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 . The second one rose from the Fourier factorisation . Rules of factorisation recently announced by Li  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 AmericaPDF Article