High-frequency Green's function for a semi-infinite array of electric dipoles on a grounded slab. Part I: Formulation

A uniform, high-frequency solution is presented for the electromagnetic field radiated at finite distance by a semi-infinite array of elementary electric dipoles placed on an infinite grounded dielectric slab. This solution is useful for the efficient analysis of printed arrays. The field is represented in terms of a series encompassing propagating and evanescent truncated Floquet waves together with their corresponding diffracted rays, which arise from the edge of the array. The high-frequency formulation also includes surface and leaky wave contributions excited at the array edge. The diffracted waves contain discontinuities which compensate the disappearance of surface, leaky and truncated Floquet waves at their pertinent shadow boundaries. The rich variety of wave phenomena and the corresponding Geometrical Theory of Diffraction generalization will be presented in Part 11 of this paper.