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Abstract
A few-mode erbium-doped fiber (FM-EDF) with a step refractive index and trench structure is designed and proposed to realize the modal gain equalization of a few-mode erbium-doped fiber amplifier (FM-EDFA). The layered-doping technology is used to reduce the mode gain difference (DMG). The doping radius and doping concentration are adjusted to obtain the optimum FM-EDF structure. When the designed FM-EDF is applied to the FM-EDFA, the DMG of the whole C-band is less than 0.15 dB and the DMG is less than 0.12 dB at 1550 nm. The minimum refractive index difference ($\Delta {n_{\text{eff}}}$) between modes can be calculated according to the refractive index and radius of the fiber core; i.e., ${1.35} \times {{1}}{{{0}}^{- 3}}$, which will greatly reduce the coupling between modes in a practical application. Tolerances in the fiber manufacturing process are also considered for reliable FM-EDFA performance. When the doping radius and concentration of each doping layer fluctuate by ${{\pm 15}}\%$ based on the precise value, the maximum DMG increases to 1.8 dB. In general, DMG can maintain a small value, which is beneficial for application in optical communications systems.
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