Comparative analysis of the diffraction on a semi-infinite dielectric slab and a semi-infinite grounded dielectric slab

The geometries under consideration correspond to basic discontinuities that are widely used in various optical and microwave applications. There are several methods that can be used to calculate diffraction effects caused by the truncation of infinite structures. A new method based on aperture integral equations has been introduced. It allows to treat both problems associated with semi-infinite structures using a common approach. This approach is based on a fringe aperture integral equation. An equivalent magnetic current backed by a perfectly conducting wall is introduced at the edge of the semi-infinite structure. This step splits space in several regions. In the case of the grounded dielectric slab space is split in 3 regions and in case of the dielectric slab in 2 regions. The continuity conditions for the magnetic field on the aperture yield an aperture integral equation.