Abstract

The appearance of modulational sidebands building up from noise has been reported when an intense cw or quasi-cw propagates in a fiber in the anomalous dispersion regime [1]. The modulation transforms the input wave into a train of pulses with ultra-high repetition rate. This process may be stimulated by seeding incoherently (i.e., by means of a different weak detuned laser) the modulational instability (MI) [2]. However the experiments and the early theory on MI [3] have led to the diffuse but erroneous belief that in the presence of MI the input wave becomes a train of solitons. On the contrary (temporally) periodic wave solutions of the nonlinear Schroedinger (NLS) equation have shown that the propagation is periodic also in space (a phenomenon known as Fermi-Pasta-Ulam recurrence [4]), leading to the formation of complex spatiotemporal patterns [5-7]. We show here that the nonlinear dynamics of modulated waves, which includes in principle the interaction of an infinite number of Fourier modes, is essentially locked to the simple interaction between three modes: the pump and the first symmetric sidebands. In this case a simple integrable one-dimensional equivalent oscillator model [8-9] enables one to unfold the role of a coherent modulation at the input in the generation of the spatio-temporal patterns. This suggests also the possibility of new experiments in which the pulse train and switching among two logical state is controlled by the input phase relation between the pump and the sidebands.

© 1991 Optical Society of America