Multi-core fibers (MCFs) are promising solutions for high power fiber based devices as they reduce nonlinearity and other unwanted detrimental effects, like transverse mode instability, by transporting, instead of a single high power beam, several low-powered ones to be coherently combined at the fiber output. This method relies on accurate evaluation of the phase differences between signals in different cores, which are significantly impacted by changes in the effective index of the propagating modes. For this to be effective, spatial heat generation must be accounted for. In particular, the heat flux from the doped cores to the external boundary causes a temperature gradient across the fiber, which affects the refractive index distribution, creating the chance for effective index change and thus dephasing of the output beams, which is harmful for beam combining. The results of in-depth numerical analysis on the performance of 9-core and 16-core MCFs under thermal effects are presented by studying the mode phase sensitivity to heat load and by introducing a coupled-mode theory model to study possible optical coupling effects. The effectively single-mode condition is also investigated by calculating the core modal overlap differences between fundamental and higher-order modes.
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