Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering

11 págs.; 10 figs.; PACS number(s): 42.65.Tg, 05.45.Yv, 47.54.−r, 47.20.Ky© 2015 American Physical Society. 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. ©2015 American Physical SocietyThis work was supported by the National Natural Science Foundation of China (Grants No. 11174050 and No. 11474051) and by the Italian Ministry of University and Research (MIUR, Project No. 2012BFNWZ2). Ph.G. was supported by the Agence Nationale de la Recherche (Projects No. ANR-2010-BLANC-0417-01 and No. ANR-2012-BS04- 0011). The work of J.M.S.C. was supported by MINECO under Contract No. TEC2012-37958-C02-02, by C.A.M. under Contract No. S2013/MIT-2790, and by the Volkswagen Foundation. M.C. acknowledges the support from the Agence Nationale de la Recherche (Project No. ANR-14-ACHN-0014 NoAWE). F.B. and S.W. are also with Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche.Peer Reviewe