Design of antireflection gratings with approximate and rigorous methods.

High-spatial-frequency gratings can be used as an alternative to thin-film antireflection coatings to reduce the reflectivity at the boundary between two different media. In the case of one-dimensional gratings, the conditions on the grating structure can be approximately determined by the effective medium theory (EMT) in combination with the thin-film theory. For two-dimensional gratings, which can be used to reduce the polarization sensitivity, a corresponding EMT does not exist. We present an estimation of the effective permittivity of two-dimensional gratings. The range of validity of the antireflection grating design by the EMT is determined by the use of rigorous electromagnetic theory. Beyond the validity of EMT, rigorous theory is used to design antireflection gratings with a maximized feature size.