Curious wave phenomena that occur in optical fibres due to the interplay of instability and nonlinear effects are reviewed.

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Instabilities, breathers and rogue waves in optics

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شیوع عوارض حاد تزریق خون در بیماران بستری در 11 بیمارستان تهران و مازندران

A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation, photonic crystal fiber

https://iopscience.iop.org/article/10.1088/2040-8978/15/6/060201/pdf

Recent progress in investigating optical rogue waves

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.

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Roadmap on optical rogue waves and extreme events

The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are generic mechanisms responsible for extreme events in different systems. Here we argue that under suitable circumstances nonlinear interaction between weak and strong waves results in intermittent giant waves with all the signatures of rogue waves. To obtain these circumstances only a few basic conditions must be met. Then reflection of waves at the so-called group-velocity horizon occurs. The connection between rogue waves and event horizons, seemingly unrelated physical phenomena, is identified as a feature common in many different physical systems.

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Rogue events in the group velocity horizon

We consider the process by which a constant or wide-pulse solution of the nonlinear Schr\"odinger equation can become converted into an ensemble of solitons by modulational instability. This process is generally believed to be one important step in the generation of supercontinuum in optical fibers. Starting from the Akhmediev breather solution we study the conversion by two methods: One is pulse shape-oriented and uses the soliton relation between width and peak power. The other is eigenvalue-oriented and uses results from scattering theory. It becomes clear that an evolution according to the unmodified nonlinear Schr\"odinger equation, even in the presence of noise, will not lead to the transformation into solitons. If one takes the Raman effect into account, however, a conversion to a soliton gas takes place.

Possibility of an Akhmediev breather decaying into solitons

Rogue waves, by definition, are rare events of extreme amplitude. At the same time, they are surprisingly ubiquitous, in the sense that they can exist in a wide range of physical contexts and possess probability distributions that exhibit heavier tails than the normal Gaussian distribution. While many mechanisms have been demonstrated to explain the appearance of rogue waves in various specific systems, there is no known generic mechanism or general set of criteria shown to rule their appearance. Presupposing only the existence of a nonlinear Schrodinger-type equation together with a concave dispersion profile around a zero-dispersion wavelength, we demonstrate that solitons may experience acceleration and strong reshaping due to the interaction with continuum radiation, giving rise to extreme-value phenomena. The mechanism appears to be widely independent from interactions specific to the optical context, e.g., the Raman effect or other scattering processes that have no equivalent in other wave-supporting physical systems. In our system, a strong increase in the peak power may appear via reshaping while the pulse energy is nearly conserved. The conservative nature of the proposed reshaping-induced appearance of rogue waves makes this mechanism particularly robust.

Rogue wave formation by accelerated solitons at an optical event horizon

This is a review of fiber-optic soliton propagation and of methods to determine the soliton content in a pulse, group of pulses or a similar structure. Of central importance is the nonlinear Schrodinger equation, an integrable equation that possesses soliton solutions, among others. Several extensions and generalizations of this equation are customary to better approximate real-world systems, but this comes at the expense of losing integrability. Depending on the experimental situation under discussion, a variety of pulse shapes or pulse groups can arise. In each case, the structure will contain one or several solitons plus small amplitude radiation. Direct scattering transform, also known as nonlinear Fourier transform, serves to quantify the soliton content in a given pulse structure, but it relies on integrability. Soliton radiation beat analysis does not suffer from this restriction, but has other limitations. The relative advantages and disadvantages of the methods are compared.

Soliton Content of Fiber-Optic Light Pulses

Recent developments in the technology of optical telecommunications are pushed forward by the rapidly growing demand for data-carrying capacity. Current approaches are discussed; most lines of investigation are limited to the linear (i.e. low power) regime. It is shown how this restriction poses a limit for further evolution. If, on the other hand, the nonlinear regime is entered, recent developments about soliton molecules offer a possibility to advance further.

Christoph Mahnke

Papers

Rogue events in the group velocity horizon

Possibility of an Akhmediev breather decaying into solitons

Rogue wave formation by accelerated solitons at an optical event horizon

Soliton Content of Fiber-Optic Light Pulses

Soliton molecules for advanced optical telecommunications