The optical rogue wave patterns in coupled defocusing systems

TL;DR

This paper explores the spatial-temporal patterns of rogue waves in multi-component defocusing nonlinear Schrödinger systems, establishing a link with modulation instability and classifying rogue wave structures for optical fiber applications.

Contribution

It provides a unified form of rogue wave solutions for both focusing and defocusing cases and develops a quantitative correspondence between modulation instability and rogue wave patterns.

Findings

Established phase diagrams for rogue wave patterns in two-component systems

Predicted rogue wave structures, including four-petaled patterns

Linked modulation instability with rogue wave pattern formation

Abstract

We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schr\"{o}dinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and defocusing cases. We establish the quantitative correspondence between modulation instability and rogue wave patterns, which develops the previously reported inequality relation into an equation correspondence. As an example, we demonstrate phase diagrams for rogue wave patterns in a two-component coupled system, based on the complete classification of their spatial-temporal structures. The phase diagrams enable us to predict various rogue wave patterns, such as the ones with a four-petaled structure in both components. These results are meaningful for controlling the rogue wave excitations in two orthogonal polarization optical fibers.