Ivan M. Uzunov ; Todor N. Arabadzhev and Zhivko D. Georgiev, " Time shift in the presence of linear and nonlinear gain, spectral filtering, third-order of dispersion and self-steepening effect ", Proc. SPIE 9447, 18th International School on Quantum Electronics: Laser Physics and Applications, 94471G (January 8, 2015); doi:10.1117/12.2175950; http://dx.doi.org/10.1117/12.2175950 Time shift in the presence of linear and nonlinear gain, spectral filtering, third-order of dispersion and self-steepening effect Ivan M. Uzunov a , Todor N. Arabadzhev *a , Zhivko D. Georgiev b a Department of Applied Physics, Technical University Sofia, 8 Kl. Ohridski Blvd., Sofia 1000, Bulgaria, b Department of Theoretical Electrical Engineering, Technical University Sofia, 8 Kl. Ohridski Blvd., Sofia 1000, Bulgaria. ABSTRACT We study the soliton time shift in the presence of linear and nonlinear gain, saturation of the nonlinear refractive index, spectral filtering, third-order of dispersion and self-steepening effect. The applied model generalizes the complex cubic- quintic Ginzburg-Landau equation (CCQGLE) with the basic higher-order effects in fibers: the intrapulse Raman scattering (IRS), third-order of dispersion (TOD) and self-steepening effect. Soliton perturbation theory (SPT) is derived with which the influence of the saturation of the nonlinear refraction index, self-steepening and TOD on the appearance of the Poincare-Andronov-Hopf bifurcation is analyzed. It has been shown that TOD and self-steepening effect can lead to reduction in the time shift of the pulse. This prediction has been verified by numerical solution of generalized CCQGLE. Keywords: nonlinear fiber optics, fiber lasers, soliton transmission systems, intrapulse Raman scattering, cubic– quintic complex Ginzburg-Landau equation, Poincare-Andronov-Hopf bifurcation, limit cycle 1. INTRODUCTION As is well known the complex cubic-quintic Ginzburg - Landau equation (CCQGLE) in optics 1-3 can model soliton transmission lines 4 as well as passively mode-locked laser systems 5 . It has been shown that narrowband filtering and nonlinear gain can be used to control the self-frequency shift due to the IRS of ultra-short optical solitons in fiber –optic systems 6 . The role of the nonlinear gain is to give an effective gain to the soliton and suppression to the noise or in other words to reduce the background instability 6 . We have numerically observed that the small change of the parameter describing IRS leads to qualitatively different behavior of the evolution of pulse amplitudes 7 . We proved that the strong dependence of the pulse dynamics on the IRS is related to the existence of the Poincare-Andronov-Hopf bifurcation 7 . It has been established that under the influence of the higher-order effects on the dynamics of the localized pulsating solutions of CCQGLE can be transformed in fixed-shape solutions 8 . The aim of this work is to study the influence of the saturation of the nonlinear refraction index, self-steepening and TOD below the bifurcation point of the appearance of the Poincare-Andronov-Hopf bifurcation 7 . We develop soliton perturbation theory (SPT) 2 for the CCQGLE with higher-order effects. Obtained results by means of SPT are verified by numerical solution of the generalized CCQGLE performed by means of the fourth-order Runge-Kutta interaction picture method. 2. BASIC EQUATION The propagation of ultra-short pulses in the presence of spectral filtering, linear and nonlinear gain/loss, as well as higher order effects: IRS, TOD and self-steepening is described by the following generalized CCQGLE 1, 6 :