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The refractive-index profile of dual-mode optical fibers which makes possible dispersion-free operation at 1.55 μm wavelength is proposed. The refractive-index profile is synthetized using methods of quantum mechanics and numerical procedure. Optical fibers with this refractive-index profile have a core diameter of about 23 μm that is much larger than the core diameter of conventional single-mode fibers. Obtained results can be used for design of broad-band optical fibers.