Simple selection rules for VUV and XUV diffraction gratings

The bulk of diffraction gratings used in the VUV and XUV regions are used at small angles of incidence and have shallow groove depths. Using rigorous electromagnetic theory, it is shown that such gratings behave in a scalar manner. It is then possible to derive universal efficiency curves from which one can obtain with simple rules the efficiencies of gratings with any metallic surface. The role of standard dielectric overcoatings is investigated and is found to be small. Some comparisons with experiments are given.