In this paper we consider an integral equation algorithm to study
the scattering of plane waves by multilayer diffraction gratings under oblique incidence.
The scattering problem is described by a system of Helmholtz equations with piecewise
constant coefficients in R2 coupled by special transmission conditions at the interfaces between different
layers. Boundary integral methods lead to a system of singular
integral equations, containing at least two equations for each interface.
To deal with an arbitrary number of material layers we present the extension of
a recursive procedure developed by Maystre for normal incidence, which transforms the problem
to a sequence of equations with 2×2 operator matrices on each interface.
Necessary and sufficient conditions for the applicability of the algorithm are derived