In this paper, based on the structure characteristic of array waveguide grat-ing(AWG), and the approximately arithmetic Bloch function, the structure mode of a planar array of taped waveguides is made. The radiation characteristics and simulation of AWG are calculated, energy density and dispersion characteristics on a tapered planar AWG are discussed. Numerical results demonstrate that the most radiation power is in the Brillouin center zone Ω, the relation between transmission coefficient Tm and diffraction angle a is obtained, and the calculation is in agreement with the simulation result.