Application of a TSMFM Planar-3D Fast Integral Equation Solver for Surface Wave Characterization of Antenna Arrays

This contribution deals with a Thin stratified medium fast multipole (TSMFM) fast integral equation framework for the characterization of Planar-3D structures consisting of planar metallizations combined with vertical components like probe feeds and other vertical interconnects (vias) and especially finite dielectric regions embedded in a multilayered environment. First formulations of this type of fast integral equation solvers were presented already in [2]. In a similar approach in [1],[3], a cumbersome decomposition in radiation and receiving patterns is performed, in contrast to this we use a generalized Green's function tensor containing all integrations with regard to the vertical directions leading to a more stringent and effective implementation. Together with the different Green's functions of the structure and the residue theorem as well as steepest descent path considerations, the radiated space domain fields and especially the fields of surface waves can be determined with very high accuracy but very low computational effort. With vertical volume polarization currents, the finite extend of the substrate can be modeled quite efficiently together with the parasitic radiation of the surface waves from the edges of the substrate. Together with impedance sheets and vias with resistors this can be used to reduce the surface wave effects within antenna arrays.