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.

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An approximate asymptotic high-frequency result which is convenient for engineering applications is obtained for the field exterior to a smooth perfectly conducting convex cylinder when it is illuminated by a plane wave. This result is uniform in the sense that it remains valid within the transition regions adjacent to the shadow boundaries where the pure ray optical solution based on the geometrical theory of diffraction (GTD) fails, and it automatically reduces to the GTD solution exterior to the transition regions where the latter solution becomes valid. Furthermore, this result is expressed in the simple format of the GTD, and it employs the same ray paths as in the GTD solution. This uniform result is not valid in the close neighborhood of the cylinder; hence a separate asymptotic result is presented for this special case in a form which is also convenient for applications. The asymptotic results presented here are useful for predicting the patterns of antennas radiating in the presence of convex conducting cylindrical structures.

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Abstract. A closed form solution is obtained to describe, in a physically appealing manner, the reflection and diffraction of a general astigmatic Gaussian beam which is incident on an arbitrary smooth, electricaJly large, slowly varying curved, perfectly conducting screen (or reflector). This dosed form solution is obtained via an asymptotic evaluation of the radiation integral for the fields scattered from the reflector, to within the physical optics approximation that remains valid for the present situation. The analysis developed here is particularly well suited for the fast analysis of electrically large reflector antennas by representing the feed illumination by a relatively small set of Gaussian beams launched from the feed plane. Each of these Gaussian beams after being launched undergoes reflection and diffraction at the reflector; the expressions for the reflected and diffracted fields are developed in this paper and utilized by Chou [1996] to compute the radiation pattern of large reflector antennas in a matter of a few seconds as compared to the conventional numerical physical optics integral method which takes hours on the same computer.