ABSTRACT
The main feature of all theoretical methods for the study of light diffraction by gratings is that the electromagnetic field is projected on some basis, and the components of the field are searched in this basis. Two principal classes of methods can be distinguished. In the first class, each of the components is a rigorous solution of Maxwell equations, but only the total sum of the components (the entire field) satisfies the boundary conditions. This implies that the field components have different expressions in the different media. After reasonable truncation, the amplitudes of the different components are determined by matching the field decompositions in the different media, which are separated by corrugated or flat interfaces. Typical example is the integral method, but the method of Chandezon and the classical modal method also belong to this class. Approximate methods based on the Rayleigh hypothesis follow the same scheme. Further on we shall refer to this class under the name of "boundary conditions methods".
