Diffraction characteristics of a slit in a thick conducting screen

The diffraction of a plane electromagnetic wave by a slit in a conducting screen of finite thickness is investigated using the Wiener-Hopf and generalized matrix techniques. For purposes of the analysis, the diffraction by two identical semi-infinite parallel-plate waveguides forming a tandem slit configuration is treated first in order to determine the interaction between the open ends of the waveguides. This interaction term is then utilized in solving for the thick slit geometry which is obtained by filling the parallel-plate regions with a dielectric whose relative permittivity is allowed to approach infinity. Although the integral equations occurring in the tandem slit configuration are similar to those given by Jones for the parallel-strip case, they are solved here by a somewhat different method. In contrast to the limitation on the strip-strip separation imposed by Jones, our solution is not restricted to the special case of large separation between the two slits. For an -polarized incident plane wave, the far field diffracted by each edge of the thick slit is viewed in ray-optical terms as that due to a thin edge centered at the middle of the thick edge modified by a multiplication factor. The thick edge-edge interaction term, on the other hand, is also modified such that each thick edge is viewed by the other as a combination of a line source as well as a line dipole which vanishes when the thickness approaches zero. It is shown that for ratios of screen thickness to slit width below , the beamwidth is larger than that of the thin slit, while for larger ratios the beamwidth is smaller. Typical diffraction patterns, which are in good agreement with experiment, are presented to illustrate this phenomenon.