Generation of dissipative solitons in a doped optical fiber modeled by the higher-order dispersive cubic-quintic-septic complex Ginzburg-Landau equation

The generation of dissipative optical solitons is explored in doped fibers with correction effects under the activation of modulational instability (MI). The model, described by the cubic-quintic-septic complex Ginzburg-Landau equation, includes higher-order dispersion and nonlinear gradient terms. The Lange-Newell's criterion for MI of Stokes wave, boundary domains of MI, and integrated gain of MI are obtained via the linear stability analysis. Particular attention is given to the physical effect on the critical frequency detuning, especially in the normal regime, when varying the values of odd dispersion coefficients. Numerical simulations are undertaken and confronted with analytical predictions. Beyond the agreement between the linear stability analysis and trains of soliton generation, the soliton map induced by MI, along with the subsequent physical effects, is debated via bifurcation diagrams. This allows accurate prediction of transitions between various types of localized modes and well-calibrated generation of a wide variety of solitons with different energies. It is argued that knowing the center of mass and the energy of the generated structures can better characterize the long-time evolution of MI and, eventually, its nonlinear manifestations.