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Space-time map showing the evolution of optical intensity. Triangles indicate pulses with intensity 5–10 times larger than the stationary localized structures without delay feedback. Parameters are θ=1.7, E i =1.2, η=0.7, t=100, and f=π.
Source publication
The pioneering paper 'Optical rogue waves' by Solli et al (2007 Nature
450 1054) started the new subfield in optics. This work launched a great deal of activity on this novel subject. As a result, the initial concept has expanded and has been enriched by new ideas. Various approaches have been suggested since then. A fresh look at the older result...
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Citations
... The physics of rogue waves, as high-intensity narrow peaks that "appear from nowhere and disappear without a trace", is currently the hot area of research related to deep ocean waves (Osborne 2010;Garrett and Gemmrich 2009), nonlinear optics (Solli et al. 2008;Dudley et al. 2008), and Bose-Einstein condensates (Bludov et al. 2009). The investigation of the origin and nature of optical rogue waves for the NLSE is given in Akhmediev (2016); Belić et al. (2022); Chin et al. (2015). The examination of RWs is becoming even more popular since a new scheme for their excitation, via the electromagnetically induced transparency (Fleischhauer et al. 2005;Nikolić et al. 2013;Krmpot et al. 2009;Nikolić et al. 2015), was reported . ...
In this work, we analyze three types of rogue wave (RW) clusters for the quintic nonlinear Schrödinger equation (QNLSE) on a flat background. These exact QNLSE solutions, composed of higher-order Akhmediev breathers (ABs) and Kuznetsov–Ma solitons (KMSs), are generated using the Darboux transformation (DT) scheme. We analyze the dependence of their shapes and intensity profiles on the three real QNLSE parameters, eigenvalues, and evolution shifts in the DT scheme. The first type of RW clusters, characterized by the periodic array of peaks along the transverse or evolution axis, is obtained when the condition of commensurate frequencies of DT components is applied. The elliptical RW clusters are computed from the previous solution class when the first m evolution shifts in the DT scheme of order n are equal and nonzero. For both AB and KMS solutions a periodic structure is obtained with the central RW and m ellipses, containing the first-order maxima that encircle the central peak. We show that RW clusters built on KMSs are significantly more vulnerable to the application of high values of QNLSE parameters, in contrast to the AB case. We next present non-periodic long-tail KMS clusters, characterized by the rogue wave at the origin and n tails above and below the central point containing first-order KMSs. We finally show that the breather-to-soliton conversion, enabled by the QNLSE system, can transform the shape of RW clusters, by setting the real parts of DT eigenvalues to particular values, while keeping all other DT parameters intact.
... Recently, a wide range of research has addressed the distinct formation of various catastrophic events, namely rogue waves in hydrodynamics and optical system [1][2][3], rare but recurrent unexpected large-amplitude events in a different complex systems [4][5][6], as well as the natural extreme events such as, earth-quicks, cyclones, droughts, and share market crashes [7]. Precisely, in the past few decades, the complex dynamical systems of neuron models [8][9][10][11], lasers [12][13][14][15], mechanical systems [16,17], electronic circuits [18,19], coupled systems [20,21], and networks of oscillators [22][23][24] studied in details to ascertain its dynamical origin and different formations. ...
We report the formation of extreme large-intensity pulses in an optically modulated CO2 laser. The sudden unexpected surge from the bounded chaotic motion into occasional expansions occurred in the system, which is rare but appears in an infrequent time interval. The CO2 laser exhibits unforeseen extreme pulses owing to the dynamical process of grazing-sliding bifurcation. To acquire a deeper understanding of its intricate dynamics, we have performed various comprehensive dynamical and statistical analyses that elucidate the transition of extreme pulses, and their emerging mechanisms. In addition, we have presented a prior anticipation technique of rare large-intensity pulses that will be shedding into the light for some specific applications.
... In 2007, the first observation of the existence of optical RWs was reported in the work of Solli ., when they investigated the heavy-tailed histograms of intensity fluctuations in supercontinuum generation [12]. Since then, optical RWs have been attracting the interest of research on both theoretical and experimental sides, due to their potential applications and relative ease of creation and capture in laboratory settings [13]. The optical RWs have now been successfully observed in many optical settings such as optical fibers [14], mode-locked lasers [15], Raman fiber lasers [16] and photorefractive ferroelectrics [17]. ...
