The general behavior of two-photon absorption-enhanced refractive-index change in a third-order nonlinear optical medium is briefly described. The nonlinear medium was the solution of a new dye, trans-4-[p-(N-hydroxyethyl-N-methylamino)styryl]-N-methyl pyridinium iodide (ASPI) in dimethyl sulfoxide as the solvent, that was poured into a 20-cm-long quartz hollow fiber of 100-mum internal diameter. This dye solution has a strong two-photon absorption and subsequent upconversion fluorescence emission when excited with 1064-nm laser radiation. When the input peak intensity reached 500-1500-MW/cm(2) levels, obvious changes in beam profiles of the output IR laser beam were observed due to a self-focusing or self-trapping process occurring inside the fiber system. As a result of this process, highly directional frequency-upconverted superradiant lasing output was obtained with a beam size ~5 times smaller than that of a linearly transmitted He-Ne probe laser beam. The demonstrated mechanism can be useful for fiber laser-amplifier and fiber-integrated optics devices.