five-level configuration via electromagnetically induced transparency (EIT). We show that the propagation velocity of these nonlinear excitations can be reduced to 10-4c and their generation power can be lowered to microwatts. We also show that the motion trajectories of the two polarization components in these excitations can be deflected significantly by using a transversal gradient magnetic field, similar to the Stern-Gerlach effect of an atomic beam. We find that the deflection angle can reach to 10-4 radian within the propagation distance of only several centimeters; at variance with the atomic Stern-Gerlach effect, the deflection angle can be made different for different polarization components and may be actively adjusted in a controllable way. The results obtained may have promising applications, including the precise measurement of gradient magnetic fields.
Collapse
|
15
|
Rao J, Porsezian K, He J. Semi-rational solutions of the third-type Davey-Stewartson equation. CHAOS (WOODBURY, N.Y.) 2017; 27:083115. [PMID: 28863505 DOI: 10.1063/1.4999083] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
General dark solitons and mixed solutions consisting of dark solitons and breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing the bilinear method. By introducing the two differential operators, semi-rational solutions consisting of rogue waves, breathers, and solitons are generated. These semi-rational solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. Under suitable parametric conditions, we derive general rogue wave solutions expressed in terms of rational functions. It is shown that the fundamental (simplest) rogue waves are line rogue waves. It is also shown that the multi-rogue waves describe interactions of several fundamental rogue waves, which would generate interesting curvy wave patterns. The higher order rogue waves originate from a localized lump and retreat back to it. Several types of hybrid solutions composed of rogue waves, breathers, and solitons have also been illustrated. Specifically, these semi-rational solutions have a new phenomenon: lumps form on dark solitons and gradual separation from the dark solitons is observed.
Collapse
Affiliation(s)
- Jiguang Rao
- Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
| | | | - Jingsong He
- Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
| |
Collapse
|
16
|
Uy CH, Rontani D, Sciamanna M. Vectorial extreme events in VCSEL polarization dynamics. OPTICS LETTERS 2017; 42:2177-2180. [PMID: 28569875 DOI: 10.1364/ol.42.002177] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2017] [Accepted: 05/03/2017] [Indexed: 06/07/2023]
Abstract
We report on the occurrence of extreme events (EEs) in the polarization dynamics of vertical cavity surface emitting lasers with optical feedback. We have identified two types of EEs based on numerical simulations: vectorial and scalar events corresponding, respectively, to the emission of a high-power pulse in both linear polarizations simultaneously and in single linear polarization. We show that these two types of events follow the typical statistics of rogue waves. Finally, we observe that an emission in both polarizations leads to a larger generation rate of EEs with a saturation over a wide range of feedback strength by comparison to a single-polarization mode emission.
Collapse
|
17
|
Toffoli A, Proment D, Salman H, Monbaliu J, Frascoli F, Dafilis M, Stramignoni E, Forza R, Manfrin M, Onorato M. Wind Generated Rogue Waves in an Annular Wave Flume. PHYSICAL REVIEW LETTERS 2017; 118:144503. [PMID: 28430520 DOI: 10.1103/physrevlett.118.144503] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2016] [Indexed: 06/07/2023]
Abstract
We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an unlimited-fetch condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment.
Collapse
Affiliation(s)
- A Toffoli
- Department of Infrastructure Engineering, The University of Melbourne, Parkville VIC 3010, Australia
| | - D Proment
- School of Mathematics, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, United Kingdom
| | - H Salman
- School of Mathematics, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, United Kingdom
| | - J Monbaliu
- K.U. Leuven, Kasteelpark Arenberg 40, 3001 Heverlee, Belgium
| | - F Frascoli
- Department of Mathematics, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn VIC 3122, Australia
| | - M Dafilis
- Department of Health and Medical Sciences, Faculty of Health, Art, and Design, Swinburne University of Technology, Hawthorn VIC 3122, Australia
| | - E Stramignoni
- Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
| | - R Forza
- Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
| | - M Manfrin
- Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
| | - M Onorato
- Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
- INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
| |
Collapse
|
18
|
Monfared YE, Ponomarenko SA. Non-Gaussian statistics and optical rogue waves in stimulated Raman scattering. OPTICS EXPRESS 2017; 25:5941-5950. [PMID: 28381064 DOI: 10.1364/oe.25.005941] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We explore theoretically and numerically optical rogue wave formation in stimulated Raman scattering inside a hydrogen filled hollow core photonic crystal fiber. We assume a weak noisy Stokes pulse input and explicitly construct the input Stokes pulse ensemble using the coherent mode representation of optical coherence theory, thereby providing a link between optical coherence and rogue wave theories. We show that the Stokes pulse peak power probability distribution function (PDF) acquires a long tail in the limit of nearly incoherent input Stokes pulses. We demonstrate a clear link between the PDF tail magnitude and the source coherence time. Thus, the latter can serve as a convenient parameter to control the former. We explain our findings qualitatively using the concepts of statistical granularity and global degree of coherence.
