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Multi-core fiber capability to deliver several independent beams in a single structure has been deeply investigated to obtain spatial multiplexing in optical communication. Recently, the coherent beam multiplexing idea has been extended to high power fiber laser field, where multi-core fiber amplifiers, combining low power beams, promise to overcome thermal mode instability, which characterizes single-core fiber amplifiers. Although coherent output beam combination is advantaged in multi-core fiber, the understanding of core phase shifts is necessary to implement efficient beam combination. In presence of thermal load, induced by pump-to-signal conversion quantum defect, a refractive index gradient is formed on the multi-core fiber amplifier cross-section, thus changing core propagation properties and possibly creating unwanted core couplings. In this work a 9-core double-cladding fiber amplifier is numerically investigated by varying the core thermal load, from 2 to 15 W/m, in order to understand the structure propagation mismatch. The 9 cores are organized in a 3×3 regular grid, each core has a diameter of 19 μm and a spacing of 55 μm. Cores numerical aperture is 0.06. The outer cladding has a diameter of 340 μm. A comparison between a rod-type fiber amplifier configuration and a flexible fiber amplifier has been performed. Results show that the cores can be divided in three groups according to their propagation properties: central core, side cores, and corner ones. The phase shift between these groups, or equivalently the effective index difference, becomes higher with the increase of thermal load. These observations are fundamental to implement a model for beam propagation in presence of thermal effect, to investigate the amplification dynamics along z-direction.
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