the integration end-points are determined by the condition z s = 0 and described by the unit step function in (5). It is worth noting that for large apertures in terms of a wavelength, F po (` 0) is a rapidly oscillating function of`0of`of`0. Consequently, the integration in (3) can be asymptotically evaluated by its stationary phase point contributions, thus, leading to a UTD-type ray-field representation. However, this latter fails in describing the field close to and at the axial caustic and it has also been found less accurate with respect to the present numerical line integration for moderate sized apertures. II. NUMERICAL RESULTS Numerical results from AI (continuous line) have been compared with those from LI (dashed line) for the case of a circular OEW with radius a. In particular, Fig. 2(a) shows results for a waveguide with radius a = 0:5, excited by the TE 11 mode. The component of the electric field in the H plane is plotted at a distance r = 1:5 and r = 0:7, respectively. Both curves are normalized with respect to the maximum value obtained in the case r = 0:7; furthermore, the field is calculated in the region external to the waveguide; i.e., < 130 for r = 0:7 and < 160 for r = 1:5. Normalized near field patterns for TM 11-mode excitation are presented in Fig. 2(b). The component of the electric field in the H plane is plotted for the two cases a = 0:65, r = 1:5, and a = , r = 2, respectively. The curves corresponding to this latter case are shifted 10 dB down to render the figure more readable. In spite of the moderate size of the apertures, the agreement between the AI and its corresponding LI has been found quite satisfactory over the total 40-dB dynamic range. The small glitches arise from the fact that the IGCO integration has been turned off when L does not intersect the edge [see Fig. 1(c)]. The result presented here also suggests an effective method to speed-up practical calculations of the interaction between modes [6]. REFERENCES [1] P. Ya. Ufimtsev, "Elementary edge waves and the physical theory of diffraction,"] S. Maci, P. Ufimtsev, and R. Tiberio "Equivalence between physical optics and aperture integration for an open-ended waveguide" IEEE Abstract-A double line integral representation of the mutual coupling between open-ended waveguides of arbitrary cross section is presented, which is useful to speed up calculations inside the framework of a Galerkin method of moments.
The diffraction of an inhomogeneous plane wave by a wedge is investigated. An integral representation for the total field is obtained and then evaluated by a uniform asymptotic procedure. The solution is expressed in the form of the uniform geometrical theory of diffraction (UTD) so that it can be applied to calculate the scattering from more complex shapes. The shadow and reflection boundaries of the geometrical optics field are found to be displaced from their conventional locations. The extent of the transition regions is also described. The solution is then extended to account for dissipative losses in the medium surrounding the wedge. To demonstrate the accuracy of the UTD solution, numerical results are presented and compared with those calculated from an eigenfunction solution.at points away from its axis or on the dark side of a caustic in the focal region of a reflector antenna. A solution is sought in terms of the conventional UTD, that is, in terms of a reflected field and a diffracted field, so that it can be applied to calculate the scattering from more complex geometries with edges. The UTD solution described in this paper is being applied to calculate the scattering from polygonal cylinders located in a lossy medium.The diffraction of an inhomogeneous plane wave by a perfectly conducting half plane has been studied previously [Bertoni et al., 1978; Deschamps et al., 1979]. The solution in these papers was obtained using a procedure described by Born and Wolfe [1980], where the real angle of incidence for a homogeneous plane wave is replaced by a complex angle of incidence. An inhomogeneous plane wave results, and its diffracted field can be found from an analytic continuation of the Sommerfeld solution. However when an inhomogeneous plane wave is incident on a wedge, this simple approach can not be used if a UTD solution, which remains valid near the shadow and reflection boundaries, is desired. The reasons 1387
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