Collapse
|
19
|
Zhang JH, Wang L, Liu C. Superregular breathers, characteristics of nonlinear stage of modulation instability induced by higher-order effects. Proc Math Phys Eng Sci 2017; 473:20160681. [PMID: 28413335 DOI: 10.1098/rspa.2016.0681] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2016] [Accepted: 02/03/2017] [Indexed: 11/12/2022] Open
Abstract
We study the higher-order generalized nonlinear Schrödinger (NLS) equation describing the propagation of ultrashort optical pulse in optical fibres. By using Darboux transformation, we derive the superregular breather solution that develops from a small localized perturbation. This type of solution can be used to characterize the nonlinear stage of the modulation instability (MI) of the condensate. In particular, we show some novel characteristics of the nonlinear stage of MI arising from higher-order effects: (i) coexistence of a quasi-Akhmediev breather and a multipeak soliton; (ii) two multipeak solitons propagation in opposite directions; (iii) a beating pattern followed by two multipeak solitons in the same direction. It is found that these patterns generated from a small localized perturbation do not have the analogues in the standard NLS equation. Our results enrich Zakharov's theory of superregular breathers and could provide helpful insight on the nonlinear stage of MI in presence of the higher-order effects.
Collapse
Affiliation(s)
- Jian-Hui Zhang
- Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, People's Republic of China
| | - Lei Wang
- Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, People's Republic of China
| | - Chong Liu
- School of Physics, Northwest University, Xi'an 710069, People's Republic of China.,Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710069, People's Republic of China
| |
Collapse
|
20
|
Chiu CP, Jiang XW, Chang KC, Wei MD. Chaos and extreme events in an azimuthally polarized Nd:GdVO 4 laser with pump modulation. OPTICS LETTERS 2017; 42:423-426. [PMID: 28146492 DOI: 10.1364/ol.42.000423] [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
Nonlinear dynamics and extreme events were explored in a spatially distributed polarization laser based on an azimuthally polarized Nd:GdVO4 laser with pump modulation. When the modulation frequency approached the relaxation oscillation frequency, a period-doubling route to chaos was observed with an increasing modulation depth, and spatiotemporal extreme events occurred with the generation of the chaos. An efficient azimuthal polarization was kept, even though the intensity fluctuated in the chaotic region.
Collapse
|
21
|
Tlidi M, Panajotov K. Two-dimensional dissipative rogue waves due to time-delayed feedback in cavity nonlinear optics. CHAOS (WOODBURY, N.Y.) 2017; 27:013119. [PMID: 28147505 DOI: 10.1063/1.4974852] [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 demonstrate a way to generate two-dimensional rogue waves in two types of broad area nonlinear optical systems subject to time-delayed feedback: in the generic Lugiato-Lefever model and in the model of a broad-area surface-emitting laser with saturable absorber. The delayed feedback is found to induce a spontaneous formation of rogue waves. In the absence of delayed feedback, spatial pulses are stationary. The rogue waves are exited and controlled by the delay feedback. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical contribution, which is often considered as a signature of the presence of rogue waves, appears for sufficiently strong feedback. The generality of our analysis suggests that the feedback induced instability leading to the spontaneous formation of two-dimensional rogue waves is a universal phenomenon.
Collapse
Affiliation(s)
- Mustapha Tlidi
- Faculté des Sciences, Optique Nonlinéaire Thérorique, Université libre de B ruxelles (U.L.B.), C.P. 231, Campus Plaine, B-1050 Bruxelles, Belgium
| | - Krassimir Panajotov
- Department of Applied Physics and Photonics (IR-TONA), Vrije Universiteit Brussels, Pleinlaan 2, B-1050 Brussels, Belgium
| |
Collapse
|
22
|
Pierangeli D, Di Mei F, Di Domenico G, Agranat AJ, Conti C, DelRe E. Turbulent Transitions in Optical Wave Propagation. PHYSICAL REVIEW LETTERS 2016; 117:183902. [PMID: 27834998 DOI: 10.1103/physrevlett.117.183902] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Indexed: 06/06/2023]
Abstract
We report the direct observation of the onset of turbulence in propagating one-dimensional optical waves. The transition occurs as the disordered hosting material passes from being linear to one with extreme nonlinearity. As the response grows, increased wave interaction causes a modulational unstable quasihomogeneous flow to be superseded by a chaotic and spatially incoherent one. Statistical analysis of high-resolution wave behavior in the turbulent regime unveils the emergence of concomitant rogue waves. The transition, observed in a photorefractive ferroelectric crystal, introduces a new and rich experimental setting for the study of optical wave turbulence and information transport in conditions dominated by large fluctuations and extreme nonlinearity.
