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 su rface 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 prob lems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence. The proposed special cho ice of polarization vectors removes an irregularity at the origin of the wa venumber space and leads to a least squared error property of the wave. Iss ues in the application to 3-D scattering from an object over a rough surfac e are discussed. Approximate 3-D scalar and vector tapered waves which can be evaluated without resorting to any numerical integrations are derived an d important limitations to the accuracy and applicability of these approxim ations are pointed out.