The Modal Method by Gegenbauer polynomials Expansion (MMGE) has been recently introduced for lamellar gratings by Edee [J. Opt. Soc. Am. 28, (2011)]. 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.
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