Modal gain characteristics of few-mode erbium-doped fiber amplifiers with pump mode beating

Using the linear polarization (LP) mode decomposition method, we theoretically analyze the beat effect between the same polarization components of the vector pump modes and propose a pump beat model of few-mode erbium-doped fiber amplifiers (FM-EDFAs). The relationship of the overlap factor with the signal gain in the beat model is verified by the amplification of LP01 and LP11 modes for the first time, that is, the differential modal gain (DMG) is dependent on the integral of the overlap factor difference over the EDF length. We also simulate the effect of pump mode beating on signal amplification: the modal gain varies periodically with the pump mode phase, and the beat length can affect the fluctuation period and amplitude of the DMG. The DMG can further be reduced by controlling the initial phases of the vector modes and properly designing the beat length of the FM-EDF. The similar process can expand to more signal modes, such as the simultaneous amplification of LP01x, LP11ex, LP11oy, LP21ex and LP21oy modes. The LP mode decomposition method is also applied to the beat effect between signal modes or the amplification of orbital angular momentum (OAM) modes. One can expect to implement an experiment on the FM-EDFA amplification with pump mode beating by optimally designing the FM-EDF structure, using a properly narrow linewidth pump laser and precisely controlling the pump mode coherence.