Modulational instability and soliton trains in optical fiber media with real and imaginary Raman gains

Abstract

We consider a higher-order nonlinear Schrödinger amplitude equation with real and imaginary Raman gain terms. This equation is shown to govern the propagation of femtosecond pulses in optical fiber media. We investigate on the modulational instability of continuous wave solution of this amplitude equation and show that the gain exist in both the anomalous and normal dispersion regimes, provided the complex intrapulse Raman terms are considered. However, when the dissipation induced by Raman process in the optical fiber is neglected; periodic bright solitary waves can only be identified in the anomalous dispersion regime. Nonlinear periodic trains of optical pulses are analytically obtained using the ansatz technique which incorporates the direct integral method. The observation of an optical shock front moving at the group velocity, is attributed to the Raman dissipation process in the optical fiber. Finally, results of numerical simulations equally underscores the influence of Raman gain terms on the evolution of optical soliton trains.