Deterministic Raman crosstalk effects in amplified wavelength division multiplexing transmission

Abstract

We study the deterministic effects of Raman-induced crosstalk in amplified wavelength division multiplexing (WDM) optical fiber transmission lines. We show that the dynamics of pulse amplitudes in an N -channel transmission system is described by an N -dimensional predator-prey model.We find the equilibrium states with non-zero amplitudes and prove their stability by obtaining the Lyapunov function. The stability is independent of the exact details of the approximation for the Raman gain curve. Furthermore, we investigate the impact of cross phase modulation and Raman self and cross frequency shifts on the dynamics and establish the stability of the equilibrium state with respect to these perturbations. Our results provide a quantitative explanation for the robustness of differential-phase-shift-keyed WDM transmission against Raman crosstalk effects.

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

“…The derivation of the model is similar to the one carried out in Refs. [7,8] for cross-talk dynamics due to stimulated Raman scattering and cubic loss, respectively. However, the resulting model and expected dynamics are quite different from those considered in Refs.…”

“…However, the resulting model and expected dynamics are quite different from those considered in Refs. [7,8]. In particular, the interaction terms in the reduced models considered in Refs.…”

“…That is, the contribution to the amplitude shift from three-body interaction is negligible. Third, the net linear gain-loss coefficients in the latter LV models are positive for some frequency channels [7,8], which might lead to second-order instability with respect to the emission of continuous waves. The third property makes these previous waveguide setups less effective for application in energy equalization in certain cases, for example, when the number of frequency channels is large.…”

“…Since pulses from different frequency channels propagate with different group velocities, interchannel pulse collisions are very frequent, and can impose severe limitations on transmission quality in high-capacity communications systems [1- 3,5,6]. On the other hand, it is possible to find ways to beneficially employ the significant cumulative collision-induced effects in broadband waveguide devices for the control and tuning of optical pulse parameters, such as energy, frequency, and phase [7,8]. A major advantage of such devices compared with singlechannel devices is that the former can simultaneously handle a large number of pulses using relatively low pulse energies.…”

“…First, the amplitude shift in a fast two-pulse collision is proportional to the product of the amplitudes of the colliding pulses [8,[21][22][23][24][25][26][27]. As a result, the interaction terms in the reduced Lotka-Volterra (LV) models for cross-talk-induced amplitude dynamics in WDM waveguide systems are only quadratic [7,8]. Second, the total amplitude shift in a typical fast three-pulse collision is given by a sum over the two-pulse interactions [8].…”