Abstract
The complete analytical solution of the diffraction problem of an arbitrary incident wave by a 2D grating of arbitrary k-vectors is provided under the Rayleigh hypothesis. It is furthermore shown by deriving an analytical solution from the exact Generalized Source Method (GSM) in the limit of small grating amplitude that the Rayleigh and the exact methods lead to the same analytical results. This proves that the results given by the Rayleigh method in the limit of shallow grooves are exact whatever the groove profile.
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