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In this paper, we propose a new approach for the generation of ultralow jitter optical pulses using optoelectronic microwave oscillators. The short pulses are obtained through time-lens soliton-assisted compression of sinusoidally modulated prepulses, which are self-started from a conventional single-loop optoelectronic oscillator. The inherent ultralow phase noise of optoelectronic oscillators is converted into ultralow timing jitter for the generated pulses. We provide a time-domain model for the slowly varying amplitudes of the microwave and optical oscillations, and our analytical study is confirmed by numerical simulations and experimental measurements. We demonstrate the generation of 4.1 ps pulses along with a microwave whose phase noise is -140 dBc/Hz at 10 kHz from the 10 GHz carrier, with 2.7 fs jitter in the 1-10 kHz frequency band.