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Résumé:

Behind the appellation “modal methods”, for diffraction gratings, one can find a variety of methods sharing in common the development of the fields in terms of basis functions that can be either Fourier exponentials hence the name Fourier Modal Method (FMM), or polynomials leading to the family of Polynomial Modal Methods (Legendre, Tchebychev, and Gegenbauer). These approaches may not behave in the same way when dealing with gratings with extreme features such as a very low or very high filling ratios. In the present work, we address such a problem and compare the performances of the different Modal Methods.