Collapse
Affiliation(s)
- D Pierangeli
- Dipartimento di Fisica, Università di Roma "La Sapienza," 00185 Rome, Italy
| | - F Di Mei
- Dipartimento di Fisica, Università di Roma "La Sapienza," 00185 Rome, Italy
| | - G Di Domenico
- Dipartimento di Fisica, Università di Roma "La Sapienza," 00185 Rome, Italy
- Center for Life Nano Science@Sapienza, Istituto Italiano di Tecnologia, 00161 Rome, Italy
| | - A J Agranat
- Applied Physics Department, Hebrew University of Jerusalem, 91904 Jerusalem, Israel
| | - C Conti
- Dipartimento di Fisica, Università di Roma "La Sapienza," 00185 Rome, Italy
- ISC-CNR, Università di Roma "La Sapienza," 00185 Rome, Italy
| | - E DelRe
- Dipartimento di Fisica, Università di Roma "La Sapienza," 00185 Rome, Italy
| |
Collapse
|
23
|
Single-shot observation of optical rogue waves in integrable turbulence using time microscopy. Nat Commun 2016; 7:13136. [PMID: 27713416 PMCID: PMC5059780 DOI: 10.1038/ncomms13136] [Citation(s) in RCA: 61] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Accepted: 09/05/2016] [Indexed: 12/05/2022] Open
Abstract
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented—up to now—time-resolved observations of the awaited dynamics. Here, we report temporal ‘snapshots' of random light using a specially designed ‘time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by ‘breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence. A rogue wave is an unexpected oscillation of large amplitude and is an example of the spontaneous formation of a coherent structure out of disorder. Here, the authors develop an experimental strategy that can provide snapshots in time and thus record the real shape of optical rogue waves emerging from random noise.
Collapse
|
24
|
Temgoua DDE, Kofane TC. Influence of optical activity on rogue waves propagating in chiral optical fibers. Phys Rev E 2016; 93:062223. [PMID: 27415269 DOI: 10.1103/physreve.93.062223] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2016] [Indexed: 11/07/2022]
Abstract
We derive the nonlinear Schrödinger (NLS) equation in chiral optical fiber with right- and left-hand nonlinear polarization. We use the similarity transformation to reduce the generalized chiral NLS equation to the higher-order integrable Hirota equation. We present the first- and second-order rational solutions of the chiral NLS equation with variable and constant coefficients, based on the modified Darboux transformation method. For some specific set of parameters, the features of chiral optical rogue waves are analyzed from analytical results, showing the influence of optical activity on waves. We also generate the exact solutions of the two-component coupled nonlinear Schrödinger equations, which describe optical activity effects on the propagation of rogue waves, and their properties in linear and nonlinear coupling cases are investigated. The condition of modulation instability of the background reveals the existence of vector rogue waves and the number of stable and unstable branches. Controllability of chiral optical rogue waves is examined by numerical simulations and may bring potential applications in optical fibers and in many other physical systems.
Collapse
Affiliation(s)
- D D Estelle Temgoua
- Laboratory of Mechanics, Materials and Structures, Post Graduate School in Sciences, Technology and Geosciences, Doctoral Research Unit in Physics and Applications, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Organization for Women in Science for the Developing World, ICTP Campus, Strada Costiera 11, 34151 Trieste, Italy
| | - T C Kofane
- Laboratory of Mechanics, Materials and Structures, Post Graduate School in Sciences, Technology and Geosciences, Doctoral Research Unit in Physics and Applications, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
| |
Collapse
|
25
|
Granese NM, Lacapmesure A, Agüero MB, Kovalsky MG, Hnilo AA, Tredicce JR. Extreme events and crises observed in an all-solid-state laser with modulation of losses. OPTICS LETTERS 2016; 41:3010-3012. [PMID: 27367088 DOI: 10.1364/ol.41.003010] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We report observations of extreme events (or dissipative optical rogue waves) in a laser with a modulated parameter (cavity losses). Experimental data supporting the hypothesis that these events are related with multi-stability and external crises is presented. It is also shown that the time separation between a pulse and an extreme event can be predicted more accurately than that between pulses of average intensity, in agreement with the theoretical description and opening the road to the prediction and control of extreme optical events.
Collapse
|
26
|
Clerc MG, González-Cortés G, Wilson M. Extreme events induced by spatiotemporal chaos in experimental optical patterns. OPTICS LETTERS 2016; 41:2711-2714. [PMID: 27304270 DOI: 10.1364/ol.41.002711] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Extreme events such as rogue waves are often associated with the merging of coherent structures. We report on experimental results in the physics of extreme events emerging in a liquid-crystal light valve subjected to optical feedback, and we establish the relation of this phenomenon with the appearance of spatiotemporal chaos. This system, under particular conditions, exhibits stationary roll patterns that can be destabilized into quasi-periodic and chaotic textures when control parameters are properly modified. We have identified the parameter regions where extreme fluctuations of the amplitude can emerge and established their origin through its direct relation with the experimental largest Lyapunov exponents, the proportion of extreme events, and the normed kurtosis.
Collapse
|
27
|
Choi D, Wishon MJ, Barnoud J, Chang CY, Bouazizi Y, Locquet A, Citrin DS. Low-frequency fluctuations in an external-cavity laser leading to extreme events. Phys Rev E 2016; 93:042216. [PMID: 27176302 DOI: 10.1103/physreve.93.042216] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2016] [Indexed: 06/05/2023]
Abstract
We experimentally investigate the dynamical regimes of a laser diode subject to external optical feedback in light of extreme-event (EE) analysis. We observe EEs in the low-frequency fluctuations (LFFs) regime. This number decreases to negligible values when the laser transitions towards fully developed coherence collapse as the injection current is increased. Moreover, we show that EEs observed in the LFF regime are linked to high-frequency pulsing events observed after a power dropout. Finally, we prove experimentally that the observation of EEs in the LFF regimes is robust to changes in operational parameters.
