Based on the conventional MEM theory,it has been exactly calculated that coupling efficiency of the 2-d grating for long-wavelength(14.7μtm)QWIPs. The result shows that the coupling efficiency is highest when grating period D=4.7μm,grating depth h=1.45μm and d/D=0.707,and it also has been proved by geometrical optical method. Moreover,the distribution of optical field has been calculated in the diffractive grating.