High-frequency description of truncated-Floquet-waves and guided-waves for a semi-infinite array of line sources on a grounded dielectric slab

Several studies have been carried out on frequency- and time-domain scattering from finite periodic or quasi-periodic structures in free-space and on an infinite dielectric slab. These studies have demonstrated the effectiveness of describing the scattering phenomena in terms of truncated Floquet waves (FWs) and/or Floquet-modulated other wave types. By using the Poisson summation formula, the Green´s function of a finite array is represented collectively as the radiation from a superposition of continuous truncated FW distributions on the aperture of the array. Since the FW series exhibits excellent convergence properties when the observation point is located away from the array surface, the above representation is found more efficient than the direct summation of the spatial contributions from each element of the array, especially when each FW aperture distribution is treated asymptotically. An investigation in terms of truncated FWs of periodic and quasiperiodic arrays of metallic filaments on a dielectric slab have been carried out by Carin et al. (1996). This study was oriented for an observable based parametrization of the Floquet mode-leaky mode interaction, and did not require a fully uniform asymptotic treatment when the observation point is located at grazing and/or close to the array edge. Here, a uniform asymptotic formulation is proposed for the same problem, that allows to predict the field radiated by the array also at a distance from the edge comparable with a half-wavelength. A grounded-slab is considered as a supporting structure to render the formulation suitable for patch antennas.