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We propose and demonstrate a flexible optical clock recovery scheme using a polarization-modulator-based frequency-doubling optoelectronic oscillator (OEO). The proposed system can extract both prescaled clock and line-rate clock from a degraded high-speed digital signal using only low-frequency devices. A simple theory is developed to study the physical basis of the optical clock recovery. The OEO operation from a free-running mode to an injection-locking mode is investigated. The locking range is quantitatively predicted. An experiment is then implemented to verify the proposed scheme. A prescaled clock at 10 GHz and a line-rate clock at 20 GHz are successfully extracted from a degraded 20 Gb/s optical time-division-multiplexed (OTDM) signal. The locking range and the phase noise performance are also experimentally investigated. Clock recovery from data signals that have no explicit subharmonic tone is also achieved. The proposed system can be modified to extract prescaled clock and line-rate clock from 160 Gb/s data signal using all 40-GHz devices.