Abstract-The Modal Method by Gegenbauer polynomials Expansion (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.

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This paper concerns a modal method for designing metal-plate lens structures. The method is based on coordinate transformation and the use of Maxwell's equations written under the covariant form. Furthermore the lens is considered as a medium with discontinuities described by Dirac Delta functions. We illustrate the method by showing the formation of the focus for various incident waves.