Since the beginning of the 70’s, the classical differential theory of diffraction gratings was severely limited in its range of applicability by a problem of convergence. The first origin of the problem was the numerical contamination due to the growing exponential terms, now eliminated using the S-matrix algorithm [1]. The second one rose from the Fourier factorisation [2]. Rules of factorisation recently announced by Li [3] allow us to establish the differential equations satisfied by the Fourier components of the field for the most general situation: a diffracting device with 1, 2 or 3 dimension periodicity, with a transparent or lossy material, isotropic or anisotropic, and with an electric and magnetic permittivity tensors.

© 2002 Optical Society of America

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