No abstract

A unidirectional optical oscillator is built by using a liquid crystal light-valve that couples a pump beam with the modes of a nearly spherical cavity. For sufficiently high pump intensity, the cavity field presents a complex spatio-temporal dynamics, accompanied by the emission of extreme waves and large deviations from the Gaussian statistics. We identify a mechanism of spatial symmetry breaking, due to a hypercycle-type amplification through the nonlocal coupling of the cavity field. . Associated with extreme waves are L-shaped statistics, with a probability of large peak occurrence much larger than predicted by Gaussian statistics. Different mechanisms to explain the origin of extreme waves have been proposed, including nonlinear focusing via modulational instability (MI) [4] and focusing of line currents [5]. In optical fibers, numerical simulations of the nonlinear Schrödinger equation (NLSE) [6] have established a direct analogy between optical and water rogue waves. In a spatially extended system, the formation of large amplitude and localized pulses, so-called optical needles, has been evidenced by numerical simulations for transparent media with saturating self-focusing nonlinearity [7]. Similar space-time phenomena, such as collapsing filaments, are also predicted in optical wave turbulence [8]. Recently, the spatio-temporal dynamics of MI-induced bright optical spots was observed in Ref. [9] and an algebraic power spectrum tail was reported due to momentum cascade [10]. Nevertheless, no experimental evidence has been given up to now of extreme waves in a spatially extended optical system.Here, we report, what is, at our knowledge, the first experimental evidence of extreme waves and non-Gaussian statistics in a 2D spatially extended optical system. The experiment consists of a nonlinear optical cavity, formed by a unidirectional ring oscillator with a liquid crystal light-valve (LCLV) as the gain medium. While for low pump the amplitude follows a Gaussian statistics, for sufficiently high pump we observe large deviations from Gaussianity, accompanied by the emission of extreme waves that appear on the transverse profile of the optical beam as genuine spatiotemporal phenomena, developing erratically in time and in space. The observations are confirmed by numerical simulation of the full model equations. Moreover, by introducing a mean-field simplified model, we show that extreme waves in the cavity are generated by a novel mechanism, which is based on a hypercycle-type amplification [11] occurring via nonlocal coupling of different spatial regions. The experimental setup is essentially the one described in [12]. The ring cavity is formed by three highreflectivity dielectric mirrors and a lens of f = 70 cm focal length. The total cavity length is L = 273.3 cm and the lens is positioned at a distance L 1 = 88.1 cm from the entrance plane of the LCLV. The coordinate system is taken such that z is along the cavity axis and x, y are on the transverse plane. A LCLV supplies the gain through a two-wave mixi...

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.