Toward Vector Generalized Source Integral Equations

The two-dimensional (2-D) transverse electric (TE) case is used for the development and demonstration of a vector generalized source integral equation (GSIE) formulation for the surface scattering problem, suitable for essentially-convex scatterers. The formulation uses magnetic current wires as sources for auxiliary dyadic components to the free-space Green’s function of point filamentary sources. The auxiliary component is designed to cancel the magnetic field tangential to a (perfect magnetic conductor) convex surface, acting as a shield. The resulting modified Green’s function exhibits a deeps shadow behind the shield, reduces the effective dimensionality of the interactions between large subdomains of the scatterer, and enhances the rank-deficiency of associated moment matrix blocks. The formulation complements the previously presented transverse magnetic (TM) effectively scalar 2-D formulations. As such, its derivation is a stepping stone toward that of three-dimensional GSIEs and vector auxiliary sources.