We introduce a new concept for stimulated-Brillouin-scattering-based slow light in optical fibers that is applicable for broadly-tunable frequency-swept sources. It allows slow light to be achieved, in principle, over the entire transparency window of the optical fiber. We demonstrate a slow light delay of 10 ns at 1.55 μm using a 10-m-long photonic crystal fiber with a source sweep rate of 400 MHz/μs and a pump power of 200 mW. We also show that there exists a maximal delay obtainable by this method, which is set by the SBS threshold, independent of sweep rate. For our fiber with optimum length, this maximum delay is ~38 ns, obtained for a pump power of 760 mW., "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82(26), 5229-5232 (1999). "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94(15), 153902 (2005). 8. K. Y. Song, M. Herráez, and L. Thévenaz, "Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering," Opt.