We investigate the dynamic of optical rogue waves induced by super-Gaussian (SG) pulses in fiber optic. SG pulses with controlled steep leading and trailing edges can produce high-intensity self-focusing when propagate in nonlinear fibers with weak dispersion and strong nonlinearity. We observe the emergence of various rogue waves, including Peregrine breathers, Akhmediev breathers (AB) and 2nd-order AB. By adjusting the steepness of the SG pulses, the generation of these rogue waves can be controlled. As the steepness of the SG pulse increases, we find the fundamental-order AB can stably coexist. Simultaneously, we reveal that the period of these ABs can be effectively controlled by adjusting the steepness of the SG pulse. At a certain steepness, the 2nd-order AB with high power can also be observed. We also investigate the propagation of SG pulses with an initial chirp in fiber optic and found that they can also control AB and 2nd-order Peregrine breathers. Our findings present a new approach to generating controllable rogue waves.
... [7] A comprehensive overview of optical RWs and extreme events, together with their developmental pathways, was provided in a seminal "roadmap paper" published in 2016. [8] More recently, a comprehensive theory of RWs has emerged, producing tremendous progress in nonlinear sciences, spanning disciplines such as nonlinear optics, plasma physics, cold atom condensates, and atmospheric science. [1] Researchers have successively observed RW phenomena in various controlled environments, including "optical rogue waves", "water tank rogue waves", and "plasma rogue waves" in the laboratory, thus providing strong support for RW research and inspiring researchers' enthusiasm for the new field. ...
We study dark localized waves within a nonlinear system based on the Boussinesq approximation, describing the dynamics of shallow water waves. Employing symbolic calculus, we apply the Hirota bilinear method to transform an extended Boussinesq system into a bilinear form, and then use the multiple rogue wave method to obtain its dark rational solutions. Exploring the first- and second-order dark solutions, we examine the conditions under which these localized solutions exist and their spatiotemporal distributions. Through the selection of various parameters and by utilizing different visualization techniques (intensity distributions and contour plots), we explore the dynamical properties of dark solutions found: in particular, the first- and second-order dark rogue waves. We also explore the methods of their control. The findings presented here not only deepen the understanding of physical phenomena described by the (1+1)-dimensional Boussinesq equation, but also expand avenues for further research. Our method can be extended to other nonlinear systems, to conceivably obtain higher-order dark rogue waves.
... Recent studies have delved into understanding the occurrence of such behaviour in dynamical systems [26][27][28][29]. Extreme events arising in nonlinear dynamical systems mimic those observed in many physical systems, including fibre optics, nonlinear optics, photonics [30,31], financial systems [32,33], electronic oscillators [34,35], mechanical oscillators [36], chemical oscillators [37] and neural models [38]. While studying nonlinear dynamical systems, the trajectory of a dynamical system typically follows a bounded attractor. ...
... The physics of rogue waves, as high-intensity narrow peaks that "appear from nowhere and disappear without a trace", is the hot area of research related to deep ocean waves [10,35], nonlinear optics [36,37], and Bose-Einstein condensates [38]. The investigation of the origin and nature of optical rogue waves for the NLSE is given in [39][40][41]. The examination of RWs is becoming even more popular since a new scheme for their excitation, via the electromagnetically induced transparency (EIT) [42][43][44][45], was published recently [46]. ...
In this work, we analyze three types of the rogue wave (RW) clusters for the quintic nonlinear Schrödinger equation (QNLSE) on a flat background. These exact QNLSE solutions, composed of the higher-order Akhmedieav breathers (ABs) and Kuznetsov-Ma solitons (KMSs), are generated using the Darboux transformation (DT) scheme. We analyze the dependence of their shapes and intensity profiles on the three real QNLSE parameters, the eigenvalues, and evolution shifts in the DT scheme. The first type of RW clusters, characterized by the periodic array of peaks along the transverse or evolution axis, is obtained when the condition on commensurate frequencies of DT components is applied. The elliptical RW clusters are computed from the previous solution class when the first m evolution shifts in the DT scheme of order n are equal and nonzero. For both AB and KMS solutions, the periodic structure is obtained with the central RW of order n-2m and m ellipses, containing the first-order maxima, that encircle the central peak. We show that RW clusters built on KMSs are significantly more vulnerable to the application of sufficiently high values of QNLSE parameters, in contrast to the AB case. We next present the non-periodic long-tail KMS clusters characterized by the central rogue wave at the origin and $n$ tails above and below the central (0,0) point containing the first-order KMS. We finally show that the breather-to-soliton conversion, enabled by the QNLSE system, can completely transform the shape of RW clusters, by simply setting the real parts of DT eigenvalues to particular values, while keeping the three quintic parameters, imaginary parts and evolution shifts in the DT scheme intact.
