We present experiments in which nonlinear random waves propagate in systems that are described at leading order by the focusing one-dimensional nonlinear Schrodinger equation. We compare the propagation of waves in a water tank and light propagation inside a single mode optical fiber.

We have performed an optical fiber experiment similar in its principle to a hydrodynamical experiment realized in 2004 [1]. In this experiment, a random complex field having a gaussian statistics at initial stage propagates inside the one-dimensional water tank. The spectrum of the fluctuations taken as initial condition is the so-called JONSWAP spectrum that has been measured in Oceanography experiments [2].

In our work, we specifically focus on the study of the statistical changes experienced by the nonlinear waves in the two propagation media. Our Optical and Hydrodynamical experiments are realized with reduced identical parameters. Using an original optical sampling method, we were able to measure the evolution of the statistics of power fluctuations with a temporal resolution of 250fs [3]. We compare these results to the ones obtained earlier in the Hydrodynamical experiment.

In the two experiments, we observe the emergence of large amplitude events resulting in heavy- tailed deviations from gaussian statistics. The results are quantitatively comparable. Two differences are noticeable : firstly the transcient regime is slower in water waves than in optical waves. Secondly, at long distance of propagation, optical waves exhibit a stationnary state whereas the kurtosis of water waves decreases.

We also perform numerical simulations of the nonlinear Schrodinger equation that describes the propagation. We explain some of the differences by the role of high order term and by the probable appearance of wave breaking phenomena after some propagation distance.

References

[1] M. Onorato, A.R. Osborne, and M Serio, Observation of strongly non-Gaussian statistics for random sea surface gravity waves in wave flume experiments, Phys. Rev. E, 70, 067302(4), (2004).

[2] G.J. Komen, L. Caveleri, M. Donelan, K. Hasselman, S. Hasselman, and P.A.E.M. Janssen, Dynamics and Modelling of Oceans Waves Cambridge University Press,(1994).

[3] P. Walczak, S. Randoux and P. Suret, Optical Rogue Waves in Integrable Turbulence Phys. Rev. Lett.,114, 143903(5)(2015).