Optical Rogue Waves in integrable turbulence

Using experiments with single mode optical fibers and numerical simulations, we investigate the statistics of partially coherent waves propagating in the anomalous dispersion regime (P. Walczak et al., 114, Phys. Rev. Lett. (2015)). Using an asynchronous optical sampling setup, we measure precisely the probability density function (PDF) of the optical power that fluctuates randomly and rapidly with time. The resolution time of our fast-measurement of the PDF is better than 250fs. Along the propagation inside the nonlinear fiber, the PDF is found to evolve from the normal law to a strong heavy-tailed distribution. Numerical simulations of the one-dimensional nonlinear Schrodinger equation (1D-NLSE) with stochastic initial conditions reproduce quantitatively the experiments. Our experimental and numerical study demonstrates the formation of rogue waves in the focusing regime of integrable turbulence. Moreover, our numerical investigations suggest that the statistical features experimentally observed rely on the stochastic generation of coherent analytic solutions of 1D-NLSE such as solitons on finite background.