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International audienceThe Modal Method by Gegenbauer polynomials Expan- sion (MMGE) has been recently introduced for lamellar gratings by Edee [8]. This method shows a promising potential of outstanding convergence but still suffers from instabilities when the number of polynomials is increased. In this work, we identify the origin of these instabilities and propose a way to remove them

MODAL METHOD BASED ON SUBSECTIONAL GEGENBAUER POLYNOMIAL EXPANSION FOR LAMELLAR GRATINGS: WEIGHTING FUNCTION, CONVERGENCE AND STABILITY