Rogue solitons in optical fibers: a dynamical process in a complex energy landscape?

Abstract

Nondeterministic giant waves, denoted as rogue, killer, monster, or freak waves, have been reported in many different branches of physics. Their physical interpretation is however still debated: despite massive numerical and experimental evidence, a solid explanation for their spontaneous formation has not been identified yet. Here we propose that rogue waves [more precisely, rogue solitons (RSs)] in optical fibers may actually result from a complex dynamical process very similar to well-known mechanisms such as glass transitions and protein folding. We describe how the interaction among optical solitons produces an energy landscape in a highly dimensional parameter space with multiple quasi-equilibrium points. These configurations have the same statistical distribution of the observed rogue events and are explored during the light dynamics due to soliton collisions, with inelastic mechanisms enhancing the process. Slightly different initial conditions lead to very different dynamics in this complex geometry; a RS turns out to stem from one particularly deep quasi-equilibrium point of the energy landscape in which the system may be transiently trapped during evolution. This explanation will prove to be fruitful to the vast community interested in freak waves. (C) 2015 Optical Society of America

Slow deterministic vector rogue waves

“…This type of rogue waves have a time scale from 20-20000 round trips and is similar to the fluctuation induced escape in asymmetric double well potential [13][14][15][16]. The asymmetric potential leads to an increased residence time in the deep well and to the emergence of rare transition events satisfying criteria of rogue waves.…”

“…We demonstrate control of the rogue wave's statistics including RWs suppression and enhancement based on tuning polarization controller for the pump wave and in-cavity polarization controller. In terms of the fluctuation induced escape (FIE) concept [13][14][15][16], this type of RWs harnessing means a transformation of the double-well potential landscape to activate polarization instability-driven trajectory escape from the state with the long residence time of trajectories in the vicinity of this state to the state with a short residence time. Time, ps…”

Incoherent Shock and Collapse Singularities in Non-Instantaneous Nonlinear Media

“…In a loose sense, this phenomenological behavior is reminiscent of a rogue-like wave phenomenon. Extreme wave events have been widely investigated in the context of optics [63][64][65][66], in particular in the presence of a non-instantaneous (Raman-like) non-linearity [67][68][69][70][71]. Note however that, although rogue waves have been shown to emerge from a turbulent environment, so far, the rogue wave itself has been always identified as being inherently a coherent localized entity [72][73][74][75][76][77][78][79][80][81][82][83][84].…”

Ultrafast rogue wave patterns in fiber lasers

“…Optical rogue waves serve as a useful test bench, thanks to their fast dynamics, which makes it possible to measure extreme events in a short time and under a controlled environment [4][5][6][7]. These waves result from the fiber nonlinearity, which is governed by the nonlinear Schrödinger equation (NLSE), and exhibit a vast variety of patterns [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Fiber lasers are far richer systems than nonlinear fibers, because the gain competition and saturable absorber give rise to unique rogue waves.…”