Experimental validation in optical fibers of multiple Fermi-Pasta-Ulam-Tsingou recurrences theory

Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence process describes the ability of a multimodal system experiencing complex nonlinear dynamics to come back to its initial state, instead of reaching thermalization. In optics, it has particularly been investigated in the context of modulation instability (MI) [1], which plays a key role in many nonlinear phenomena such as rogue wave formation or supercontinuum generation. Recently, we reported a novel experimental setup [2] consisting in a heterodyne time-domain detection system which allows to perform along an optical fiber distributed measurement in phase and intensity of a pump wave and its modulation sidebands. Thanks to an active compensation of the losses, it enabled the observation of two FPUT recurrences cycle for the first time (Fig. 1(b,c)). Moreover, Grinevich and Santini recently reported [3] an advanced theoretical model to predict the characteristics of these recurrences which have been verified experimentally in a 3D photorefractive crystal [4]. Based on the setup described in [2], we report here its verification in an optical fiber.