Cross-talk dynamics of optical solitons in multichannel waveguide systems with a Ginzburg-Landau gain-loss profile

Abstract

We investigate energy exchange in fast optical soliton collisions in Kerr nonlinear waveguides with weak linear loss, cubic gain, and quintic loss, i.e., with a Ginzburg-Landau (GL) gain-loss profile. We find that the amplitude shift in a single two-soliton collision in the presence of quintic loss is quartic in the initial soliton amplitudes, and that three-soliton interaction gives a significant contribution to the amplitude shift in a three-soliton collision. Moreover, we show that collision-induced dynamics of soliton amplitudes in a two-channel waveguide system with a GL gain-loss profile is described by a Lotka-Volterra (LV) model with quadratic and quartic interaction terms. Using the LV model, we show that linearly stable transmission with equal prescribed amplitudes can be achieved by a proper choice of the time-slot width and the ratio between the cubic gain and quintic loss coefficients. The linear stability of the transmission is confirmed by the numerical solution of a perturbed system of coupled nonlinear Schrödinger equations. Further numerical simulations show that transmission in waveguides with a GL gain-loss profile is less susceptible to radiation emission effects compared with waveguides with linear gain and cubic loss.

On the amplitude dynamics of solitons in waveguide systems with the generic Kerr nonlinearity coefficient and nonlinear gain-loss

“…We take into account the effects of the second-order dispersion, the linear gain-loss, the GL gain-loss profile, and Kerr nonlinearity with the generic Kerr nonlinearity coefficient γ. The propagation is described by the following system of coupled perturbed NLS equations [13][14][15][16] :…”

“…It is well known that the propagation of solitons in silicon waveguides can be affected by nonlinear loss, which arises due to gain or loss saturation or multiphoton absorption (MPA) 13,[18][19][20] . This can lead to a downshift of the soliton amplitude and frequency in a two-soliton collision.…”

“…16,18,21 for cubic loss and in Ref. 13 for quintic loss. The LV models were also established to study the amplitude dynamics of soliton sequences with cubic loss in Ref.…”

“…The LV models were also established to study the amplitude dynamics of soliton sequences with cubic loss in Ref. 13 and with the GL gain-loss profile in Refs. 13,14,16,22 for γ = 2.…”

“…13 and with the GL gain-loss profile in Refs. 13,14,16,22 for γ = 2. However, the expression for the collision-induced amplitude shift of two solitons with nonlinear loss and a reduced model for deterministic amplitude dynamics due to the GL gain-loss profile have not been uncovered for the generic Kerr nonlinearity coefficient.…”