  In this Letter, a ring-core erbium-doped fiber (RC-EDF), with two-layer
erbium-doped structure, supporting up to the fourth-order orbital angular
momentum (OAM) mode is designed and fabricated for OAM mode multiplexed
amplification. Using the RC-EDF, the third- and fourth-order OAM modes
amplification with ultra-low differential mode gain (DMG) is demonstrated by
observing both the modal intensity and phase distribution and measuring the
modal gain under the fundamental mode core-pumping. The measured average gain
of four modes (l=+3, -3, +4, -4) multiplexed amplification is higher than 19dB
cover the C-band and the DMG is less than 1dB. Additionally, the gain of two
conjugate OAM modes are almost the same under different pump power no matter
they are amplified simultaneously or separately.
