Dissipative solitons with extreme spikes in the normal and anomalous dispersion regimes

Prigogine's ideas of systems far from equilibrium and self-organization (Prigogine & Lefever. 1968 J. Chem. Phys.48, 1695-1700 (doi:10.1063/1.1668896); Glansdorff & Prigogine. 1971 Thermodynamic theory of structures, stability and fluctuations. New York, NY/London, UK: Wiley) deeply influenced physics, and soliton science in particular. These ideas allowed the notion of solitons to be extended from purely integrable cases to the concept of dissipative solitons. The latter are qualitatively different from the solitons in integrable and Hamiltonian systems. The variety in their forms is huge. In this paper, one recent example is considered-dissipative solitons with extreme spikes (DSESs). It was found that DSESs exist in large regions of the parameter space of the complex cubic-quintic Ginzburg-Landau equation. A continuous variation in any of its parameters results in a rich structure of bifurcations. This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.The work of J.M.S.-C. was supported by MINECO under contract TEC2015-71127-C2-1-R, and by C.A.M. under contract S2013/MIT-2790. The three authors, P.V., W.C. and N.A., acknowledge the support of the Australian Research Council (DE130101432 and DP150102057). J.M.S.-C. and N.A. also acknowledge the support of the Volkswagen Foundation

Extreme Waves in Dissipative Systems

The research focus of this dissertation is the generation of pulses with extreme characteristics. The presented pulses possess self-organising dynamics. The new extreme wave dynamics is demonstrated using numerical simulations of the well-established cubic-quintic complex Ginzburg-Landau equation (CQCGLE). The CQCGLE models highly nonlinear regimes of wave propagation in media with gain and loss applicable to laser operation. The study reveals rich bifurcation structure of localised CQCGLE solutions in both the anomalous and the normal dispersion regimes. Notably, the discovery of spiny solitons offers new insight into the nature of dissipative systems. These types of extreme wave dynamics may have essential applications in laser science

Extreme pulse dynamics in mode-locked lasers

This chapter is devoted to dissipative solitons that produce sharp peaks (spikes) on top of its high amplitude central part. The peak amplitude of these spikes can exceed several times the amplitude of the soliton base. This unusual phenomenon is found for solutions of the complex cubic-quintic Ginzburg-Landau equation (CGLE) in a special region of its free parameters. Depending on them, the spikes can appear chaotically or regularly. Both regimes are discussed in this chapter. The spikes with chaotic appearance can be considered as rogue waves and the probability density function confirms this. The solitons with spikes can also be considered as noise-like pulses that have been discussed in several recent publications without actually revealing the nature of the noise. The wide spectrum of these pulses suggests their application for generation of super-continuum directly out of lasers. The transition from regular to chaotic dynamics can be used in experiments to investigate this new interesting phenomenon.The authors acknowledge the support from the Australian Research Council (DE130101432, DP140100265, DP15102057)

Extreme amplitude spikes in a laser model described by the complex Ginzburg-Landau equation

We have found new dissipative soliton in the laser model described by the complex cubic-quintic Ginzburg- Landau equation. The soliton periodically generates spikes with extreme amplitude and short duration. At certain range of the equation parameters, these extreme spikes appear in pairs of slightly unequal amplitude. The bifurcation diagram of spike amplitude versus dispersion parameter reveals the regions of both regular and chaotic evolution of the maximal amplitudes

Dissipative solitons with extreme spikes

We have found dissipative solitons with extreme spikes in the laser model described by the complex cubic-quintic Ginzburg-Landau equation. They exist in both normal and anomalous dispersion cases.The work of JMSC was supported by MINECO under contract TEC2015-71127-C2-1-R, and by C.A.M. under contract S2013/MIT-2790. The three authors, P.V., W.C. and N.A., acknowledge the support of the Australian Research Council (DE130101432 and DP150102057). JMSC and NA also acknowledge the support of the Volkswagen Foundation

Roadmap on optical rogue waves and extreme events

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 results and new discoveries has been undertaken, stimulated by the concept of ‘optical rogue waves’. Presently, there may not by a unique view on how this new scientific term should be used and developed. There is nothing surprising when the opinion of the experts diverge in any new field of research. After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation. We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems. Theorists, in turn, have suggested many other situations when rogue waves may be observed. The strict definition of a rogue wave is still an open question. For example, it has been suggested that it is defined as ‘an optical pulse whose amplitude or intensity is much higher than that of the surrounding pulses’. This definition (as suggested by a peer reviewer) is clear at the intuitive level and can be easily extended to the case of spatial beams although additional clarifications are still needed. An extended definition has been presented earlier by N Akhmediev and E Pelinovsky (2010 Eur. Phys. J. Spec. Top. 185 1–4). Discussions along these lines are always useful and all new approaches stimulate research and encourage discoveries of new phenomena. Despite the potentially existing disagreements, the scientific terms ‘optical rogue waves’ and ‘extreme events’ do exist. Therefore coordination of our efforts in either unifying the concept or in introducing alternative definitions must be continued. From this point of view, a number of the scientists who work in this area of research have come together to present their research in a single review article that will greatly benefit all interested parties of this research direction. Whether the authors of this ‘roadmap’ have similar views or different from the original concept, the potential reader of the review will enrich their knowledge by encountering most of the existing views on the subject. Previously, a special issue on optical rogue waves (2013 J. Opt. 15 060201) was successful in achieving this goal but over two years have passed and more material has been published in this quickly emerging subject. Thus, it is time for a roadmap that may stimulate and encourage further research