The longitudinal electro optic effect and the multi dimensional isotropic acousto optic effect in square system and cubic system are researched. KDP of the square system and GaP of the cubic system are determinated as optimum crystals for multi dimensional isotropic acousto electro optic devices. Through calculating the function characters of acousto optic interaction in the two crystals, some optimum operating modes for its two dimensional, three dimensional and four dimensional isotropic acousto electro optic effect are determinated. The results will lay a foundation for design and manufacture this kind of devices. Multi dimensional acousto electro optic devices have applications in multi channel optic communication and optic signal processing.