Complementary optical rogue waves in parametric three-wave mixing

10 págs.; 5 figs.; OCIS codes: (190.3100) Instabilities and chaos; (190.5530) Pulse propagation and temporal solitons; (190.4410) Nonlinear optics, parametric processes.We investigate the resonant interaction of two optical pulses of the same group velocity with a pump pulse of different velocity in a weakly dispersive quadratic medium and report on the complementary rogue wave dynamics which are unique to such a parametric three-wave mixing. Analytic rogue wave solutions up to the second order are explicitly presented and their robustness is confirmed by numerical simulations, in spite of the onset of modulation instability activated by quantum noise. © 2016 Optical Society of AmericaThis 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 (Project No. ANR-2012-BS04-0011). The work of J. M. S. C. was supported by MINECO under contract TEC2012-37958-C02-02, by C.A.M. under contract S2013/MIT-2790, and by the Volkswagen Foundation.Peer Reviewe