Rogue waves and analogies in optics and oceanography

Abstract

We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement techniques, whilst in oceanography we consider insights obtained from analysis of real-world ocean wave data and controlled experiments in wave tanks. Although significant progress in understanding rogue waves has been made based on an analogy between wave dynamics in optics and hydrodynamics, these comparisons have predominantly focused on one-dimensional nonlinear propagation scenarios. As a result, there remains significant debate about the dominant physical mechanisms driving the generation of ocean rogue waves in the complex environment of the open sea. Here, we review stateof-the-art of rogue wave studies in optics and hydrodynamics, aiming to clearly identify similarities and differences between the results obtained in the two fields. In hydrodynamics, we take care to review results that support both nonlinear and linear interpretations of ocean rogue wave formation, and in optics, we also summarise results from an emerging area of research applying the measurement techniques developed for the study of rogue waves to dissipative soliton systems. We conclude with a discussion of important future research directions. the underlying carrier wave is considered sinusoidal at frequency ω whereas in hydrodynamics, the NLSE envelope modulates the Stokes wave which (to second-order) contains contributions at both ω and the second harmonic 2ω [31]. In addition, even though the terminology "optical wave breaking" is used in an NLSE context to describe the steepening of an optical envelope from nonlinear focussing [32], optical carrier waves themselves do not "break" or plunge as they do in hydrodynamics [33,34]. There are also important differences concerning measurements. Specifically, experiments in optical fibres generally measure only the time-domain envelope intensity, and information about carrier oscillations is not recorded. In contrast, measurements in hydrodynamics directly record the individual carrier wave amplitudes (although envelope information can be reconstructed straightforwardly [35]). Particular care must therefore be taken when comparing statistics between optics and hydrodynamics, because statistics in fibre optics experiments are determined

Recent progress on optical rogue waves in fiber lasers: status, challenges, and perspectives

“…There are various physical processes in ocean systems, such as wave breaking, dissipation, currents, and wind force. 41 The wave breaking is a natural nonlinear process while the dissipation, currents, and wind force are either nonlinear or linear. In a word, the observations of ocean RWs are very complicated.…”

“…In both cases, there is a similar mathematical equation in the form of an NLSE, which can be used for describing the evolutionary process of the envelope in time and space. 41,42 In fiber laser, there is the sinusoidal underlying carrier wave at frequency ω while there is the Stokes wave modulated by the NLSE envelope, which (to the second order) includes contributions at both ω and the second harmonic 2ω. 43 In both cases, the measurement methods in the domain are also different.…”

Engineering optical rogue waves and breathers in a coupled nonlinear Schrödinger system with four-wave mixing effect

“…Though they are initially observed as extreme waves in the oceans, now a days they appear in a wider range of fields such as fiber optics as extreme amplitude pulses, optical cavities as high amplitudes, laser outputs as extreme pulses, Bose-Einstein condensates (BEC) as high atomic concentration, etc. [8,9].…”

Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide

“…Therefore, polaritonic frequency combs, and generally space-time control of nonlinear SPWs, are unfortunately challenging due to material limitations and driving field characteristics [26-28].Propagation of an optical pulse in nonlinear media leads to the appearance of strongly localized bright and dark waves such as soliton [29], rogue waves and breathers in nearly conservative systems [30]. Bright rogue waves and breathers are highly localized nonlinear solitary waves with oscillatory amplitudes [31,32]. These waves are valuable for their applications to phase and intensity modulation schemes [33,34], as well as the formation of bound states and molecule-like behavior [35].…”