Abstract

Modulational instability (MI) is a fundamental and ubiquitous phenomenon of nonlinear science. It refers to a process in which a nonlinear and dispersive continuous wave breaks up into a periodic train of localized wave packets. In the context of nonlinear discrete systems, Fermi, Pasta and Ulam (FPU) have shown that, rather unexpectedly, this process is reversible and exhibits recurrence [1]. Since then, many nonlinear wave equations were shown to exhibit FPU recurrence among which the nonlinear Schrödinger equation plays a central role owing to its ubiquity in almost all branches of physics. However, despite this ubiquity, the FPU recurrence of the NLS equation has only been the object of experimental demonstrations in the field of hydrodynamics [2]. This situation is due to the practical difficulties to maintain the NLS model valid over the long propagation distances that characterize the recurrence dynamics. In this respect, nonlinear optics appears to be a promising field of investigation because of the availability of silica optical fibers in which light propagation is accurately ruled by the NLS equation over long distances. Nevertheless, although these favorable conditions have led to numerous experimental studies of MI [3], FPU recurrence has never been demonstrated in optical fibers. The reason of this failure is the existence of competing nonlinear effects that invalidate the NLS model over long distances. The Brillouin scattering, which is the most detrimental of these effects, is simply avoided in practice by studying MI in laser pulses instead of cw signals. Though this solution is well adapted to the study of MI in the first stage of nonlinear evolution [3], the spectral complexity inherent to the pulse profile prevents from studying FPU recurrence. Indeed, FPU recurrence involves a delicate balance in the energy transfers between a large number of spectral modes and thus requires spectral purity. In order to satisfy this requirement at best, we considered the use of square-shaped laser pulses. The large plateau (~550 psec) of these pulses makes the cw component dominant in the initial spectrum and, in this way, allows for the observation of FPU recurrence.

© 2000 IEEE