Acceleration of the mixed-potential layered-medium Green´s functions for problems with thin layers

The mixed-potential Green´s functions arising from the Method of Moments (MoM) discretization for problems involving layered media require the computation of costly Sommerfeld integrals. The convergence of Sommerfeld integrals is usually accelerated by means of asymptotic techniques, usually based on the extraction of the asymptotic forms of the spectral integrands, which yields terms that are interpreted as images in a homogeneous medium. However, when the stratification includes very thin layers, the standard extraction scheme fails in accelerating the convergence of the integrals. Here we propose alternative extraction schemes for problems with thin layers, based on algebraic series expansions of the reflection coefficient from a thin layer. Numerical experiments will be presented to demonstrate the effectiveness of the approaches in accelerating the convergence rate of the Sommerfeld integrals.