Abstract
We provide a systematic study of the rogue-wave dynamics in phase-matched weakly dispersive nonlinear media, which arise either from the parametric mixing or from the stimulated backscattering process, both of which are modeled by the three-wave resonant interaction equations. The explicit rogue-wave solutions up to the second order are presented. These solutions reveal the markedly different vector rogue-wave behaviors of the parametric and the scattering processes. In the degenerate situation where two interacting optical fields share the same group velocity, the sum of the intensities of this pair of optical wave components is spatiotemporally invariant. The close link between the existence of rogue-wave solutions and the presence of baseband modulation instability is confirmed. Finally, numerical simulations confirm that the generation of vector rogue waves is robust in the presence of spontaneous modulation instability activated by quantum noise.
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