The 3-D beam propagation method (BPM) and a complementary mode solver for the passive fiber were applied for modeling fiber amplifiers with a hexagonal structure of evanescently coupled cores that have been recently experimentally realized. The modes and modal gains were calculated for 7- and 19-core systems. Diminishing the core index step from Δn = 2.57 · 10<sup>-3</sup> to Δn = 1.27 · 10<sup>-3</sup> leads to a reduction of the amount of the guided modes from 7 to 3 and from 19 to 10 for the 7- and 19-core structures, respectively. The in-phase mode that has the lowest small-signal gain for the larger index step turns to have the highest small-signal gain at the lower index step. The mechanism lying behind the observed convergence of the wave field in the laser to the in-phase-like mode was analyzed by a study of propagation of a linear combination of two multicore modes. It was found that evolution of the amplified wave field in gain saturation regime can change from dominance of one to another multicore mode at a small variation of the input wave field. The 3-D BPM modeling shows the shortage of modal approach for analyzing the multicore fiber amplifier and indicates the importance of interference between the competing modes, leading to the beatings in saturated gain.
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