Numerical Solution of The Solitons Propagation IN Optical Fibers Using Sptit-Step Fourier method

Abstract

Despite the vast research in 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 Nonlinear Schrodinger Equation (NLSE) which will take into consideration the dispersion and non-linearity effects. That most of the systems in this universe qualify to be nonlinear so that, the immediate objective of this research project is to study some phenomena that occur in optical fibers during the propagation of an ultra-short pulse "Electromagnetic wave", which are nonlinear. One factor which has led to a numerical method is used in the analytical solution of such equation is difficult and sometimes impossible. As a result, the most appropriate tool to solve this type of problem, called the Split Step Fourier Method (SSFM). To this end, this process leads to the formation of optical solitons which retain shape during propagation, the compression mechanism fundamentally due to high order solution. This a numerical simulation increases our understanding 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".