We report optical experiments and numerical simulations devoted to the investigation of integrable turbulence in the focusing regime of 1D-NLSE [1, 2]. We present in particular the first real time observation of rogue waves (RWs) generated in optical fibers by using a specially-designed Time Microscope (TM) ultrafast acquisition system [2]. RWs with time scale of the order of 300 fs are found to emerge from the propagation of partially coherent waves having initial time scale of 5ps.

Using our TM and another optical sampling setup, we measure precisely the probability density function (PDF) of optical power of the nonlinear random waves rapidly fluctuating with time. The PDF of optical power is found to evolve from the exponential distribution to a strong heavy-tailed distribution. The exponential distribution of the power corresponds to a Gaussian statistics for the field. Our experiments thus reveal the occurrence of extreme events (RWs) in integrable turbulence with a probability much higher than predicted by the normal law. Finally we will emphasize the crucial question of the dependence of the stationary statistics on the initial statistics [5, 6].

References:

[1] P. Walczak et al., Phys. Rev. Lett. 114, 143903 (2015)

[2] P. Suret et al., arXiv:1603.01477 (2016)

[3] J. M. Dudley et al., Nat. Photon. 8, 755 (2014)

[4] S. Randoux, et al., arXiv preprint arXiv:1512.04707.

[5] D.S. Agafontsev and V E Zakharov Nonlinearity, 28, 8 (2015)

[6] J. M. Soto-Crespo et al., Phys. Rev. Lett. 116 (2016) 103901.