Extreme waves in stimulated backscattering and frequency conversion processes

Abstract

We present the extreme rogue wave dynamics that originate from the three-wave resonant interaction equations, which describe the transient stimulated scattering processes, in cubic media, and the parametric frequency conversion processes, in phase-matched dispersive quadratic media. Explicit theoretical fundamental and second-order rogue wave solutions are presented and characterized. The link between the existence of rogue wave solutions and the presence of baseband modulation instability is highlighted. We also present numerical simulations that confirm the robustness and possible manifestation of these rogue waves for various parameters and initial conditions.