In simulations of photonic crystals the use of Rayleigh-Fourier (plane-wave) basis is widely accepted.Incorrect discretization of piece-vice dielectric permittivity using this basis may lead to lacking the convergence upon increase of the truncation order. In this communication we review the correct rules of the plane-wave discretization for diffraction by 1D gratings in TM polarization and in conical case, which were found in numerical experiments [1,2] and mathematically justified [3]. The idea behind is to preserve the continuity of the relevant fields in real space.
[1] P. Lalanne and G.M. Morris, J. Opt. Soc. Am. A 13, 779 (1996);
G. Granet and B. Guizal, J. Opt. Soc. Am. A 13, 1019 (1996).
[2] M. Auslender and S. Hava, Opt. Lett. 21, 1765 (1996).
[3] L. Li, J. Opt. Soc. Am. A 13, 1870 (1996)