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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The transient appearance of bright spots in the beam profile of optical filaments formed in xenon is experimentally investigated. Fluence profiles are recorded with high-speed optical cameras at the kilohertz repetition rate of the laser source. A statistical analysis reveals a thresholdlike appearance of heavy-tailed fluence distributions together with the transition from single to multiple filamentation. The multifilament scenario exhibits near-exponential probability density functions, with extreme events exceeding the significant wave height by more than a factor of 10. The extreme events are isolated in space and in time. The macroscopic origin of these experimentally observed heavy-tail statistics is shown to be local refractive index variations inside the nonlinear medium, induced by multiphoton absorption and subsequent plasma thermalization. Microscopically, mergers between filament strings appear to play a decisive role in the observed rogue wave statistics.

Using experimental data from three different rogue wave supporting systems, determinism and predictability of the underlying dynamics are evaluated with methods of nonlinear time series analysis. We included original records from the Draupner platform in the North Sea as well as time series from two optical systems in our analysis. One of the latter was measured in the infrared tail of optical fiber supercontinua, the other in the fluence profiles of multifilaments. All three data sets exhibit extreme-value statistics and exceed the significant wave height in the respective system by a factor larger than two. Nonlinear time series analysis indicates a different degree of determinism in the systems. The optical fiber scenario is found to be driven by quantum noise whereas rogue waves emerge as a consequence of turbulence in the others. With the large number of rogue events observed in the multifilament system, we can systematically explore the predictability of such events in a turbulent system. We observe that rogue events do not necessarily appear without a warning, but are often preceded by a short phase of relative order. This surprising finding sheds some new light on the fascinating phenomenon of rogue waves.