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We show a special effect of localization in the temporal frequency domain of light pulses that propagate in a dispersive single-mode f iber in the presence of a time-periodic phase modulation that is repeatedly applied at equally spaced locations along the f iber. The effect is analogous to the dynamical localization that occurs for the quantum kicked rotor, which is similar to Anderson localization in disordered solids. The wave behavior eliminates the diffusive spread of sidebandsdoi:10.1364/ol.24.001463 pmid:18079833 fatcat:orxdst3wfnhxdkvlnmizfkwoua