Based on the eigen mode field distribution of single mode waveguide,the RayleighSommerfeld diffraction integral formula and the reciprocal theorem of antenna theory,the coupling characteristic between two non-contact single mode planar waveguides in the coupler are presented. As the optical field superposition theorem of multiple beam interference with equal optical path difference and unequal amplitudes is engaged,the original analytic function expression of spectral response efficiency of arrayed waveguide grating multi/demultiplexer is deduced. This expression affords the theoretical basis for analyzing the characteristics of arrayed waveguide grating multi/demultiplexer accurately and quickly. An example of computing the spectral responsivity and crosstalk of arrayed waveguide grating multi/demultiplexer is presented.