Recent stat of art in applications of diffraction gratings and stratifed materials with one or several modulated interfaces impose specific requirements on elelctromagnetic theory of gratings. 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 theoriers used is given. Their specific domain of validity is discussed, together with their advantages and shortcomings, aiming to serve as a guide in selecting a theoretical method to a scientist confronted with a specific grating problem.
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