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LiNbO(3) single-crystal fibers with diameters of 63 and 230 mum were grown, and the second-harmonic-generation (SHG) process was studied with femtosecond laser pulses perpendicularly focused to the fiber. SHG occurred without collinear phase matching, leading to wavelength-independent overall conversion efficiency, unlike in a bulk crystal. The scattering pattern of the second harmonic exhibited an intense forward peak and an almost-uniform, less-intense distribution around the fiber, owing to trapping in high-Q whispering modes. Implementation of a second-order autocorrelator with the 63-mum fiber demonstrates its application potential.