Guided-mode launching in a slab waveguide by way of diffraction at the edge of a conducting screen residing on one surface of the slab

The behavior of electromagnetic fields in the presence of a dielectric waveguide or in the presence of a perfectly electrically conducting (p.e.c.) half plane constitute two general classes of problems in the study of electromagnetics. In this report we consider the case of a p.e.c. half plane residing on one surface of a dielectric slab waveguide in a homogeneous, lossless medium. A transverse magnetic plane wave impinges on the waveguide from the side of the slab on which the half plane resides. The boundary conditions for the electric field tangential to the half plane are cast in a form amenable to a Wiener-Hopf solution, from which the scattered electric field in the interior of the slab waveguide is obtained in terms of a radiation integral. This integral is evaluated using the method of steepest descents, and the resulting electric field is separated into a geometrical optics contribution, a contribution from diffraction at the edge of the half plane, a contribution from refraction by the waveguide, and guided-mode contributions.