Diffraction of a plane electromagnetic wave by a parallel plate grating with dielectric loading: the case of transverse magnetic incidence

Wave scattering and diffraction problems concerning objects with complex cross sections have been widely investigated so far with the advance of electronic computers. In this paper, a periodically placed parallel plate grating with dielectric loading is considered, and the problem of diffraction of a TM polarized plane wave is analyzed with the aid of the Wiener–Hopf technique. Introducing the Fourier transform pair for the unknown scattered field and applying boundary conditions in the transform domain, one can formulate this problem as the single Wiener–Hopf equation. This functional equation is then solved by a decomposition procedure and a rigorous solution is obtained. Furthermore, approximate solutions are derived by applying the modified residue calculus technique. Based on the above analysis, several numerical examples are given and the characteristics of this grating are discussed.