Impact of higher-order dispersions and non-kerr nonlinearities on soliton pulse trains induced by modulational instability in doped and undoped optical fibers

Abstract

We start by considering the theory of electromagnetic waves, from the Maxwell’s equa tions, the extended (1+1)D complex Ginzburg-Landau equation, higher-order nonlin ear Schr¨odinger equation are derived with the third, fourth, fifth and sixth-order dis persions and the cubic, quintic, and septic nonlinear terms, describing the dynamics of extremely short pulses in nonlinear undoped and doped optical fibers. The linear stability analysis is employed to extract an expression for the modulational instability gain of a CW solution. The sensitivity of the system to higher-order dispersions and nonlinear terms is extensively shown the insinstance on the balance of interactions between the sixth-order dispersion and nonlinerarity, septic self-steepening and the septic self-frequency shift terms. The system is confronted to full numerical simula tions, pointing out that the input CW gives rise to a broad range of behaviors, in relation to nonlinear patterns formations in the derived HNLS equation. To much excitement, under the motivation of modulational instability, a suitable balance be tween the sixth-order dispersion and the septic self-frequency shift term is achieved to bring forth some high influence on the propagation direction of the optical wave patterns.