Collapse
Affiliation(s)
- Daeyoung Choi
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| | - Michael J Wishon
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| | - J Barnoud
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| | - C Y Chang
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
| | - Y Bouazizi
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| | - A Locquet
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| | - D S Citrin
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| |
Collapse
|
28
|
Self-Replicating Spots in the Brusselator Model and Extreme Events in the One-Dimensional Case with Delay. ENTROPY 2016. [DOI: 10.3390/e18030064] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
29
|
Gibson CJ, Yao AM, Oppo GL. Optical Rogue Waves in Vortex Turbulence. PHYSICAL REVIEW LETTERS 2016; 116:043903. [PMID: 26871334 DOI: 10.1103/physrevlett.116.043903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2015] [Indexed: 06/05/2023]
Abstract
We present a spatiotemporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction, and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg-Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatiotemporal vortex-mediated turbulence with high excursions in amplitude. Nonlinear amplification leads to rogue waves close to turbulent optical vortices, where the amplitude tends to zero, and to probability density functions (PDFs) with long tails typical of extreme optical events.
Collapse
Affiliation(s)
- Christopher J Gibson
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
| | - Alison M Yao
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
| | - Gian-Luca Oppo
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
| |
Collapse
|
30
|
Selmi F, Coulibaly S, Loghmari Z, Sagnes I, Beaudoin G, Clerc MG, Barbay S. Spatiotemporal Chaos Induces Extreme Events in an Extended Microcavity Laser. PHYSICAL REVIEW LETTERS 2016; 116:013901. [PMID: 26799020 DOI: 10.1103/physrevlett.116.013901] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2015] [Indexed: 06/05/2023]
Abstract
Extreme events such as rogue waves in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme event appearance in a spatially extended semiconductor microcavity laser with an intracavity saturable absorber. This system can display deterministic irregular dynamics only, thanks to spatial coupling through diffraction of light. We have identified parameter regions where extreme events are encountered and established the origin of this dynamics in the emergence of deterministic spatiotemporal chaos, through the correspondence between the proportion of extreme events and the dimension of the strange attractor.
Collapse
Affiliation(s)
- F Selmi
- Laboratoire de Photonique et de Nanostructures, CNRS, Université Paris Saclay, Route de Nozay, 91460 Marcoussis, France
| | - S Coulibaly
- Université de Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Z Loghmari
- Laboratoire de Photonique et de Nanostructures, CNRS, Université Paris Saclay, Route de Nozay, 91460 Marcoussis, France
| | - I Sagnes
- Laboratoire de Photonique et de Nanostructures, CNRS, Université Paris Saclay, Route de Nozay, 91460 Marcoussis, France
| | - G Beaudoin
- Laboratoire de Photonique et de Nanostructures, CNRS, Université Paris Saclay, Route de Nozay, 91460 Marcoussis, France
| | - M G Clerc
- Departamento de Física, Facultad de ciencias Fśicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - S Barbay
- Laboratoire de Photonique et de Nanostructures, CNRS, Université Paris Saclay, Route de Nozay, 91460 Marcoussis, France
| |
Collapse
|
31
|
Pierangeli D, Di Mei F, Conti C, Agranat AJ, DelRe E. Spatial Rogue Waves in Photorefractive Ferroelectrics. PHYSICAL REVIEW LETTERS 2015; 115:093901. [PMID: 26371654 DOI: 10.1103/physrevlett.115.093901] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2015] [Indexed: 06/05/2023]
Abstract
Rogue waves are observed as light propagates in the extreme nonlinear regime that occurs when a photorefractive ferroelectric crystal is undergoing a structural phase transition. The transmitted spatial light distribution contains bright localized spots of anomalously large intensity that follow a signature long-tail statistics that disappears as the nonlinearity is weakened. The isolated wave events form as out-of-equilibrium response and disorder enhance the Kerr-saturated nonlinearity at the critical point. Self-similarity associable to the individual observed filaments and numerical simulations of the generalized nonlinear Schrödinger equation suggests that dynamics of soliton fusions and scale invariance can microscopically play an important role in the observed rogue intensities and statistics.
Collapse
Affiliation(s)
- D Pierangeli
- Dipartimento di Fisica, Università di Roma "La Sapienza", 00185 Rome, Italy
| | - F Di Mei
- Dipartimento di Fisica, Università di Roma "La Sapienza", 00185 Rome, Italy
- Center for Life Nano Science@Sapienza, Istituto Italiano di Tecnologia, 00161 Rome, Italy
| | - C Conti
- Dipartimento di Fisica, Università di Roma "La Sapienza", 00185 Rome, Italy
- ISC-CNR, Università di Roma "La Sapienza", 00185 Rome, Italy
| | - A J Agranat
- Applied Physics Department, Hebrew University of Jerusalem, 91904 Jerusalem, Israel
| | - E DelRe
- Dipartimento di Fisica, Università di Roma "La Sapienza", 00185 Rome, Italy
| |
Collapse
|
32
|
Abstract
There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an “optical sea” with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.
