Few-Mode Gain-Flattening Filter Using LPFG in Weakly-Coupled Double-Cladding FMF

Recently, few-mode Erbium-doped fiber amplifiers (FM-EDFA) for mode-division multiplexing (MDM) transmission have attracted much interest. In this paper, we propose a novel few-mode gain-flattening filter (FM-GFF) based on long-period fiber gratings (LPFG) in double-cladding few-mode fiber (DC-FMF). Due to weak coupling among all the core modes and limited number of inner-cladding modes, the phase matching condition for a specific FM-LPFG can be satisfied only between one core mode and one inner-cladding mode each time and independent gain flattening can be realized for each core mode without influencing the other ones. Moreover, both DC-FMF and transmission FMF have the same core refractive index and radius, while the inner-cladding of DC-FMF and the cladding of transmission FMF have the same refractive index, which can effectively maintain the weakly-coupled condition for their connections. We show by simulation that the output gain spectra for all the 4 or 6 linearly-polarized (LP) core modes in two kinds of DC-FMFs can be independently flattened to less than 0.6-dB in the whole C-band by the cascading LPFGs in the DC-FMF. The proposed FM-GFF scheme is beneficial for the practical design of FM-EDFAs.