Experimental Investigation of Phase-Space Portraits of Ideal Four-Wave Mixing
Résumé
We develop a fiber-based experimental setup dedicated to the demonstration of an ideal four-wave mixing process. With an experimental technique based on the iteration of initial conditions and propagation over short distances of fibers, we are able to alleviate the impact of high-order harmonics and optical losses. We can therefore mimics nearly ideal propagation over tens of kilometers and reveal the complete phase-space topology exhibiting several Fermi-Pasta-Ulam-Tsingou recurrence cycles, the existence of a stationary wave as well as the presence of a system separatrix, which marks the transition between two distinct spatiotemporal evolution regimes. The experimental dynamics agrees well the theoretical predictions with close orbits that do not intersect.
We also investigate theoretically and experimentally an impact of control parameters on orbits’ dynamics. We use an abrupt change in power to connect two states on the phase-space plane that do not belong to the same trajectory. Finally, we apply machine learning techniques: firstly, we train a feed-forward neural network with non-iterated sampled measurements that allows to extract the key characteristics of the dynamics; and secondly, we use a sparce identification of nonlinear dynamics to retrieve differential equations governing the four-wave mixing dynamics affected by noise.
Origine | Fichiers produits par l'(les) auteur(s) |
---|