Modélisation de la propagation des Soltions dans un milieu Non linéaire dispersif - Application aux fibres optiques.

Abstract

In this work we have presented a study of some non-linear phenomena that occur at optical fibres during the propagation of an ultra-short pulse "Electromagnetic wave" . The notions of Maxwell's equations, the propagation equation of an electromagnetic wave and the notion of soliton allowed us to derive a model known in optics as the Non-Linear Schrödinger (ENLS) which will take into consideration the dispersion and non-linearity effects. The analytical solution of such equation is difficult and sometimes impossible, which is why a numerical method is used, considered to be the most appropriate tool to solve this type of problem, called the "Split Step Fourier Method" SSFM. A numerical simulation allowed us to describe the evolution of a pulse in an optical fiber while revealing the advantage of the coexistence of the two phenomena "dispersion and non-linearity of the medium".