Fast Estimation of Nonlinear Interference Noise in Distributed Raman-Amplified Few-Mode Fiber Links

We present a model, based on the calculation of collision integrals, for evaluating nonlinear interference noise (NLIN) in a distributed Raman-amplified, few-mode fiber (FMF), wavelength division multiplexed (WDM) link. It is first demonstrated, neglecting dispersion and power evolution along the fiber, that the collision integrals have asymptotic limits for low and high differential group delay (DGD) between the channels. A general approximated model is then derived for any DGD regime. Dispersion and power evolution are incorporated into the model via correction factors applied to the asymptotic limits, which require only a very limited number of integrals to be numerically evaluated. The accuracy of the analytical estimates is confirmed through comparison with full numerical evaluations of the collision integrals. The proposed method offers a substantial reduction in computational effort compared with direct numerical calculations, which become prohibitive in FMFs due to the large number of interfering channels and the large number of collisions caused by large DGDs between mode groups. We apply the model to a link based on a FMF supporting four mode groups and with counterpropagating distributed Raman amplification. We confirmed the significant computational efficiency and accuracy, since the largest number of channel pairs present high DGD where the model is fast and accurate. The comparison of the FMF-based system with one based on a standard single-mode fiber (SMF), loaded by the same WDM grid of each mode group of the FMF, and comparable Raman amplification scheme, shows, as expected, that the NLIN is lower in the FMF link. However, NLIN in FMF can vary significantly, with subsets of channels exhibiting notably stronger intermodal NLIN due to group-velocity (GV) matching conditions.