A numerical integration method based on Kirchhoff’s diffraction integral is used to determine the approximate location and shape of so-called anomalies of a blazed grating in both polarizations. Although a scalar theory is used, the phase shift on reflection accounts for the differences in polarization. Multiple diffraction within the single grating groove accounts for the anomalous behavior. The theory is compared with new experimental data on two microwave gratings.
C. Harvey Palmer and Howard W. LeBrun, "Anomalous Behavior of Blazed Gratings," Appl. Opt. 11, 907-913 (1972)