On Computation of Green’s Function for 1-D Periodic Structures in Planar Layered Media

Efficient resolutions of recurring source [1] or medium boundary [2] configurations are robust tools in computational electromagnetics for developing modern engineering systems. Herein we touch upon the Green’s function (GF) of Helmholtz equation for a scatterer with infinite periodicity in a planar layered medium, as a proper combination of formulations in [1] and [2] conveying the benefits of each to the end usage. In [2], for a single electromagnetic line source (SELS) situated in the layer $\# i$, the GF observed at the layer $\# j$, the scattered field contributions through continuous integration of all the spectrum of plane waves that are reflected back and transmitted through the medium of arbitrary number of planar layers is efficiently performed via the suitable quadratures, in addition to the closed form identities of the same spectrum for the direct part representing radiation in the free-space with the wave number $k_{s}$.