Highly controllable stabilization and switching of multiple colliding soliton sequences with generic Ginzburg-Landau gain-loss
arXiv:2401.17685 · doi:10.1016/j.physd.2024.134222
Abstract
We investigate propagation of J soliton sequences in a nonlinear optical waveguide array with generic weak Ginzburg-Landau (GL) gain-loss and nearest-neighbor (NN) interaction. The propagation is described by a system of J perturbed coupled nonlinear Schrödinger (NLS) equations. The NN interaction property leads to the elimination of collisional three-pulse interaction effects, which prevented the observation of stable multisequence soliton propagation with J>2 sequences in the presence of generic GL gain-loss in all previous studies. We show that the dynamics of soliton amplitudes can be described by a generalized J-dimensional Lotka-Volterra (LV) model. Stability and bifurcation analysis for the equilibrium points of the LV model, which is augmented by an application of the Lyapunov function method, is used to develop setups that lead to robust and scalable transmission stabilization and switching for a general J value. The predictions of the LV model are confirmed by extensive numerical simulations with the perturbed coupled-NLS model with J=3, 4, and 5 soliton sequences. Furthermore, soliton stability and the agreement between the LV model's predictions and the simulations are independent of J. Therefore, our study provides the first demonstration of robust control of multiple colliding sequences of NLS solitons in the presence of generic weak GL gain-loss with an arbitrary number of sequences. Due to the robustness and scalability of the results, they can have important applications in stabilization and switching of broadband soliton-based optical waveguide transmission.
arXiv comment46 pages, 15 figures. The paper provides the first demonstration of robust control of multiple soliton sequences of the NLS equation in the presence of generic GL gain-loss with an arbitrary number of sequences. It significantly extends the results of all previous works on the topic, which were limited to two-sequence transmission or to transmission with nongeneric GL gain-loss
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