Study of the soliton self-frequency shift in the photonic crystal fiber

The photonic crystal fiber allows the control of dispersion and nonlinear effects. The propagation of pulses is described by the generalized nonlinear Schrodinger equation. High order dispersion and nonlinear effects like SPM, self steepening and Raman scattering render the analytical solution of the GNLSE inaccessible. The fourth-order Range-Kutta interaction picture (RK4IP) is an efficient and stable method to determine the numerical solution. In this paper, we present our numerical simulating results relating to the influence of the high order dispersion and nonlinear effects on the soliton self-frequency shift (SSFS). Using the RK4IP algorithm we compute the numerical solutions of an initial hyperbolic secant pulse for some lengths z of a PCF. We calculate the corresponding SSFS, where only the GVD and Raman or GVD, TOD and Raman effects act simultaneously. We show that our numerical results agree well with the theoretical results found in the literature.