A general numerical solution for the analysis of a class of infinite parallel plate gratings

The problem of electromagnetic scattering by a planar array of metallic rectangular cylinders, shown in Figure 1, has long been the subject of considerable interest because of their relevance to the design of microwave polarizers, filters, reinforced radomes, power dividers, artificial dielectrics, etc. Although numerous analyses and experiments of the same or similar subject can be found in the literature [1-4], most of them deal with special cases in which the plane of incidence is either perpendicular or parallel to the edges of parallel plates. Furthermore, each of the different geometries has been treated individually, thus, formulation and computation procedures set up for one geometry cannot be readily adapted to solve another geometry of similar nature. In this paper, the scattered fields of a class of infinite grating problems such as shown in Figures 1 through 3 can be predicted accurately by one computer program. There is no restriction on the polarization or the direction of the incident plane wave. The space between the conducting plates may be filled with dielectric. If the grid spacing is less than one half free space wavelength, which is true for most practical engineering applications, the computation only involves a three by three complex matrix inversion which can be easily done with a small computer.