The Ergodic GN Model for Space-Division Multiplexing With Strong Mode Coupling

The Gaussian noise (GN) model, thanks to its simplicity, is the most widely used model to describe the nonlinear interference (NLI) in fiber-optic systems. This paper gives an extension of the GN model to space-division multiplexed (SDM) systems operating in the regime of strong coupling between modes, where the understanding of the effect of spatial mode dispersion (SMD) on the accumulation of the NLI noise stands as an open problem of utmost importance. We show that SMD may significantly reduce the NLI power and that a reliable estimation can be done with the extended GN model in very fast times, of the order of seconds per channel. We derive a closed-form expression for the NLI power averaged with respect to the frequency-dependence random-mode coupling introduced by mode dispersion, and show that its random fluctuations around the average value are negligible for all practical purposes. The derived expression is proved to be very accurate in the relevant range of SMD values. Scaling properties of the NLI variance with respect to the main system parameters are also discussed to gain some physical insight.