Collapse
|
33
|
Temgoua DDE, Kofane TC. Nonparaxial rogue waves in optical Kerr media. Phys Rev E 2015; 91:063201. [PMID: 26172812 DOI: 10.1103/physreve.91.063201] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2014] [Indexed: 11/07/2022]
Abstract
We consider the inhomogeneous nonparaxial nonlinear Schrödinger (NLS) equation with varying dispersion, nonlinearity, and nonparaxiality coefficients, which governs the nonlinear wave propagation in an inhomogeneous optical fiber system. We present the similarity and Darboux transformations and for the chosen specific set of parameters and free functions, the first- and second-order rational solutions of the nonparaxial NLS equation are generated. In particular, the features of rogue waves throughout polynomial and Jacobian elliptic functions are analyzed, showing the nonparaxial effects. It is shown that the nonparaxiality increases the intensity of rogue waves by increasing the length and reducing the width simultaneously, by the way it increases their speed and penalizes interactions between them. These properties and the characteristic controllability of the nonparaxial rogue waves may give another opportunity to perform experimental realizations and potential applications in optical fibers.
Collapse
Affiliation(s)
- D D Estelle Temgoua
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
| | - T C Kofane
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
| |
Collapse
|
34
|
Walczak P, Randoux S, Suret P. Optical rogue waves in integrable turbulence. PHYSICAL REVIEW LETTERS 2015; 114:143903. [PMID: 25910126 DOI: 10.1103/physrevlett.114.143903] [Citation(s) in RCA: 63] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2014] [Indexed: 06/04/2023]
Abstract
We report optical experiments allowing us to investigate integrable turbulence in the focusing regime of the one-dimensional nonlinear Schrödinger equation (1D NLSE). In analogy with broad spectrum excitation of a one-dimensional water tank, we launch random initial waves in a single mode optical fiber. Using an original optical sampling setup, we measure precisely the probability density function of optical power of the partially coherent waves rapidly fluctuating with time. The probability density function is found to evolve from the normal law to a strong heavy-tailed distribution, thus revealing the formation of rogue waves in integrable turbulence. Numerical simulations of 1D NLSE with stochastic initial conditions quantitatively reproduce the experiments. Our numerical investigations suggest that the statistical features experimentally observed rely on the stochastic generation of coherent analytic solutions of 1D NLSE.
Collapse
Affiliation(s)
- Pierre Walczak
- Laboratoire de Physique des Lasers, Atomes et Molecules, UMR-CNRS 8523, Université de Lille, France
| | - Stéphane Randoux
- Laboratoire de Physique des Lasers, Atomes et Molecules, UMR-CNRS 8523, Université de Lille, France
| | - Pierre Suret
- Laboratoire de Physique des Lasers, Atomes et Molecules, UMR-CNRS 8523, Université de Lille, France
| |
Collapse
|
35
|
Mercier É, Even A, Mirisola E, Wolfersberger D, Sciamanna M. Numerical study of extreme events in a laser diode with phase-conjugate optical feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042914. [PMID: 25974569 DOI: 10.1103/physreve.91.042914] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2014] [Indexed: 06/04/2023]
Abstract
Extreme intensity pulses sharing statistical properties similar to rogue waves have been recently observed in a laser diode with phase-conjugate feedback [A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Opt. Lett. 38, 703 (2013)], but remain unexplained. We demonstrate here that a rate equation model of a laser diode that includes an instantaneous phase-conjugate feedback field reproduces qualitatively well the statistical features of these extreme events as identified in the experiment, i.e., the deviation of the intensity statistics to a Gaussian-shape statistics and the statistics of the time separating extreme events. The numerical simulations confirm the importance of the feedback strength in increasing the number of such extreme events and allow us to explain how extreme events emerge from a sequence of bifurcations on self-pulsating solutions, the so-called external cavity modes.
Collapse
Affiliation(s)
- Émeric Mercier
- OPTEL Research Group, Laboratoire Matériaux Optiques, Photonique et Systèmes, EA No. 4423, CentraleSupélec, 2 Rue Édouard Belin, 57070 Metz, France
| | - Armelle Even
- OPTEL Research Group, Laboratoire Matériaux Optiques, Photonique et Systèmes, EA No. 4423, CentraleSupélec, 2 Rue Édouard Belin, 57070 Metz, France
| | - Elodie Mirisola
- OPTEL Research Group, Laboratoire Matériaux Optiques, Photonique et Systèmes, EA No. 4423, CentraleSupélec, 2 Rue Édouard Belin, 57070 Metz, France
| | - Delphine Wolfersberger
- OPTEL Research Group, Laboratoire Matériaux Optiques, Photonique et Systèmes, EA No. 4423, CentraleSupélec, 2 Rue Édouard Belin, 57070 Metz, France
| | - Marc Sciamanna
- OPTEL Research Group, Laboratoire Matériaux Optiques, Photonique et Systèmes, EA No. 4423, CentraleSupélec, 2 Rue Édouard Belin, 57070 Metz, France
| |
Collapse
|
36
|
Zhang Y, Belić MR, Petrović MS, Zheng H, Chen H, Li C, Lu K, Zhang Y. Two-dimensional linear and nonlinear Talbot effect from rogue waves. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032916. [PMID: 25871181 DOI: 10.1103/physreve.91.032916] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2014] [Indexed: 06/04/2023]
Abstract
We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a π phase shift; no other recurrences are observed. Differing from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue-wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.
