Statistical Properties of the Nonlinear Stage of Modulation Instability in Fiber Optics
Résumé
We present an optical fiber experiment in which we examine the space-time evolution of a modulationally unstable plane wave initially perturbed by a small noise. Using a recirculating fiber loop as an experimental platform, we report the single-shot observation of the noise-driven development of breather structures from the early stage to the long-term evolution of modulation instability. Performing single-point statistical analysis of optical power recorded in the experiments, we observe decaying oscillations of the second-order moment together with the exponential distribution in the long-term evolution, as predicted by Agafontsev and Zakharov [Nonlinearity 28, 2791 (2015).]. Finally, we demonstrate experimentally and numerically that the autocorrelation of the optical power g((2))(tau) exhibits some unique oscillatory features typifying the nonlinear stage of the noise-driven modulation instability and of integrable turbulence.