Diffraction at the edge of a truncated grounded dielectric slab

A uniform high-frequency solution is presented for the diffraction of a horizontal electric dipole located upon a truncated, semi-infinite grounded dielectric slab. This solution is achieved by an asymptotic evaluation of a diffraction Sommerfeld-type integral, which is derived by using a physical optics formulation. The final uniform result is given in terms of a geometrical optics contribution and ray-diffracted contributions from space waves, surface waves, and leaky waves. Although this asymptotic expression is derived by assuming a large distance between the source and the edge, comparisons with a numerical integration have shown very good accuracy also for a distance about 0.2 wavelength. This solution provides physical insight into the diffraction phenomenon and an effective tool for predicting the effects of finite substrates in patch antennas. Indeed, within the expected limitations of the PO approximation, the present formulation is applicable to most of the substrate thicknesses and dielectric constants of practical interest in patch antennas.