The propagation of Gaussian beams is analyzed for an acousto-optic deflector by varying the refractive index in two-dimensions with a row of phased array piezoelectric transducers. Inhomogeneous domains of phase grating are produced by operating the transducers at different phase shifts, resulting in two-dimensional index modulation of periodic and sinc function profiles. Also different phase shifts provide a mechanism to steer the grating lobe in various directions and, therefore, the incident angle of the laser beam on the grating plane is automatically modified without moving the beam. Additionally, the acoustic frequency can be varied to achieve the Bragg condition for the new incident angle of the laser beam so that the diffraction efficiency of the deflector is maximized. The Gaussian beam is expressed in terms of planes and the second order coupled mode theory is implemented to analyze the diffraction of the beam. The diffraction efficiency is found to be nearly unity for optimal operating parameters of the acousto-optic device.