Rogue Waves

We discuss propagation of ultrashort solitary pulses in nonlinear single-mode optical fibers. Each pulse creates a moving perturbation of the refractive index; the perturbation is capable to scatter co-propagating pulses. An ultrashort optical soliton serves, under suitable conditions, as an impenetrable mirror for the group-velocity matched small-amplitude waves. Reflection of such waves by a quickly moving mirror in dispersive media is a rich source of the intriguing phenomena including analogue event horizons and radiation at negative frequencies. On the other hand, energy exchange between the scattered pump waves and the soliton provides an effective way to manipulate the soliton, e.g., to fix its frequency or to compress it to a large extent.

Caustic light revolutionized optics in the last decade in the areas of structured light and random waves. On the one hand, tailored caustic beams serve as fabricating light for (nonlinear) material processing, transfer complex momentum flows for advanced micro-manipulation, and enable novel high-resolution imaging methods. On the other hand, the random focusing of light rays forms networks of caustics that appear as high-intensity ramifications in many optical systems. This linear focusing, caused by strong wavefront aberrations and denoted as branched flow, yields waves with extreme amplitudes – so called rogue waves, originally studied in oceanography. Optics has proven to be a vast testbed to investigate different linear and nonlinear mechanisms for the formation of rogue waves as spatio-temporal wave phenomena. Though there are indications that the two different mechanisms described above, branched flows and nonlinear modulation instabilities, contribute to the formation of rogue waves, the influence of their mutual interplay on the rogue wave statistic is still an open question.

In our contribution, we exploit a nonlinear photorefractive material as an optical platform to investigate these different mechanisms for rogue wave formation simultaneously in a single system. We show that free-space branched flows of light caused by wavefront distortions in form of correlated Gaussian random fields (GRFs) focus to caustic networks with controllable extension and sharpness, which in turn determine the probability for the occurrence of optical rogue waves. This focusing can be enhanced by propagating GRFs in a nonlinear refractive index structure with focusing nonlinearity. Beyond propagating in homogeneous media, we fabricate two-dimensional tailored photonic disorder in such a photorefractive crystal and investigate the mutual interplay of linear focusing by GRFs and scattering. We find optimal conditions for enhanced focusing of waves with extreme intensities by controlling the size and strength of the disordered photonic refractive index structure.

Thus, in our contribution, we will link different mechanisms for rogue wave formation that are commonly studied separately and discuss their interplay. Our work demonstrates that different focusing mechanisms can enhance or depress the formation of rogue waves, thereby introducing an optical platform that allows exploring rogue waves far beyond the optical realization, and allows new insights into general spatio-temporal wave dynamics.

Solitons and breathers are known to model stationary and extreme localizations in nonlinear dispersive media. Indeed, a series of laboratory experiments, for instance in water waves, optics and BEC, confirmed the validity of the the uni-directional nonlinear Schrödinger equation (NLSE) to describe the spatio-temporal dynamics of such waves. In this study, we report observations of slanted, and thus, directional localized envelope soliton and breather dynamics in a water wave basin. The water surface displacement has been stereo-reconstructed using a marker-net, deployed at the center of the basin, and two synchronized high-speed cameras. The results are in very good agreement with the hyperbolic 2D+1 NLS predictions and confirm for the first time that short-crested as well as slanted strongly-localized waves can be also described by a simplified nonlinear wave framework.