A planar optical waveguide based on two-dimensional grating includes an optical waveguide substrate which is a transparent plane-parallel plate, and a functional grating element which includes a two-dimensional grating having two grating directions with an angle of 60° in between. The two-dimensional grating is either protruded or recessed into the top surface of the optical waveguide substrate. The output image from a micro-projector can enter the optical waveguide and then gets projected to cover the entire area of the functional grating element, enabling a human eye to view the output image across a large eye-box.