Differential modal gain optimization for weakly-coupled few-mode multi-core erbium-doped fiber amplifiers

Space-division multiplexing (SDM) is a key technology to overcome the capacity limit of single-mode fiber systems, using multiple spatial channels in few-mode fibers, multi-core fibers, and few-mode multi-core fibers. Few-mode multi-core erbium-doped fiber amplifiers (FM-MC-EDFAs) can compensate for transmission loss via either core or cladding pumping. While both pumping schemes have been studied, a detailed quantitative comparison is still lacking. In this work, we propose a more accurate numerical model for cladding-pumped, weakly coupled FM-MC-EDFAs and design three MCF configurations: a single-mode 7-core EDF, a 2-mode 7-core EDF, and a 4-mode 7-core EDF. The doping profile of the 4-mode fiber is optimized to reduce differential modal gain. Simulations comparing core and cladding pumping show that, when gain spectra are nearly identical in the C-band, the maximum noise figure (NF) differences are 0.734 dB, 0.75 dB, and 1.18 dB for the three designs, with minimum differences of 0.302 dB, 0.31 dB, and 0.374 dB at 1565 nm. Core pumping also achieves higher power conversion efficiency (PCE) in all cases: 41.92%, 43.83%, and 30.74%, respectively. This study provides practical insights for the design of SDM optical amplifiers.