Diffraction from a Slit in an Impedance Plane Placed at the Interface of Two Semi-infinite Half Spaces of Different Media

Diffraction of an electromagnetic plane wave from a slit in an impedance plane placed at the interface of two different media, has been formulated rigorously. Both the principal polarizations are considered. The method of analysis is Kobayashi Potential (KP). To determine the unknown weighting functions, boundary conditions are imposed which resulted into dual integral equations (DIEs). These DIEs are solved by using the discontinuous properties of WeberSchafheitlin’s integrals. The resulting expressions are then expanded in terms of Jacobi’s polynomials. The problems are then, reduced to matrix equations with infinite number of unknowns whose elements are expressed in terms of infinite integrals. These integrals are hard to solve analytically. The integrals contain poles for particular values of surface impedance and are solved numerically. Illustrative computations are given for far diffracted fields and other physical quantities of interest. To check the validity of our work, we compared the far field patterns with those of obtained through Physical Optics (PO). The agreement is good.