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We analyze binary radially chirped Bragg fiber (RCBF) having the geometry of a binary multi-zoned microstructured fiber (MSF). As it is, in effect, a longitudinally extended binary Fresnel lens, we find that it propagates light via periodic refocusing into the center of the fiber. Zoning produces unusual dispersion properties, so we present a comparative analysis with other zoned MSF geometries, such as single-mode fiber (SMF; effectively consisting of only one zone) and conventional (unchirped) Bragg fiber. We perform an eigenmode expansion of Maxwell's equations for the three fiber geometries and find that the SMF and Bragg fiber have similar modal dispersion, with monotonic waveguide dispersion for all modes at high frequencies, whereas RCBF exhibits oscillatory behavior, with modal dispersion varying between positive and negative values as the frequency increases. This demonstrates that zoning introduces flexibility in the engineering of desired waveguide-dispersion characteristics.