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The significant advantages in bandwidth and low material dispersion of perfluorinated (PF) polymer-based graded-index polymer optical fiber (GI POF) are theoretically and experimentally reported for the first time. It is confirmed that the low attenuation and low material dispersion of the PF polymer enables 1 Gb/s km and 10 Gb/s km transmission at 0.85-/spl mu/m and 1.3-/spl mu/m wavelengths, respectively. The PF polymer-based CI POF has very low material dispersion (0.0055 ns/nm/spl middot/km at 0.85 /spl mu/m), compared with those of the conventional PMMA-based POF and of multimode silica fiber (0.0084 ns/nm km at 0.85 /spl mu/m). Since the PF polymer-based GI POF has low attenuation from the visible to near infrared region, not only the 0.65-/spl mu/m wavelength which is in the low attenuation window of the PMMA-based GI POF, but other wavelengths such as 0.85-/spl mu/m or 1.3-/spl mu/m etc. can be adopted for the transmission wavelength. It is clarified in this paper that the wavelength dependence of the optimum index profile shape of the PF polymer-based GI POF is very small, compared to the optimum index profile shape of the silica-based multimode fiber. As a result, the PF polymer-based GI POF has greater tolerance in index profile variation for higher speed transmission than multimode silica fiber. The impulse response function of the PF polymer-based GI POF was accurately analyzed from the measured refractive index profile using a Wentzel, Kramers, Brillouin (WKB) numerical computation method. By considering all dispersion factors involving the profile dispersion, predicted bandwidth characteristic of the PF polymer-based GI POF agreed well with that experimentally measured.