Lattice sums for off-axis electromagnetic scattering by gratings

We consider both the spatial domain and spectral domain forms of the Green’s function, appropriate in the electromagnetic diffraction of a plane wave incident at a general angle in the xy plane on a singly periodic structure, or grating, oriented along the x axis. We equate the spatial and spectral forms of the Green’s function, and so establish expressions from which grating lattice sums can be evaluated for oblique incidence. We also obtain a set of identities among the lattice sums. We use these lattice sums in an expression for the Green’s function, which we show to be computationally fast, if knowledge of this function at several points is required, for small values of y.