Engineering Optical Rogue Waves and Breathers in a Coupled Nonlinear Schr\"odinger System with Four-Wave Mixing Effect

TL;DR

This paper develops a method to engineer and manipulate various localized wave phenomena, including rogue waves and breathers, in a coupled nonlinear Schrödinger system with modulated nonlinearities and refractive index.

Contribution

It introduces a similarity transformation approach to derive localized wave solutions in a coupled nonlinear Schrödinger system with engineered nonlinearities and refractive index variations.

Findings

Demonstrates stable solitons, breathers, and rogue waves in the system.

Shows how to manipulate localized waves via engineered nonlinearities.

Provides graphical analysis of wave dynamics.

Abstract

We consider a coherently coupled nonlinear Schr\"odinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium. By identifying an appropriate similarity transformation, we obtain a general localized wave solution and investigate their dynamics with a proper set of modulated nonlinearities. In particular, our study reveals different manifestations of localized waves such as stable solitons, Akhmediev breathers, Ma breathers, and rogue waves of bright, bright-dark, and dark-dark type and explores their manipulation mechanism with suitably engineered nonlinearity parameters. We have provided a categorical analysis with adequate graphical demonstrations.