Mode competition in multi-core fiber amplifier

3D beam propagation numerical code and a newly developed optical mode solver were implemented for studies on the recently experimentally realized Yb fiber amplifier with 7-core hexagonal structure. It was found that the launched seven single-frequency beams matched with the cores converge to a wave field with permanently diminishing space beating patterns, but the result is sensitive to phases of separate beams. Namely, at a spread of phases of individual beams within a few tenths of radian, the convergence of the wave field to the in-phase mode is observed, while at phases random spread on the order of π the out-of-phase mode is dominating. Such behavior is observed at strong gain saturation in the cores. Both effects take place even if the guiding index of the cores fluctuates within a limited range. The mode solver predicts that the in-phase mode has the minimal small signal gain, and the gain of the out-of-phase mode is maximal one. This fact proves that there is no strict correlation between modal gains and amplification in strong saturated multi-core fiber. The smaller core index step significantly improves the convergence of the amplified radiation to the in-phase mode. An approach to the waveguide structure tailoring is described which assures the single in-phase mode stability.