Collapse
Affiliation(s)
- Yiqi Zhang
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| | - Milivoj R Belić
- Science Program, Texas A&M University at Qatar, P. O. Box 23874, Doha, Qatar
| | - Milan S Petrović
- Science Program, Texas A&M University at Qatar, P. O. Box 23874, Doha, Qatar
- Institute of Physics, P. O. Box 68, 11001 Belgrade, Serbia
| | - Huaibin Zheng
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| | - Haixia Chen
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| | - Changbiao Li
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| | - Keqing Lu
- School of Electronics and Information Engineering, Tianjin Polytechnic University, Tianjin 300387, China
| | - Yanpeng Zhang
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| |
Collapse
|
37
|
Zhong WP, Belić M, Zhang Y. Second-order rogue wave breathers in the nonlinear Schrödinger equation with quadratic potential modulated by a spatially-varying diffraction coefficient. OPTICS EXPRESS 2015; 23:3708-3716. [PMID: 25836223 DOI: 10.1364/oe.23.003708] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Nonlinear Schrödinger equation with simple quadratic potential modulated by a spatially-varying diffraction coefficient is investigated theoretically. Second-order rogue wave breather solutions of the model are constructed by using the similarity transformation. A modal quantum number is introduced, useful for classifying and controlling the solutions. From the solutions obtained, the behavior of second order Kuznetsov-Ma breathers (KMBs), Akhmediev breathers (ABs), and Peregrine solitons is analyzed in particular, by selecting different modulation frequencies and quantum modal parameter. We show how to generate interesting second order breathers and related hybrid rogue waves. The emergence of true rogue waves - single giant waves that are generated in the interaction of KMBs, ABs, and Peregrine solitons - is explicitly displayed in our analytical solutions.
Collapse
|
38
|
Soto-Crespo JM, Devine N, Hoffmann NP, Akhmediev N. Rogue waves of the Sasa-Satsuma equation in a chaotic wave field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032902. [PMID: 25314499 DOI: 10.1103/physreve.90.032902] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2014] [Indexed: 06/04/2023]
Abstract
We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter-the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant k, showing that probability of appearance of rogue waves depends on k.
Collapse
Affiliation(s)
- J M Soto-Crespo
- Instituto de Óptica, C.S.I.C., Serrano 121, 28006 Madrid, Spain
| | - N Devine
- Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia
| | - N P Hoffmann
- Dynamics Group, Hamburg University of Technology, 21073 Hamburg, Germany and Department of Mechanical Engineering, Imperial College, London SW7 2AZ, United Kingdom
| | - N Akhmediev
- Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia
| |
Collapse
|
39
|
Marsal N, Caullet V, Wolfersberger D, Sciamanna M. Spatial rogue waves in a photorefractive pattern-forming system. OPTICS LETTERS 2014; 39:3690-3693. [PMID: 24978569 DOI: 10.1364/ol.39.003690] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We have experimentally analyzed pattern formation in an optical system composed of a bulk photorefractive crystal subjected to a single optical feedback. In a highly nonlinear regime far above the modulational instability threshold, we are reporting on turbulent spatiotemporal dynamics that leads to rare, intense localized optical peaks. We have proven that the statistics and features of those peaks correspond to the signatures of two-dimensional spatial rogue events. These optical rogue waves occur erratically in space and time and live typically the same amount of time as the response time of the photorefractive material.
Collapse
|
40
|
Kundu A, Mukherjee A, Naskar T. Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents. Proc Math Phys Eng Sci 2014; 470:20130576. [PMID: 24711719 PMCID: PMC3928955 DOI: 10.1098/rspa.2013.0576] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2013] [Accepted: 01/17/2014] [Indexed: 11/12/2022] Open
Abstract
Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.
Collapse
Affiliation(s)
| | - Abhik Mukherjee
- Theory Division, Saha Institute of Nuclear Physics, Kolkata, India
| | | |
Collapse
|
41
|
Zhang Y, Belić MR, Zheng H, Chen H, Li C, Song J, Zhang Y. Nonlinear Talbot effect of rogue waves. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032902. [PMID: 24730908 DOI: 10.1103/physreve.89.032902] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2013] [Indexed: 06/03/2023]
Abstract
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
Collapse
Affiliation(s)
- Yiqi Zhang
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| | - Milivoj R Belić
- Science Program, Texas A&M University at Qatar, P.O. Box 23874 Doha, Qatar
| | - Huaibin Zheng
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| | - Haixia Chen
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| | - Changbiao Li
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| | - Jianping Song
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| | - Yanpeng Zhang
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
| |
Collapse
|
42
|
Zhong WP, Belić MR, Huang T. Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:065201. [PMID: 23848816 DOI: 10.1103/physreve.87.065201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2013] [Revised: 04/28/2013] [Indexed: 06/02/2023]
Abstract
A similarity transformation is utilized to reduce the generalized nonlinear Schrödinger (NLS) equation with variable coefficients to the standard NLS equation with constant coefficients, whose rogue wave solutions are then transformed back into the solutions of the original equation. In this way, Ma breathers, the first- and second-order rogue wave solutions of the generalized equation, are constructed. Properties of a few specific solutions and controllability of their characteristics are discussed. The results obtained may raise the possibility of performing relevant experiments and achieving potential applications.
