Nonlinear Dynamics of Optical Systems
Spatial and/or temporal localization of information is a cross-disciplinary challenging topic. In the recent years it has become very attractive subject of research with the connection of extreme events. So called events are rare and large deviation of the average behavior of an observable. Example include power grid outage, earthquakes, floods, financial cracks or oceanic rogue waves. In the context of global climate changing, these events are expected to become more frequent and more damaging according to the Intergovernmental Panel on Climate Change (IPCC). Decision makers will need accurate forecasting for the reduction of human and societal cost. Hence, after years of trying to understand mechanisms behind extreme events the challenge has moved on their forecasting or inference. Here again, by their demonstrated analogy with a large variety of physical systems, optics is a precious asset. Turbulence dominates the physical behavior of a huge variety of scenarios and lies at the basis of our understanding of systems ranging from small scales such as optical waves in photonic fluids and matter waves in Bose-Einstein condensates, to intermediate scales such as ocean water waves, or even on cosmic scales through the formation of coherent structures in the Universe.
Optical turbulence also constitutes a growing field of research covering various topics in modern optics, e.g., supercontinuum generation, rogue waves, fiber lasers, optical filamentation, and random lasers. Nonlinear optics offers a unique platform to study fully developed turbulence, which remains one of the most challenging unsolved problems, not only of theoretical physics but also in the field of experimental real-time ultrafast measurements, which are needed to fully quantify turbulent spatiotemporal evolution. Over the 2013-2018 period, the team focused primarily on two issues related to the study of extreme events: (i) the study of turbulence and its ramifications as spatiotemporal chaos and extreme events appearing in the strongly nonlinear regime of optical systems far from equilibrium and (ii) the predictability of extreme events.
The study of turbulence started in the wake of the ANR OptiRoC yield to the development of tools that were used in a fiber ring cavity to unveil the second order-like phase transition (Phys. Rev. X 9, 011054 (2019)). In the scope of the prediction of extreme events the group has provided a proof of concept that tools of dynamical systems theory, information theory and machine learning can be gathered together to forecast when, where and the profile of extreme events in fiber ring cavity and semi-conductor laser (Phys. Rev. Lett. 130, 223801 (2023), Chaos, Solitons & Fractals 160, 112199 (2023)). Our recent work has shown how machine learning can be powerful when combined with the tools of dynamical system theory. On the other hand, there is another kind of localization in time with growing interest: the time crystals. These crystals were theoretically introduced in 2012 by Frank Wilczek. Similar to "classic" crystals in condensed matter, the goal here is to create a temporal signal with discrete translation symmetry. In many systems the dynamics beyond these crystals are still relatively unknown and poorly studied at this stage.
The group also strengthens its skills in the discovery of new mechanisms of localization of light. Indeed, the study of the localization of light in a small region of the available domain is one of the historical research topics of the group. The interest around e.g. the frequency combs and optical dam break topics are proofs that localization of light remains a prior topic in Nonlinear Dynamics. Achievement in this topic include localization induced by nonlocal and stochastic medium [Phys. Rev. E 103, 022701 (2021)], time delayed response [Phys. Rev. Research 2, 013024] and high dimensionality [Phys. Rev. Lett. 126, 153902 (2021)].
More detailed information can be found below about the activities on the Influence of spatial nonlocality and stochasticity on the propagation of light structures:
