This paper presents a new photonic integrated circuit, namely optical pulse-train generator, which is developed based on the transfer matrix analysis of microrings and utilizes a time-interleaved architecture. This circuit can generate multiple optical pulses sequentially from a single trigger pulse, with the timing and amplitude of each pulse determined by circuit design. Hence it can be applied in optical arbitrary waveform generation and ultrafast electro-optic modulation. A four-tap prototype pulse-train generator design is demonstrated, and the challenge of distributed optical power combining is discussed. The design techniques presented in this paper will find use in other large scale photonic integrated circuit applications.