An asymptotic closed-form representation for the grounded double-layer surface Green´s function

An efficient closed-form asymptotic representation for the grounded double-layer (substrate-superstrate) Green´s function is presented. The formulation is valid for both source (a horizontal electric dipole) and observation points anywhere inside the superstate or at the interfaces. The asymptotic expressions are developed via a steepest descent evaluation of the original Sommerfeld-type integral representation of the Green´s function, and the large parameter in this asymptotic development is proportional to the lateral separation between source and observation points. The asymptotic solution is shown to agree with the exact Green´s function for lateral distances even as small as a few tenths of the free-space wavelengths, thus constituting a very efficient tool for analyzing printed circuits/antennas. Since the asymptotic approximation gives separate contributions pertaining to the different wave phenomena, it provides physical insight into the field behavior, as shown by examples