Numerical study of the fibre dispersion contribution in the pulse propagation problem

This work explains in detail the role of the dispersion contribution provided by a single-mode optical fibre (SMF) in the pulse propagation problem modelled by the nonlinear Schrödinger equation. Firstly, the basics of chromatic dispersion in fibre are presented, including a modified Sellmeier equation for representing the dispersion contribution of the fibre core material (in an illustrative case of fused silica doped with germanium dioxide) that is modified by the waveguide dispersion contribution. At the same time, the contribution of the second-, third- and fourth-order dispersion parameters are illustrated for a SMF. Finally, a numerical analysis of the propagation problem is presented in order to understand the dispersion effects for a sech2 pulse profile, as well as the interplay of its contribution with the nonlinear Kerr effect, which is also involved in the pulse propagation. For a better understanding of the numerical methods applied to develop the propagation problem, we include a guide detailing the stages to follow in the numerical approach, considering how to select the initial parameters as well as the iterative steps of the numerical method.