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A low-loss criterion for bend transitions in optical fibers is proposed. An optical fiber can be tightly bent with low loss to be adiabatic for the fundamental mode, provided that an approximate upper bound on the rate of change of bend curvature for a given bend curvature is satisfied. Two typical adiabatic bend transition paths, the optimum profile and linear profile, are analyzed and studied numerically. A realizable adiabatic transition with an Archimedean spiral profile is introduced for low bend loss in tightly bent optical fibers. Design of the transitions is based on modeling of the propagation and coupling characteristics of the core and cladding modes,which clearly illustrate the physical processes involved.