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

Changchang Pan,Dumitru Mihalache,Shihua Chen,Lili Bu,Philippe Grelu,Fabio Baronio

doi:10.1103/physrevresearch.3.033152

Abstract

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 Schr\"odinger 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.

Highlights

The study of deterministic rogue wave events of integrable models [1,2,3] has attracted an increasing interest in the past decade, in diverse disciplines ranging from hydrodynamics [4,5] to optics and photonics [6,7,8], acoustics [9], magnetics [10], Bose-Einstein condensation [11,12], and even artificial intelligence [13]
It is revealed that coexisting rogue waves can occur in a broad range of parameters, which leads us to qualify this coexistence as omnipresent. Such omnipresent coexistence can be anticipated by the appearance of two peaks in the modulation instability (MI) spectrum, whose map is typically composed of one sub-baseband and one passband spectral region
The rogue wave dynamics on a periodic background as well as their omnipresent coexistence were investigated, within the framework of the vector CLL–nonlinear Schrödinger (NLS) equation, which can govern the interaction of two FF optical waves in a quadratic nonlinear medium

Summary

INTRODUCTION

The study of deterministic rogue wave events of integrable models [1,2,3] has attracted an increasing interest in the past decade, in diverse disciplines ranging from hydrodynamics [4,5] to optics and photonics [6,7,8], acoustics [9], magnetics [10], Bose-Einstein condensation [11,12], and even artificial intelligence [13]. The quest of high-order rogue wave dynamics involving interacting Peregrine solitons has attracted a surge of research activities [36,37,38], notably on the multiple rogue wave patterns [39,40] and the so-called super rogue wave states [41,42] All these studies on deterministic rogue waves, either theoretical or experimental, have greatly enriched our understanding on the nature of rogue waves, whereby one can observe, generate, and utilize the otherwise elusive and indocile rogue waves in a practical environment [43,44].

VECTOR CLL MODEL AND GENERAL ROGUE WAVE SOLUTIONS

FUNDAMENTAL PEREGRINE SOLITONS AND THEIR OMNIPRESENT COEXISTENCE

CONCLUSION