EFFICIENT CALCULATION OF THE GREENS-FUNCTION FOR ELECTROMAGNETIC SCATTERING BY GRATINGS

We consider both the spatial domain and spectral domain forms of the G reen's function, appropriate in the electromagnetic diffraction of a p lane wave incident in the xy plane on a singly periodic structure, or grating, oriented along the x axis. For the spectral domain form, we e xhibit, for an obliquely incident plane wave, cubically convergent for ms for the Green's function and both its x and y derivatives. We compa re the spatial and spectral forms of the Green's function, and so esta blish expressions from which grating lattice sums can be efficiently e valuated for normal incidence. We use these lattice sums in an alterna tive expression for the Green's function, which we show to be computat ionally faster than the accelerated spectral domain expressions for th e Green's function if knowledge of this function at several points is required, for small values of y.