Omnipresent coexistence of rogue waves in a nonlinear two-wave interference system and its explanation by modulation instability

We investigate the coexisting rogue wave dynamics associated with two fundamental-frequency optical waves interacting in a quadratic nonlinear medium. Using the vector Chen-Lee-Liu nonlinear Schrödinger equation model, we obtain exact rogue wave solutions at first and higher orders on the more general periodic backgrounds. We unveil that the inherent self-steepening effect may allow an omnipresent rogue wave coexistence over a broad range of parameters in both the normal and anomalous dispersion regimes, in addition to allowing ultrastrong peak amplitudes. We also demonstrate that such universality of coexistence can be anticipated by the appearance of two peaks in the modulation instability spectrum. We numerically confirm the robustness of the coexisting Peregrine solitons against initial noise as well as their excitation from a turbulent wave field caused by modulation instability. We expect that these findings will shed light on the generation of extreme wave events resulting from the interference of multiple continuous-wave fields.