Numerical Simulations of Femtosecond Pulse Propagation in Photonic Crystal Fibers Comparative Study of the S-SSFM and RK4IP

We investigate the propagation of femtosecond pulse in photonic crystal fibers PCFs which is actually of great interest for studies. The generalized nonlinear Schrodinger equation (GNLSE) describes the different physical phenomena, like dispersion and some nonlinear effects including the SPM, self steepening and Raman scattering encountered when the femtosecond pulses propagate in the PCF. In our simulation, we use the symmetric split-step Fourier method (SSSFM) and the fourth-order Range-Kutta interaction picture (RK4IP) method whose are often used to calculate the numerical solutions of the GNLSE. In this paper, we present our implementation algorithms; and we will show that for a given step size, the calculate S-SSFM number of fast Fourier transforms (FFTs) is less than the one of the RK4IP by a factor 3 in spite of a large errors. In order to evaluate the performance, we have also measured the global relative error by using linear and nonlinear characteristics of a PCF found in the literature. Our numerical results allow showing that for a fixed errors the total number of FFTs of the RK4IP is much smaller. The O(h) and O(h 4 ) orders of the S-SSFM and RK4IP