Generation of solitons in Nonlocal media

Abstract

In this thesis, we present a systematic study, both analytically and numerically, of the formation and propagation of soliton trains by modulational instability in nonlocal as well as doped media. Firstly, we investigate, the modulational instability of continuous plane waves in weakly cubic-quintic nonlocal nonlinear media. Theoretically, the Lenz transformation and the linear stability analysis are used to study the impact of cubic and quintic nonlocalities on modualtional instability through the stability diagram in different modes of nonlinearity. Moreover, the time-dependent criterion predicting the existence of the modulational instability for any value of the wave number is expressed. In the numerical part, the direct integration of the nonlinear Schrödinger equation, with the split-step method, shows the disintegration dynamics of plane wave in weakly quintic media. Theoretical predictions are in good agreement with numerical results. Particularly, the impact of the cubic and quintic nonlocalities on modulational instability is such that higher values of the quintic nonlocality contribute to reduce the modulational instability in the system. Moreover, the three-body interaction in the model gives rise to Akhmediev breathers, which are the nonlinear manifestation of modulational instability. Secondly, we present a generation of dissipative optical soliton through modulation instability (MI), in doped fiber with correction effects. The cubic-quintic-septic complex Ginzburg-Landau equation with higher-order dispersion and gradient nonlinear terms which governs thepropagation of dispersive pulses in doped optical fiber is used. The linear stability analysis leads to the Lange-Newell’s criterion for MI of Stokes waves, boundaries domain of MI and integrated gain of MI, for the model of under consideration. We apply a statistical method to observe the influence of any physical effect on the critical frequency detuning. In the normal regime, the pyramidal form of the maximum gain is obtained when varying the values of odd dispersion coefficients. For the full model equation, the number of instability regions varies incoherently for the even dispersion coefficients, but remains constant for the odd dispersion coefficients in the same dispersion regime. Using the pseudo-spectral method, we observe the generation of train of pulses and found the soliton map induced by MI as a function of some physical effects, through the bifurcation diagram. In the absence of the gradient terms, the even complex dispersion coefficients increase the MI, and with the presence of odd dispersion coefficient, MI decreases.