Large stable oscillations due to Hopf bifurcations in amplitude dynamics of colliding soliton sequences

Abstract

We demonstrate that the amplitudes of optical solitons in nonlinear multisequence optical waveguide coupler systems with weak linear and cubic gain-loss exhibit large stable oscillations along ultra-long distances. The large stable oscillations are caused by supercritical Hopf bifurcations of the equilibrium states of the Lotka-Volterra (LV) models for dynamics of soliton amplitudes. The predictions of the LV models are confirmed by numerical simulations with the coupled cubic nonlinear Schrödinger (NLS) propagation models with 2 ≤ N ≤ 4 pulse sequences. Thus, we provide the first demonstration of intermediate nonlinear amplitude dynamics in multisequence soliton systems, described by the cubic NLS equation. Our findings are also an important step towards realization of spatio-temporal chaos with multiple periodic sequences of colliding NLS solitons.

Transmission stabilization in soliton-based optical-waveguide systems by frequency-dependent linear gain-loss and the Raman self-frequency shift

“…A possible way for achieving this goal is by employing frequency dependent linear gain-loss, such that the weak effects of cubic loss are balanced by weak linear gain in a frequency interval centered around the soliton frequency, while radiation emission effects are mitigated by relatively strong linear loss outside this frequency interval [16][17][18][19]. Indeed, it was shown in several recent works that the implementation of such frequency dependent linear gain-loss can lead to significant enhancement of transmission stability in multisequence soliton-based optical waveguide systems [16][17][18][19]. We therefore turn to investigate soliton propagation in the presence of frequency dependent linear gain-loss and weak cubic loss.…”

“…[16][17][18][19] in studies of multisequence soliton-based transmission: W = 10, ρ = 10, and g L = 0.5. These values were found to lead to enhanced stability of soliton propagation in multisequence transmission systems [16][17][18][19]. The values of the transmission quality distance and the final propagation distance obtained in the simulations were z q = 432 and z f = 750, which are the same as the values found for waveguides with frequency independent linear gain.…”

“…In several earlier works, we developed a general method for stabilizing the dynamics of optical soliton amplitudes in multisequence nonlinear optical waveguide systems with weak nonlinear dissipation [11][12][13][14][15][16][17][18]. The method is based on showing that amplitude dynamics induced by the dissipation in N -sequence optical waveguide systems can be approximately described by N -dimensional Lotka-Volterra (LV) models.…”

“…Further analysis showed that a major mechanism for transmission destabilization in these systems is associated with resonant emission of radiation during intersequence soliton collisions, where the emitted radiation undergoes unstable growth and develops into radiative sidebands [16,17,19]. Significant increase in the stable propagation distances was achieved by the introduction of frequency dependent linear gain-loss in N -waveguide couplers [16][17][18][19].…”

“…It was shown in these works that the presence of frequency dependent linear gain-loss leads to efficient suppression of the instability due to resonant radiation emission. The limiting cause for transmission instability in N -waveguide couplers with frequency dependent linear gain-loss was associated with non-resonant radiation emission due to the effects of the dissipation on single-soliton propagation [16,18]. Therefore, the latter process is a serious obstacle for further enhancement of transmission stability in nonlinear optical waveguide systems, where conventional optical solitons are used.…”