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Tunable optical true time-delay modules based on highly dispersive photonic crystal fibers (PCFs) are demonstrated to provide continuous radio-frequency squint-free beam scanning for an X-band (8-12 GHz) phased array antenna system. The dispersion of the fabricated PCF is as high as -600 ps/nm · km at 1550 nm. The time delay is continuously tunable from -31 to 31 ps between adjacent delay lines by tuning the laser wavelength continuously from 1528 to 1560 nm. The far field radiation patterns of a 1×4 subarray were measured from -45° to 45° scanning angles. Squint-free operation is experimentally confirmed.