Frequency shifting for solitons based on transformations on the Fourier domain and applications

TL;DR

This paper introduces a method for shifting the frequency of solitons using Fourier domain transformations, verified through simulations, with applications in stabilizing soliton propagation and inducing collisions in waveguides.

Contribution

It presents a novel theoretical approach for frequency shifting of solitons based on Fourier domain transformations, validated by numerical simulations.

Findings

The frequency shifting procedures match theoretical predictions.

Applications include stabilizing soliton propagation in waveguides.

Inducing repeated soliton collisions with weak cubic loss.

Abstract

We develop the theoretical procedures for shifting the frequency of a single soliton and of a sequence of solitons of the nonlinear Schr\"odinger equation. The procedures are based on simple transformations of the soliton pattern in the Fourier domain and on the shape-preserving property of solitons. These theoretical frequency shifting procedures are verified by numerical simulations with the nonlinear Schr\"odinger equation using the split-step Fourier method. In order to demonstrate the use of the frequency shifting procedures, two important applications are presented: (1) stabilization of the propagation of solitons in waveguides with frequency dependent linear gain-loss; (2) induction of repeated soliton collisions in waveguides with weak cubic loss. The results of numerical simulations with the nonlinear Schr\"odinger model are in very good agreement with the theoretical predictions.