Soliton propagation in lossy optical fibers

TL;DR

This paper investigates how solitons behave in lossy optical fibers, developing a numerical scheme to analyze energy loss and its effects, and demonstrating that nonlinear amplification can extend soliton propagation distance.

Contribution

The paper introduces a numerical method combining Taylor series, FDM, and RGSM to simulate soliton propagation with loss and gain in optical fibers.

Findings

Solitons experience attenuation, dispersion, and oscillation in lossy fibers.

Nonlinear amplification can partially compensate for signal attenuation.

A 9% gain triples the soliton propagation distance at 1% dissipation.

Abstract

In this work, we study the propagation of solitons in lossy optical fibers. The main objective of this work is to study the loss of energy of the soliton wave during propagation and then to evaluate the impact of this loss on the transmission of the soliton signal. In this context, a numerical scheme was developed to solve a system of complex partial differential equations (CPDE) that describes the propagation of solitons in optical fibers with loss and nonlinear amplification mechanisms. The numerical procedure is based on the mathematical theory of Taylor series of complex functions. We adapted the Finite Difference Method (FDM) to approximate derivatives of complex functions. Then, we solve the algebraic system resulting from the discretization, implicitly, through the relaxation Gauss-Seidel method (RGSM). The numerical study of CPDE system with linear and cubic attenuation showed that soliton waves undergo attenuation, dispersion, and oscillation effects. On the other hand, we find that by considering the nonlinear term (cubic term) as an optical amplification, it is possible to partially compensate for the attenuation of the optical signal. Finally, we show that a gain of 9% triples the propagation distance of the fundamental soliton wave, when the dissipation rate is 1%.