Raman amplification and ISRS in SDM links: Analytical evaluation and closed-form models for optical transmission

In optical communications, the Raman effect is exploited for its lasing properties in distributed Raman amplification (DRA) and leads to spectral distortions through inter-channel stimulated Raman scattering (ISRS). In single-mode fibers, these effects are well understood and modeled, but equivalent closed-form expressions for arbitrarily coupled space-division multiplexing (SDM) links are lacking. In this work, we expand upon previous literature by providing closed-form expressions modelling DRA and ISRS in common SDM fiber designs that support arbitrarily-coupled degenerate mode-groups, incorporate mode coupling, and accounting for inter-modal non-linear effects, showing excellent agreement with simulations. The derived formulas are then applied to representative scenarios, illustrating how distinct pump and fiber configurations influence gain and mode-dependent gain (MDG). Finally, we describe suggested routines for experimentally estimating the Raman response profiles of SDM fibers.