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Multi-core optical fibers are provided in various embodiments of the present invention which include a plurality of cores. At least two cores of the plurality of cores have different associated mean propagation constants at a reference wavelength. The difference between the associated mean propagation constants may be selected to reduce cross-talk between the at least two cores as compared to cores having a same associated mean propagation constant. A primary coating of light absorbing material may be positioned between the cores to further reduce cross-talk. Also provided are methods for manufacturing the same and wavelength division multiplexing systems using the same.