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It has already been shown that the dif- ferential method of Chandezon is well suited for analysing multilayer diffraction gratings [1]. Lifeng Li has reported significant improvments to this method [2] . He used the R-matrix propagation algo- rithm to remove the limitation on the layer thickness and on the number of layers. As far as we are con- cerned, we have allowed for different interface pro- files within the grating structure although all must share the same periodicity [3]. Preist et al have done it also [4]. Boundary conditions were expressed with the scattering matrix approach which is an alterna- tive to the R-matrix approach. The aim of this paper is to analyze multi- layer crossed gratings with the Chandezon method and the S-matrix formulation. It consists of a genera- lization of the formalism already used for 2D multi- coated gratings. The basic features lies in the use of a coordinate system that maps the interface onto a plane. In the new frame, the structure is analogous to a planar stratified medium. As in the 2D case, we are led to a linear system of differential equations whose solution is obtained through the calculation of the ei- genvalues and eigenvectors of a matrix dependant on the geometry and on the index of the medium. As an example, we shall consider cases where "anomalies" in the diffracted efficiencies occur, that is when a suitable phase matching between the incident wave and the guided wave is achieved.
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