High-spatial-frequency, surface-relief binary gratings have been shown to have diffraction properties that are similar to homogeneous layers of equivalent refractive indices, which depend on the grating characteristics, angle of incidence, and polarization. Thus these gratings in the long-wavelength limit could be used as equivalent thin-film coatings. Because of their polarization discrimination these gratings can function as polarization-selective mirrors. A procedure for designing these gratings to be antireflective for one polarization (TE or TM) and to maximize their reflectivity for the orthogonal polarization (TM or TE) is presented. Multilevel stairstep gratings can similarly exhibit characteristics that resemble those of multilayer antireflection coatings (quarter-wave impedance transformers), thus permitting a broader wavelength bandpass. A systematic procedure for designing multilevel stairstepgratings to operate as multilayer thin-film antireflection surfaces is presented. These design methods are valid for both TE and TM polarizations and for any angle of incidence. Example designs are presented, and the rigorous coupled-wave diffraction analysis is used to evaluate the performance of these gratings as functions of the ratio of their period to the incident wavelength. Comparisons are included with homogeneous layers that are equivalent to the gratings in the long-wavelength limit.