A nematic liquid-crystal spatial light modulator based on a transverse electro-optic effect is demonstrated. The transverse field is derived from the write light intensity gradient; therefore the device operates in a differentiating or edge enhancing mode. The longitudinal component of the electric field increases the write speed and provides erasure. This drive-off capability is unusual in nematic devices. A bismuth silicon oxide crystal provides photoconductive addressing in a primitive nematic device which demonstrates the effect. Initial experimental results and theory are presented.