Collapse
Affiliation(s)
- Wei-Ping Zhong
- Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300, China.
| | | | | |
Collapse
|
43
|
Ni X, Lai YC, Wang WX. Emergence of scaling associated with complex branched wave structures in optical medium. CHAOS (WOODBURY, N.Y.) 2012; 22:043116. [PMID: 23278051 DOI: 10.1063/1.4766757] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Branched wave structures, an unconventional wave propagation pattern, can arise in random media. Experimental evidence has accumulated, revealing the occurrence of these waves in systems ranging from microwave and optical systems to solid-state devices. Experiments have also established the universal feature that the wave-intensity statistics deviate from Gaussian and typically possess a long-tail distribution, implying the existence of spatially localized regions with extraordinarily high intensity concentration ("hot" spots). Despite previous efforts, the origin of branched wave pattern is currently an issue of debate. Recently, we proposed a "minimal" model of wave propagation and scattering in optical media, taking into account the essential physics for generating robust branched flows: (1) a finite-size medium for linear wave propagation and (2) random scatterers whose refractive indices deviate continuously from that of the background medium. Here we provide extensive numerical evidence and a comprehensive analytic treatment of the scaling behavior to establish that branched wave patterns can emerge as a general phenomenon in wide parameter regime in between the weak-scattering limit and Anderson localization. The basic physical mechanisms to form branched waves are breakup of waves by a single scatterer and constructive interference of broken waves from multiple scatterers. Despite simplicity of our model, analysis of the scattering field naturally yields an algebraic (power-law) statistic in the high wave-intensity distribution, indicating that our model is able to capture the generic physical origin of these special wave patterns. The insights so obtained can be used to better understand the origin of complex extreme wave patterns, whose occurrences can have significant impact on the performance of the underlying physical systems or devices.
Collapse
Affiliation(s)
- Xuan Ni
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | | | | |
Collapse
|
44
|
Abstract
The ability to measure real-time fluctuations of ultrashort pulses propagating in optical fiber has provided significant insights into fundamental dynamical effects such as modulation instability and the formation of frequency-shifting rogue wave solitons. We report here a detailed study of real-time fluctuations across the full bandwidth of a fiber supercontinuum which directly reveals the significant variation in measured noise statistics across the spectrum, and which allows us to study correlations between widely separated spectral components. For two different propagation distances corresponding to the onset phase of spectral broadening and the fully-developed supercontinuum, we measure real time noise across the supercontinuum bandwidth, and we quantify the supercontinuum noise using statistical higher-order moments and a frequency-dependent intensity correlation map. We identify correlated spectral regions within the supercontinuum associated with simultaneous sideband generation, as well as signatures of pump depletion and soliton-like pump dynamics. Experimental results are in excellent agreement with simulations.
Collapse
|
45
|
Sabry R, Moslem WM, Shukla PK. Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:036408. [PMID: 23031035 DOI: 10.1103/physreve.86.036408] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2012] [Indexed: 06/01/2023]
Abstract
It is shown that the dynamics of amplitude-modulated compressional dispersive Alfvénic (CDA) waves in a collisional megnetoplasma is governed by a complex Ginzburg-Landau (CGL) equation. The nonlinear dispersion relation for the modulational instability of the CDA waves is derived and investigated numerically. It is found that the growth rate of the modulational instability decreases (increases) with the increase of the normalized electron-ion collision frequency α (the plasma β). The modulational instability criterion for the CGL equation is defined precisely and investigated numerically. The region of the modulational instability becomes narrower with the increase of α and β, indicating that the system dissipates the wave energy by collisions, and a stable CDA wave envelope packet in the form of a hole will be a dominant localized pulse. For a collisionless plasma, i.e., α=0, the CGL equation reduces to the standard nonlinear Schrödinger (NLS) equation. The latter is used to investigate the modulational (in)stability region for the CDA waves in a collisionless magnetoplasma. It is shown that, within unstable regions, a random set of nonlinearly interacting CDA perturbations leads to the formation of CDA rogue waves. In order to demonstrate that the characteristics of the CDA rogue waves are influenced by the plasma β, the relevant numerical analysis of the appropriate nonlinear solution of the NLS equation is presented. The application of our investigation to space and laboratory magnetoplasmas is discussed.
Collapse
Affiliation(s)
- R Sabry
- Theoretical Physics Group, Physics Department, Faculty of Science, Mansoura University, Damietta-Branch, New Damietta 34517, Egypt.
| | | | | |
Collapse
|
46
|
Lecaplain C, Grelu P, Soto-Crespo JM, Akhmediev N. Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser. PHYSICAL REVIEW LETTERS 2012; 108:233901. [PMID: 23003957 DOI: 10.1103/physrevlett.108.233901] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2011] [Indexed: 06/01/2023]
Abstract
Rare events of extremely high optical intensity are experimentally recorded at the output of a mode-locked fiber laser that operates in a strongly dissipative regime of chaotic multiple-pulse generation. The probability distribution of these intensity fluctuations, which highly depend on the cavity parameters, features a long-tailed distribution. Recorded intensity fluctuations result from the ceaseless relative motion and nonlinear interaction of pulses within a temporally localized multisoliton phase.
