article · Physical Review A
Theoretical and numerical investigations examine the formation of dissipative optical solitons in doped optical fibres governed by modulational instability. The underlying system is modelled using the cubic-quintic-septic complex Ginzburg-Landau equation, accounting for higher-order dispersion and nonlinear gradient terms. Linear stability analysis provides the Lange-Newell criterion for Stokes wave instability, alongside boundary domains and integrated gain profiles. Varying odd dispersion coefficients reveals notable effects on critical frequency detuning, particularly within the normal dispersion regime. Bifurcation diagrams and soliton maps induced by modulational instability match numerical simulations, enabling precise predictions of transitions between localized modes. This framework allows calibrated generation of diverse solitons across varying energy states, demonstrating that tracking the centre of mass and energy effectively characterizes long-term nonlinear evolution.
Understanding how light pulses form and maintain stability in doped optical fibres helps scientists control complex wave phenomena. By predicting transitions between different pulse states, researchers gain greater control over high-energy light structures, providing foundational knowledge for advanced optical signal processing and laser systems.
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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.
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DOI: 10.1103/physreva.105.023502
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