  Few-mode fiber amplifier is widely under study to overcome the issue of
internet traffic in optical communication. This article proposes annulus core
few-mode erbium doped fiber (FM-EDF) with annulus or extra annulus doping for
amplification of the LP01, LP11, LP21, and LP31 signal mode groups with low
differential modal gain (DMG). Our simulations confirm that extra annulus
doping helps in reducing DMG of higher order mode groups. We have achieved less
than 2.2 dB DMG over C-band for 4-mode groups using extra annulus doping. The
proposed EDF would be useful for space division multiplexing (SDM) based
optical fiber communication system.
