Tapered wave with dominant polarization state for all angles of incidence

Typical applications of the method of moments (MoM) to rough surface three-dimensional (3-D) electromagnetic scattering require a truncation of the surface considered and call for a tapered incident wave. It is shown how such a wave can be constructed as a superposition of plane waves, avoiding problems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence. The proposed special choice of polarization vectors removes an irregularity at the origin of the wavenumber space and leads to a least squared error property of the wave. Issues in the application to 3-D scattering from an object over a rough surface are discussed. Approximate 3-D scalar and vector tapered waves which can be evaluated without resorting to any numerical integrations are derived and important limitations to the accuracy and applicability of these approximations are pointed out