Collision of Akhmediev Breathers in Nonlinear Fiber Optics

Abstract

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.

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

“…[40,41]. A similar synchronized collision of Akhmediev breathers has recently been studied in optics experiments [30], by controlling the phase and velocity differences between the breathers. Figure 1(c) shows the quasiannihilation of breathers at the origin when θ 1;2 ¼ π=2.…”

“…These cases provided, as a first step, a powerful framework for interpretation of a specific range of MI-related dynamics that play a fundamental role in the theory of freak waves [23]. Only recently, some unique features of these solutions have been confirmed experimentally for various nonlinear media [24][25][26][27][28][29][30][31]. It concerns the simplest solutions that are either periodic in space and localized in time or periodic in time and localized in space; they are referred to as Kuznetsov-Ma breathers and Akhmediev breathers, respectively.…”

“…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].…”

Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation

“…Recent experiments in water waves [26], [9] and in fibre optics [31], [21], [22], [16] (see also review articles [5], [10]) have convincingly demonstrated that rogue waves are a generic physical phenomenon deserving a comprehensive investigation [27], [5]. It has also been understood that rogue waves play important role in the characterization of the nonlinear stage of modulational instability [41], [17] and particularly, in the development of integrable turbulence [40], [1], [37], [33].…”

Extreme events in resonant radiation from three-dimensional light bullets

“…Extreme events have since been observed in many other systems illustrating the wide range of underlying dynamics that can lead to their appearance [2,3]. In an optical context, the recent observation that solitons with extreme spectral red-shifts can emerge from an incoherent fibre supercontinuum [4] has attracted considerable attention and subsequent studies have highlighted the role of nonlinear noise amplification in the spontaneous emergence of highly localised structures [5,6] and the role of collisions in observing long tail statistics [7][8][9].While most rogue waves studies in optics have focussed on the 1+1D fibre case (one spatial dimension and one temporal dimension), the emergence of extreme events during full 3D propagation of light pulses with nonlinear spatio-temporal dynamics has been much less studied [11][12][13][14]. In the normal group velocity dispersion (GVD) regime, the combined action of spatial and temporal selffocusing leads to the formation of a dynamically stable filament characterised by an intense, localised peak surrounded by a weaker reservoir that continuously refuels the central core region [10].…”