Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation

Dudley, John M.; Genty, Goëry; Dias, Frédéric; Kibler, Bertrand; Akhmediev, Nail

doi:10.1364/oe.17.021497

Cited by 490 publications

(371 citation statements)

References 38 publications

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“…In the following, we focus on the particular family of AB solutions [2], c AB ¼ c SFB ð0 < a < 1=2Þ, which describes the nonlinear compression of a modulated continuous wave field into a periodic train of ultrashort pulses with temporal period T ¼ 2 =!. c AB is valid over the range of modulation frequencies that experience MI gain (0 < !…”

Section: Analytical and Numerical Predictionsmentioning

confidence: 99%

“…However, certain initial conditions used in practice are known to yield periodic evolution as a function of propagation [2], but even in this case, the first growth-return cycles remain well-described individually by the analytic AB solution. Figures 1(c) and 1(d) illustrate such a biperiodic behavior through the evolution of the following periodic perturbation c IN ¼ ½1 þ mod cosð!…”

Section: Analytical and Numerical Predictionsmentioning

confidence: 99%

“…These simple initial conditions enable the creation of nonideal ABs so that only the evolution over the first growth-return cycles is described almost accurately by analytical AB solutions [2]. Note that we present here specific conditions that lead to the collision before the end of the second growth-return cycle of single breather evolutions.…”

Section: Analytical and Numerical Predictionsmentioning

confidence: 99%

“…In particular, much attention has been focused on the common solitary wave structures, known as solitons, and their interactions in almost conservative media. Recently, nonlinear fiber optics has proved its capabilities to demonstrate the existence of solitons (or breathers) on finite background (SFB) solutions to the NLSE [2][3][4] predicted for more than 25 years. These coherent localized waves evolving on a continuous background exactly describe the dynamical growth of perturbations on a continuous wave related to the nonlinear modulation instability.…”

Section: Introductionmentioning

confidence: 99%

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Collision of Akhmediev Breathers in Nonlinear Fiber Optics

2013

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We report here a novel fiber-based test bed using tailored spectral shaping of an optical-frequency comb to excite the formation of two Akhmediev breathers that collide during propagation. We have found specific initial conditions by controlling the phase and velocity differences between breathers that lead, with certainty, to their efficient collision and the appearance of a giant-amplitude wave. Temporal and spectral characteristics of the collision dynamics are in agreement with the corresponding analytical solution. We anticipate that experimental evidence of breather-collision dynamics is of fundamental importance in the understanding of extreme ocean waves and in other disciplines driven by the continuous nonlinear Schrödinger equation.

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Section: Analytical and Numerical Predictionsmentioning

confidence: 99%

Section: Analytical and Numerical Predictionsmentioning

confidence: 99%

Section: Analytical and Numerical Predictionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Collision of Akhmediev Breathers in Nonlinear Fiber Optics

2013

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“…In practice, most of spontaneous pattern formations and localized structures induced by MI could now be described by using such generalized solutions, even when the background itself is localized in time (i.e., a laser pulse). It was already shown that breather dynamics with pulsed excitation can be interpreted in terms of local breather states at different points on the pulse envelope [36,37]. Superregular breathers give an enlarged and generalized picture of the collision features with respect to recent numerical and experimental studies of breather structures and their interactions in optics or hydrodynamics [29][30][31]38].…”

Section: Introductionmentioning

confidence: 99%

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

et al. 2015

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Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the selfmodulation of the continuous "envelope waves" with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superregular breathers. Observations are done in two different branches of wave physics, namely, in optics and hydrodynamics. Based on the common framework of the nonlinear Schrödinger equation, this multidisciplinary approach proves universality and reversibility of nonlinear wave formations from localized perturbations for drastically different spatial and temporal scales.

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Modulation Instability, Four‐Wave Mixing and their Applications

Hansson¹,

Tonello²,

Trillo³

et al. 2017

Shaping Light in Nonlinear Optical Fibers

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Modulation instability (MI) of a continuous wave (CW) background solution of the nonlinear Schrödinger (NLS) equation is a well-known phenomenon that occurs in a variety of fields, such as nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation [1, 2]. In the nonlinear optics context, MI is the main mechanism for the generation of optical solitons, supercontinuum (SC) [3, 4], and rogue waves [5]. MI may be induced either by quantum noise or by a weak seed signal [6]: in the latter case, the initial stage of exponential signal amplification is followed first by the generation of higher-order sideband pairs by cascade four-photon mixing processes. Next, nonlinear gain saturation occurs, owing to pump depletion. After the maximum level of pump depletion is reached, which depends on the initial sideband detuning, the pump power and the fiber dispersion, energy flows back from the sidebands into the pump, until the initial condition is recovered, and so on. This phenomen provides a classical example of the so-called Fermi-Pasta-Ulam (FPU) recurrence [7, 8]. This process can be described in terms of exact solutions of the NLS equation [9-12], and has been experimentally observed in different physical settings, such as deep water waves [13, 14], in nonlinear optical fibers [15-20], in nematic liquid crystals [21], magnetic film strip-based active feedback rings [22], and bimodal electrical transmission lines [23]. Important qualitative physical insight into the FPU recurrence dynamics (e.g., the existence of a homoclinic structure and the associated dependence of the FPU recurrence period upon the input relative phase between pump and initial sidebands) may be obtained by means of a truncation to a finite number of Fourier modes, which may lead to simple, low-dimensional models [24-26]. In Section 1.1, we present an overview of the analysis of the nonlinear dynamics of MI by means of a simple three-mode truncation. Next we discuss how the coupling between two polarization modes in a birefringent optical fiber may extend the domain of MI to the normal dispersion regime. Also in the vector case, an important qualitative

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Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation

Cited by 490 publications

References 38 publications

Collision of Akhmediev Breathers in Nonlinear Fiber Optics

Collision of Akhmediev Breathers in Nonlinear Fiber Optics

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

Modulation Instability, Four‐Wave Mixing and their Applications

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