Multi-core fibers (MCFs) have been the subject of extensive research in the last ten years due to their promise as high-power, single-mode lasers [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. The lowest-order mode (or so-called supermode) of an MCF represents the mode where the fields in the cores are in phase. The advantages of this in-phase supermode are that it has a large mode area with relatively low peak irradiance allowing for higher nonlinear thresholds, and hence higher output power; and is less sensitive to bend loss compared to a comparatively sized single-core step-index fiber (SIF). Several techniques have been proposed for forcing the MCF to operate in this in-phase mode, but these techniques typically use internal or external optical elements [3]. To our knowledge no one has yet precisely defined how to adjust fiber parameters to ensure the existence of this desired mode.
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