Stable scalable control of soliton propagation in broadband nonlinear optical waveguides

Abstract

We develop a method for achieving scalable transmission stabilization and switching of $N$ colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in $N$-sequence transmission is described by a generalized $N$-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of $M$ out of $N$ soliton sequences. Numerical simulations for single-waveguide transmission with a system of $N$ coupled nonlinear Schrödinger equations with $2\le N\le 4$ show excellent agreement with the predator-prey model's predictions and stable propagation over significantly larger distances compared with other broadband nonlinear single-waveguide systems. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated by the simulations. We discuss the reasons for the robustness and scalability of transmission stabilization and switching in waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss, and explain their advantages compared with other broadband nonlinear waveguides.

37 pages, 7 figures, Eur. Phys. J. D (accepted)

References in corpus (7)

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Cited by in corpus (6)

• Enhancement of transmission quality in soliton-based optical waveguide systems by frequency dependent linear gain-loss and the Raman self-frequency shift
• Frequency shifting for solitons based on transformations on the Fourier domain and applications
• Large stable oscillations due to Hopf bifurcations in amplitude dynamics of colliding soliton sequences
• Highly controllable stabilization and switching of multiple colliding soliton sequences with generic Ginzburg-Landau gain-loss
• Stabilizing optical solitons by frequency-dependent linear gain-loss and the collisional Raman frequency shift
• Fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2