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We study the deterministic effects of Raman-induced crosstalk in amplifiedwavelength division multiplexing (WDM) optical fiber transmission lines. Weshow that the dynamics of pulse amplitudes in an N-channel transmission systemis described by an N-dimensional predator-prey model. We find the equilibriumstates with non-zero amplitudes and prove their stability by obtaining theLyapunov function. The stability is independent of the exact details of theapproximation for the Raman gain curve. Furthermore, we investigate the impactof cross phase modulation and Raman self and cross frequency shifts on thedynamics and establish the stability of the equilibrium state with respect tothese perturbations. Our results provide a quantitative explanation for therobustness of differential-phase-shift-keyed WDM transmission against Ramancrosstalk effects.

Deterministic Raman crosstalk effects in amplified wavelength division multiplexing transmission