Recent state-of-art applications of diffraction gratings and stratified materials with one or several modulated interfaces impose specific requirements on electromagnetic grating theory. A review of such applications is presented here with an emphasis on the aspects of the theoretical methods required for their efficiency prediction and optimization. A brief review of the basic ideas of the various electromagnetic theories used is given. The specific domain of validity for each theory is discussed together with advantages and shortcomings. The aim is to serve as a guide in selecting the most appropriate theoretical method for handling specific grating problems.
M. Nevière, E. Popov, "Grating Electromagnetic Theory User Guide" in Journal of Imaging Science and Technology, 1997, pp 315 - 323, https://doi.org/10.2352/J.ImagingSci.Technol.1997.41.4.art00003