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A spatial sampler for detecting transient RF and microwave signals is proposed. The sampler consists of a series of electrooptic directional couplers spatially located along an integrated-optic waveguide beneath a coplanar RF stripline. It is theoretically shown that the sampler has the potential of sampling with a temporal resolution of a few picoseconds and a sampling rate in excess of 40 billion samples per second. An electrooptic coupler with a coupling characteristic that is asymmetric with voltage is analyzed and experimentally evaluated for consideration in the sampler.