Rogue wave modes for the coupled nonlinear Schrodinger system with three components: A computational study

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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.Peer ReviewedPostprint (author's final draft

Complex extreme nonlinear waves: classical and quantum theory for new computing models

The historical role of nonlinear waves in developing the science of complexity, and also their physical feature of being a widespread paradigm in optics, establishes a bridge between two diverse and fundamental fields that can open an immeasurable number of new routes. In what follows, we present our most important results on nonlinear waves in classical and quantum nonlinear optics. About classical phenomenology, we lay the groundwork for establishing one uniform theory of dispersive shock waves, and for controlling complex nonlinear regimes through simple integer topological invariants. The second quantized field theory of optical propagation in nonlinear dispersive media allows us to perform numerical simulations of quantum solitons and the quantum nonlinear box problem. The complexity of light propagation in nonlinear media is here examined from all the main points of view: extreme phenomena, recurrence, control, modulation instability, and so forth. Such an analysis has a major, significant goal: answering the question can nonlinear waves do computation? For this purpose, our study towards the realization of an all-optical computer, able to do computation by implementing machine learning algorithms, is illustrated. The first all-optical realization of the Ising machine and the theoretical foundations of the random optical machine are here reported. We believe that this treatise is a fundamental study for the application of nonlinear waves to new computational techniques, disclosing new procedures to the control of extreme waves, and to the design of new quantum sources and non-classical state generators for future quantum technologies, also giving incredible insights about all-optical reservoir computing. Can nonlinear waves do computation? Our random optical machine draws the route for a positive answer to this question, substituting the randomness either with the uncertainty of quantum noise effects on light propagation or with the arbitrariness of classical, extremely nonlinear regimes, as similarly done by random projection methods and extreme learning machines