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The results of a detailed study of electrooptic waveguide grating modulators are presented. Using low-loss epitaxial ZnO on sapphire waveguides with deposited interdigital electrodes diffraction percentages up to 80 percent at 80 V with rise times below 3 ns are observed. Capacitive power requirements on the order of 4 mW/MHz are predicted. A theoretical description which includes carrier and piezoelectric effects is given and is shown to be adequate for designing this type of modulator. The grating waveguide modulator spatially separates the diffracted from the main beam and thus can be used for switching. In addition, the spatial separation allows a number of these to be cascaded on a common waveguide. These features make it probable that grating modulators will find a variety of uses in integrated optics.