Azimuthal dependence of modal gain and its impact on gain equalization in multimode erbium-doped fiber amplifiers

Azimuthal-dependent modal gain for spatially degenerate signal modes in multimode erbium-doped fiber amplifiers (MEDFAs) has been numerically investigated by integrating the differential power rate equations dealing with multiple spatial modes. Results show that if the azimuthal mode numbers in signal modes are different from that in the pump modal, gain is nearly independent of the azimuthal orientations of the pump intensity pattern. High differential modal gain (DMG) between spatially degenerate signal modes is produced if signal and pump shares the same azimuthal mode number when modal gain varies periodically with the pump azimuthal angle. Such azimuthal dependence of modal gain is caused by the transverse azimuthal dependence of population inversion of erbium ions created by pump modes. Adjusting the power and azimuth of the pump mode has also been examined to reduce azimuthal-induced DMG and several optimal parameters for achieving gain equalization have been obtained for an MEDFA supporting the two lowest LP signal mode groups. Our results can be employed to equalize mode-dependent gain in MEDFAs.