Limits of scalar diffraction theory for conducting gratings.

Scalar diffraction theory and electromagnetic vector theory are compared by analyzing plane-wave scattering by a perfectly conducting, rectangular-grooved grating. General field solutions for arbitrary angles of incidence are derived by using scalar and vector theories. Diffraction efficiencies for the scalar and the vector cases as functions of wavelength, grating period, and angles of incidence are determined numerically and plotted. When the wavelength of the incident field is much shorter than the grating period, the diffraction efficiencies match. But when the wavelength is of the order of the grating period, large differences between the scalar and the vector solutions emerge. One general conclusion is that, depending on polarization, scalar theory should not be used when the grating period becomes smaller than ten wavelengths.