Diffraction of electromagnetic plane wave by a rectangular plate and a rectangular hole in the conducting plate

The problems of diffraction of an electromagnetic plane wave by a perfectly conducting rectangular plate and its complementary problem-diffraction by a rectangular hole in an infinite conducting plate-are rigorously solved using the method of the Kobayashi (1931) potential. The mathematical formulation involves dual integral equations derived from the potential integrals and the boundary condition on the plane where a plate or hole is located. The weighting functions in the potential integrals are determined by applying the properties of the Weber-Schafheitlin's integrals and the solution is obtained in the form of a matrix equation. Illustrative computations are given for the far diffracted field pattern and the current densities induced on the plate. The results of the patterns are compared with the results obtained from physical optics (PO) and the physical theory of diffraction (PTD). The agreement is fairly good, particularly with the PTD solutions.