Nonlinear compression of autonomous similaritons in the cubic-quintic nonlinear Schr\"odinger equation model with nonlinear gain

TL;DR

This paper investigates the propagation and compression of similariton pulses in double-doped optical fibers modeled by a cubic-quintic nonlinear Schrödinger equation, revealing exact solutions and optimal conditions for pulse compression.

Contribution

It introduces a fractional transform method to find exact similariton solutions and identifies conditions for optimal pulse compression in a complex nonlinear fiber model.

Findings

Exact similariton solutions were derived using fractional transform.

Optimal dispersion and nonlinearity profiles for pulse compression were identified.

Nonlinear chirping effects in trigonometric solutions were demonstrated.

Abstract

We describe similariton pulse propagation in double-doped optical fibers with the aid of self-similarity analysis of the cubic-quintic nonlinear Schr\"odinger equation with varying dispersion, nonlinearity, gain or absorption, and nonlinear gain. Exact similariton pulses that can propagate self similarly subject to simple scaling rules of this model have been found using a fractional transform. By appropriately tailoring the dispersion profile and nonlinearity, the condition for optimal pulse compression has been obtained. Also, nonlinear chirping of the trigonometric solution has been demonstrated.