A uniform geometrical theory of diffraction (UTD) for curved edges illuminated by electromagnetic beams

A uniform geometrical theory of diffraction (UTD) is presented for an arbitrary curved edge in an otherwise smooth curved surface that is a perfect electric conductor (PEC), when the latter is illuminated by an electromagnetic (EM) beam. the beam type illumination may be generated by an EM point source positioned in complex space, or be due to an astigmatic Gaussian beam (ABG) incident on the edge. The UTD for an EM beam type illumination is developed from the asymptotic high frequency (HF) solutions to appropriate canonical problems of diffraction of a complex source beam (CSB) by a straight PEC wedge. The asymptotic saddle point evaluation of the canonical wedge diffraction integral is treated by the two available standard methods, namely the Pauli-Clemmow method (PCM) and the Vander Waerder Method (VWM), respectively. It is noted that the dominant terms in PCM are valid for wedge excitation by a source in real space (which produces real waves) but it is strictly not valid for a complex source (which produces a beam); however, it is the set of dominant terms in PCM that lead directly to the simple UTD format for the total field consisting of the geometrical (incident and reflected) field and diffracted field where the latter contains the UTD transition functions. Hence, it is not justifiable, apriori, to just analytically continue the previously well developed UTD solution based on PCM for PEC wedges excited by real sources and expect it to work directly for complex sources. The VWM, on the other hand, is a more general asymptotic procedure valid for complex waves, but when one retains the dominant VWM terms in their original form, it does not lead to the simpler UTD format for the total field (that is generally preferred in applications). Nevertheless, it is shown after some rearrangement of terms that it is indeed possible to write the dominant terms as VDM=PCM+Δ, where Δ is the missing correction to PCM for complex waves. Surprisingly, the �- - 394; is found to be negligible for the present problem of beam diffraction by wedges thereby allowing the PCM to remain accurate and hence allow the solution to return to the simple UTD format even though it is strictly not expected to. The explanation for why PCM is generally not valid for complex waves, and also why it works in the present problem (where Δ→O) will be given. An application of this work to the rapid analysis of large reflector antenna systems will be described.