Numerical stability of solitons waves through splices in optical fibers

TL;DR

This study investigates the numerical stability of soliton wave propagation in optical fibers with Gaussian fluctuations in dielectric properties, finding that perturbed solitons tend to stabilize over long distances despite local fluctuations.

Contribution

It introduces a mathematical model for local dielectric fluctuations in optical fibers and demonstrates the numerical stability of solitons under these perturbations through simulations.

Findings

Perturbed solitons show increased sensitivity to dielectric parameter fluctuations.

Soliton amplitude oscillations decrease over long propagation distances.

Propagation remains numerically stable despite local Gaussian fluctuations.

Abstract

The propagation of soliton waves is simulated through splices in optical fibers, in which fluctuations of dielectric parameters occur. The mathematical modeling of these local fluctuations of dielectric properties of fibers was performed by Gaussian functions. By simulating soliton wave propagation in optical fibers with Gaussian fluctuations in their dielectric properties, it was observed that the perturbed soliton numerical solution presented higher sensitivity to fluctuations in the dielectric parameter $\beta$, a measure of the intensity of nonlinearity in the fiber. In order to verify whether the fluctuations of $\beta$ parameter in the splices of the optical fiber generate unstable solitons, the propagation of a soliton wave, subject to this perturbation, was simulated for large time intervals. Considering various geometric configurations and intensities of the fluctuations of parameter $\beta$, it was found that the perturbed soliton wave stabilizes, i.e., the amplitude of the wave oscillations decreases for increasing values of propagation distance. It is concluded that the propagation of perturbed soliton wave presents numerical stability when subjected to local Gaussian fluctuations (perturbations) of the dielectric parameters of the optical fiber.