Collapse
Affiliation(s)
- C Lecaplain
- Laboratoire Interdisciplinaire Carnot de Bourgogne, U.M.R. 6303 C.N.R.S., Université de Bourgogne, 9 avenue A. Savary, BP 47870 Dijon Cedex 21078, France
| | | | | | | |
Collapse
|
47
|
Moslem WM, Sabry R, El-Labany SK, Shukla PK. Dust-acoustic rogue waves in a nonextensive plasma. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:066402. [PMID: 22304203 DOI: 10.1103/physreve.84.066402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2011] [Revised: 11/16/2011] [Indexed: 05/31/2023]
Abstract
We present an investigation for the generation of a dust-acoustic rogue wave in a dusty plasma composed of negatively charged dust grains, as well as nonextensive electrons and ions. For this purpose, the reductive perturbation technique is used to obtain a nonlinear Schrödinger equation. The critical wave-number threshold k(c), which indicates where the modulational instability sets in, has been determined precisely for various regimes. Two different behaviors of k(c) against the nonextensive parameter q are found. For small k(c), it is found that increasing q would lead to an increase of k(c) until q approaches a certain value q(c), then further increase of q beyond q(c) decreases the value of k(c). For large k(c), the critical wave-number threshold k(c) is always increasing with q. Within the modulational instability region, a random perturbation of the amplitude grows and thus creates dust-acoustic rogue waves. In order to show that the characteristics of the rogue waves are influenced by the plasma parameters, the relevant numerical analysis of the appropriate nonlinear solution is presented. The nonlinear structure, as reported here, could be useful for controlling and maximizing highly energetic pulses in dusty plasmas.
Collapse
Affiliation(s)
- W M Moslem
- International Centre for Advanced Studies in Physical Sciences, Faculty of Physics and Astronomy, Ruhr University Bochum, D-44780 Bochum, Germany.
| | | | | | | |
Collapse
|
48
|
Kovalsky MG, Hnilo AA, Tredicce JR. Extreme events in the Ti:sapphire laser. OPTICS LETTERS 2011; 36:4449-4451. [PMID: 22089593 DOI: 10.1364/ol.36.004449] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We report experimental and theoretical evidence of the existence of extreme value events in the form of scarce and randomly emerging giant pulses in the femtosecond (self-pulsing or Kerr-lens mode-locked) Ti:sapphire laser. This laser displays complex dynamical behavior, including deterministic chaos, in two different regimes. The extreme value pulses are observed in the chaotic state of only one of these two regimes. The observations agree with the predictions of a well-tested theoretical model that does not include noise or self-Q-switching into its framework. This implies that, in this laser, the extreme effects have a nontrivial dynamical origin. The Ti:sapphire laser is hence revealed as a new and convenient system for the study of these effects.
Collapse
Affiliation(s)
- Marcelo G Kovalsky
- Centro de Investigaciones en Láseres y Aplicaciones (CEILAP), CITEDEF-CONICET, Villa Martelli, Argentina
| | | | | |
Collapse
|
49
|
Onorato M, Proment D, Toffoli A. Triggering rogue waves in opposing currents. PHYSICAL REVIEW LETTERS 2011; 107:184502. [PMID: 22107634 DOI: 10.1103/physrevlett.107.184502] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2011] [Indexed: 05/31/2023]
Abstract
We show that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow. We demonstrate that the maximum amplitude of the rogue wave depends on the ratio between the current velocity U(0) and the wave group velocity c(g). We also reveal that an opposing current can force the development of rogue waves in random wave fields, resulting in a substantial change of the statistical properties of the surface elevation. The present results can be directly adopted in any field of physics in which the focusing nonlinear Schrödinger equation with nonconstant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results.
Collapse
Affiliation(s)
- Miguel Onorato
- Dipartimento di Fisica Generale, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
| | | | | |
Collapse
|
50
|
Bonatto C, Feyereisen M, Barland S, Giudici M, Masoller C, Leite JRR, Tredicce JR. Deterministic optical rogue waves. PHYSICAL REVIEW LETTERS 2011; 107:053901. [PMID: 21867071 DOI: 10.1103/physrevlett.107.053901] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2011] [Indexed: 05/31/2023]
Abstract
Experimental observations of rare giant pulses or rogue waves were done in the output intensity of an optically injected semiconductor laser. The long-tailed probability distribution function of the pulse amplitude displays clear non-Gaussian features that confirm the rogue wave character of the intensity pulsations. Simulations of a simple rate equation model show good qualitative agreement with the experiments and provide a framework for understanding the observed extreme amplitude events as the result of a deterministic nonlinear process.
Collapse
Affiliation(s)
- Cristian Bonatto
- Departament de Fìsica i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Barcelona, Spain
| | | | | | | | | | | | | |
Collapse
|