Improving the Physical Optics Approximation

Abstract

The method of physical optics (PO) is a powerful algorithm for calculation of scattering and radiation of high-frequency electromagnetic fields. The method is an approximation because it assumes that the scattered field can be found by integration of a simplified current distribution (deduced by application of geometrical optics) over the scattering surface. Despite such a simplification, PO is known to provide reasonable numerical results for the first order effects, which is the magnitude of the backscattered field or - in the case of an antenna application - the level of the main lobe in directivity diagram. For objects, whose characteristic dimension is much greater than the wavelength, PO is in many cases the only technique allowing practical calculations. As a result, PO-based computer programs have become a standard simulation tool in a broad variety of microwave applications, including antenna analysis and RCS estimations for such scatterers as an aircraft, a ship or alike. On the other hand, evolvement of new applications, progress in material science and antenna technologies have increased the demand for simulation accuracy and for an extended applicability range of the simulation methods (higher frequencies, larger and more complex scatterers, non-metallic objects, bistatic observation angles, cross-polarized field components, etc.). The goal of this paper is to estimate possible improvements which can be achieved by correcting the PO surface currents at places, where these are considerably in error. We subsequently discuss the role of the correcting currents concentrated near tips and edges in the scattering surface, as well as around shadow boundaries. The paper focuses, therefore, mostly on the fundamental limitations of the method and pays little attention to technical improvements of the standard PO algorithm, like refined meshing schemes for the scattering surface, more efficient evaluation of the radiation integral, etc. The correcting currents are derived by looking at solutions of associated problems of scattering from canonical shapes. To this end, we survey recent advances in the theory of diffraction by a wedge, a cylinder and a cone, with an emphasis on impedance configurations. Specific results include expressions for the shadow boundary currents (SBCs) on the surface of a circular impedance cylinder under oblique illumination and the edge-diffracted currents (EDCs) on a face of an impedance wedge. It is interesting to note that the EDCs are not directly representable in terms of the diffraction coefficient of the geometrical theory of diffraction, whereas the SBCs are well approximated by the known asymptotic solutions. In contrast to the SBCs and EDCs, currents induced by an incident wave near conical points on a scattering surface are very close to what the geometrical optics predicts, such that a PO solution is typically a good approximation to the scattering from a tip. The paper concludes with presenting a comparative chart of the correcting contributions.