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 ≤ N ≤ 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.

Radiation dynamics in fast soliton collisions in the presence of cubic loss

“…Almost all intersequence collisions in multisequence soliton transmission are complete collisions, i.e., collisions in which the two solitons are well-separated before and after the collision [10,14]. In addition, most intersequence collisions in these systems are fast, that is, the difference between the central frequencies (and group velocities) of the pulses is much larger than the spectral width of each pulse [10,14,15]. For this reason, in the current paper, we focus attention on the investigation of complete fast two-soliton collisions.…”

Frequency shifting for solitons based on transformations in the Fourier domain and applications

“…This ODE model was used to validate the robust propagation of solitons experiencing the linear loss and experiencing the linear gain. The soliton dynamics studied in this paper can be useful for controlling and guiding solitons, for example, for switching soliton dynamics (see [15,18] for another approach to stabilize and switch sequences of solitons by using hybrid waveguides and analyzing the ODE model for amplitude dynamics). In addition, the use of the frequency shifting was demonstrated to enable repeated two-soliton collisions in the presence of weak cubic loss and the theoretical prediction for the accumulative collision-induced amplitude shift was also measured.…”

“…In this section, we demonstrate the use of the frequency shift to enable repeated two-soliton collisions in the presence of weak cubic loss and measure the theoretical prediction for the accumulative amplitude shift. The propagation model in terms of coupled NLS equation is [15] i∂…”

“…8(d) can be used for switching soliton dynamics or for transmission recovery. In these switching processes, one can turn off (or turn on) a sequence of solitons by guiding its amplitude below (or above) a threshold amplitude value η th (see [15,18] for another approach to study the switching dynamics by using hybrid waveguides and stability analysis of the equilibrium states of the ODEs describing amplitude dynamics). The amplitude threshold value in Fig.…”

“…The use of frequency dependent linear gain-loss for the transmission stability of NLS solitons was investigated in several earlier studies such as [13,14,15]. In these papers, it has been shown that the use of frequency dependent linear gain-loss can suppress radiative effects and stabilize multisequence soliton propagation at long distances.…”