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In many practical electromagnetic (EM) antenna and scattering problems it is often useful to efficiently describe directional wave fields. It is known that a given but arbitrary radiating wave field, such as the field radiated by an aperture antenna, may be efficiently represented in terms of a distribution of Complex Point Sources (CPS) [1] on a sphere [2]. As a consequence, a CPS field representation, when combined with analytic continuation in complex space of typical ray-techniques such as the Uniform Geometrical Theory of Diffraction (UTD) [3], may provide a very efficient tool to estimate the fields radiated by large antennas in the operative environment. In this framework an extension of the Incremental Theory of Diffraction (ITD) formulation for the scattering by wedges illuminated by CPS has been recently introduced [4], which provides a description of the CPS diffraction by objects. It is found that in many cases the use of this technique overcomes the typical impairments of the GTD/UTD ray techniques associated with possible ray caustics and with the difficulties of ray tracing in complex space. On the other hand, when dealing with the description of the field radiated by large apertures or reflectors, many of the existing electromagnetic codes resort to a Physical Optics field representation also when they are illuminated by an arbitrary field. In order to augment the accuracy and the efficiency of the PO radiated field predictions, in this paper a fringe formulation of the field diffracted by edges in planar perfect electric conductor (PEC) objects when illuminated by a CPS representation of arbitrary field is presented. To this end, it is supposed that the canonical scatterer be illuminated by a proper linear combination of a finite number N of tilted and scaled CPSs in the complex space C3. The number of the expansion terms required to represent the directional field radiated by general aperture antennas are significantly less than those required for a plane-wave expansion. The advantage of this representation is that each CPS is in fact treated separately and then the final representation is recovered using the superposition principle. The formulation proceeds by first identifying spurious incremental end-point contributions that arise at the truncation of the CPS-PO induced currents over a canonical lit surface [5]. In particular these contributions are obtained by properly applying the generalized ITD localization process [6] to the integral representation of the PO diffracted field by the canonical lit half-plane. Subsequently, the incremental contributions due to the PO endpoints are subtracted from the ITD field contributions presented in [4] in order to obtain the incremental fringe coeffcients. Finally, the fringe field to be added to the PO representation is obtained by adiabatically distributing and integrating the incremental fringe contributions along the edge discontinuities of the actual surfaces. It is found that this formulation produces more accurate predictions of the diffracted field by complex objects or reflectors in presence of CPS illuminations, for which PO is commonly and extensively used. Numerical results relevant to the diffraction by a metallic disc are also presented and discussed. |