... This is the case for the most common model of waves described by the nonlinear Schrödinger equation (NLSE). It is also known that MI can cause appearance of rogue waves (RW) in systems described by the NLSE [9,10]. This model is universal in the sense that it describes wide range of nonlinear waves in physics. ...
"We show that linear stability analysis not only describes the effect of modulation instability of a plane wave in nonlinear media but it also predicts significant wave amplification outside of the standard instability band. As an example, we consider the classic MI in the case of the nonlinear Schr¨odinger equation. However, similar amplification may take place in many other nonlinear media that admit modulation instability."
... It is worth mentioning the important overviews of the optical rogue waves were presented in Refs. [34,35]. ...
... Rogue waves (RWs) represent one type of extremely large amplitude wave phenomena, occurring as rare events with nonpredictability [1][2][3][4]. Originally found in the ocean, RWs appear as a complex interaction between waves of different frequencies and amplitudes. The large amplitude of the waves can cause disasters for ships; thus, oceanic RWs have attracted a great deal of attention [5,6]. ...
... Although several attempts tried to understand the mechanism for RW formation without nonlinearity, it is still a subject of debate and active investigation [35][36][37]. Usually, the bright localized spots created in an RW have anomalously large intensities with extremely rare probability, so the probability density function (PDF) with long-tail statistics is used to identify the RWs [3,16,35]. RWs are generally considered as unpredictable, in either hydrodynamics [4] or optics [18,38]. Nevertheless, recent advances in the neural network have led to prediction of the evolution of breaking waves with trained network using a large dataset of existing observations [39][40][41], so RW prediction may be achievable. ...
Rogue waves are ubiquitous in nature, appearing in a variety of physical systems ranging from acoustics, microwave cavities, optical fibers, and resonators to plasmas, superfluids, and Bose–Einstein condensates. Unlike nonlinear solitary waves, rogue waves are extreme events that can occur even without nonlinearity by, for example, spontaneous synchronization of waves with different spatial frequencies in a linear system. Here, we report the observation of rogue-wave-like events in human red blood cell (RBC) suspensions under weak light illumination, characterized by an abnormal L-shaped probability distribution. Such biophotonic extreme events arise mostly due to the constructive interference of Mie-scattered waves from the suspended RBCs, whose biconcave shape and mutable orientation give rise to a time-dependent random phase modulation to an incident laser beam. We numerically simulate the beam propagation through the colloidal suspensions with added disorder in both spatial and temporal domains to mimic random scattering due to Brownian motion. In addition, at high power levels, nonlinear beam self-focusing is also observed, leading to a dual-exponential probability distribution associated with the formation of multiple soliton-like spots. Such rogue wave events should also exist in environments with cells of other species such as swimming bacteria, and understanding of their underlying physics may lead to unexpected biophotonic applications.
... Kaur et al studied RW in tapered waveguide amplifiers and proved that optical polarization RW originates from vector multi-wave-mixing [12]. Akhmediev et al unified the definition of RW and summarized the generation of RW in different lasers [13]. D.Buccoliero et al proved that fiber loss limited the generation of RW in SC to a certain extent [14]. ...
We numerically simulate the enhancement of rogue wave generation by adding two weak femtosecond pulse seeds at two fixed modulation frequencies. The results showed that two weak pulse seeds have better promotion effect on rogue wave generation than one weak pulse seed. In addition, the modulation depth and pulse width of the weak pulse seeds also affect the generation of rogue waves. With the increase of the modulation depth and pulse width of the two weak pulse seeds, the control effect of rogue waves gradually becomes better.
