Efficient algorithm for evaluating electromagnetic scattering from cylinder illuminated by three-dimensional sources

An efficient method is presented for the analysis of the electromagnetic scattering from a cylinder illuminated by distributed three-dimensional (3D) sources. The motivation of the work arises by the need to include in the analysis of large reflector antennas the effect of the spherical wave blockage of struts of various cross-section (A. Toccafondi et al., IEEE AP–45, May 1997, pp 851–857). For this application, the scattered field from the strut illuminated by the primary field is used to correct the physical optics (PO) currents on the main reflector. Due to the large amount of calculation involved in this process, our goal is the numerical efficiency. The basic building block of the problem is the derivation of the dyadic dipole source Green’s function. It is well known that the exact solution can be found from the spectral synthesis of 2D Green’s function (2D-GF) (i.e. by spectral integration of the response to phased line source excitation). The fundamental steps of this procedure can be found in the Felsen and Marcuvitz book, with reference to circular cross section and perfectly conducting cylinders. The extension of this ”spectral synthesis” to general cross section and boundary conditions was presented in (P-S. Kildal et al., IEEE AP–44, Aug. 1996, pp 1183–1192) and subsequently applied in a series of papers concerning antenna problems; there, the 2D-GF has been calculated numerically by solving, for each longitudinal spectral wavenumber, the 2D integral equation relevant to the transverse cross-section. The above method is rigorous and accurate, but not so fast as required for the purpose. On the other hand, a brute application of PO to the cylinder surface is not accurate enough for small radius in terms of a wavelength and it does not account creeping waves and/or shadow region diffraction effects. Other method (M. Lumholt et al., AP–2000 Millenium Conf. on Antennas and Propagat.,9-14 April 2000, Davos, Switzerland) that leads to good results in various cases, has been presented to reduce numerical complexity of the problem and to describe the induced currents in shadow region. As a good compromise of efficiency and accuracy, we have developed a method, similar to the last cited, which is presently valid for perfectly conducting cylinders. For a given source, the cylinder is subdivided along its axis in small slices, in terms of wavelengths. On each slices the incident and scattered electric field are expanded in terms of cylindrical harmonics. Then, the unknown coefficients of the scattered field are evaluated considering an indefinite cylinder having equal cross section and by imposing appropriate boundary conditions. Moreover, on each slice only a single spectral component is considered effective and the pertinent induced current distribution is evaluated and used for calculating the 3D scattered field. It’s worth nothing that, contrary to the PO approach, the constructed solution respects the boundary conditions on the strut. It also takes into account the creeping wave effects on the cylinder surface.