A waveguide, such as a holey fiber or other optical fiber, is tapered to control the dispersion in a manner which varies along the length of the tapered portion of the fiber, thus providing the desired characteristics of the fiber. The longitudinal variation of the phase-matching conditions for Cherenkov radiation (CR) and four-wave mixing (FWM) introduced by DMM allow the generation of low-noise supercontinuum. The flexibility of the design permits the designer to control the tapering to select the bandwidth, the center frequency, or both. The holey fiber can be a polarization-maintaining fiber.