Green's Functions in Lossy Layered Media: Integration Along the Imaginary Axis and Asymptotic Behavior

This paper presents an efficient technique for eval- uating Green's functions associated to layered media, when for- mulated as Sommerfeld integrals in the space domain. The key step in the formulation is that Sommerfeld integrals are computed choosing a suitable integration path which is closed through the imaginary axis of the complex spectral plane. It is shown that with this original choice of the integration contour, the numerical effort usually involved in the evaluation of Sommerfeld integrals can be greatly reduced, specially when large source-observer distances are involved. One asset of this technique is that it can be easily incorpo- rated into integral equation based CAD packages for the efficient analysis of complex printed microwave circuit and antennas. In ad- dition, the theoretical developments needed to set up the numerical algorithm throw a new light on the asymptotic behavior of the lay- ered media Green's functions for large source-observer distances.Universidad Politécnica Federal de Lausann