The generalized Fresnel Integral appears as a canonical\ud
function in the uniform ray field representation of several high-frequency diffraction mechanisms, such as double wedge or vertex diffraction. Here we propose an algorithm for its calculation which is valid both for real and imaginary arguments as required for treating the general case in the uniform geometrical theory of diffraction framework
Measurement results to validate the UTD triple diffraction coefficient are presented. The experimental setup consists of multiple metallic objects, with triangular and rectangular profiles, located inside an anechoic chamber and illuminated by a sector antenna to reproduce a spherical wavefront with a Transverse Electromagnetic (TEM) incident field. Another sector antenna is moved vertically to collect electromagnetic fields across the second order UTD Incident Shadow Boundaries and in the triple diffraction transition region. The measured and theoretical fields are compared using a free space normalization. Such comparison is also validated by calculating the mean error, the standard deviation, and root mean square error that occur between the theoretical model and the measured field. The results show excellent agreement between the theoretical third order UTD solution, employing the novel triple diffraction coefficient, and the experimental results.
The purpose of this work is the description of the diffraction of a pulsed ray field, with spherical wavefront, by the vertex (tip) of a pyramid. In the framework of the uniform geometrical theory of diffraction (UTD), we augment the existing time-domain (TD) solutions available in the literature by introducing the field diffracted by a perfectly conducting faceted structure made by interconnected flat plates, for source and observation points at finite distance from the tip. The proposed closed-form expression for an exciting impulsive source has been obtained by employing the analytic time transform of the frequency-domain solution. The solution obtained is able to compensate for the discontinuities of the field predicted by standard TD-UTD, i.e., time-domain geometrical optics (TD-GO) combined with the TD-UTD wedge singly diffracted rays. The proposed result is valid only for early times, at and close to (behind) the vertex diffracted ray wavefront. The TD-UTD response to a more general pulsed excitation can be found via an efficient convolution of the TD-UTD solution for an impulsive (delta) excitation, and the general pulsed excitation itself. In particular, this convolution integral is evaluated in closed form, after expressing the analytic time transform of the general pulsed excitation as a sum of simple signals. The proposed TD-UTD vertex diffracted field is therefore suitable for analyzing the dispersion of a pulsed field due to diffraction from the tip and provides a new effective engineering tool within the UTD framework, as required in modern ray-based codes.
Index Terms-Asymptoticdiffraction theory, electromagnetic diffraction, electromagnetic transient scattering, geometrical theory of diffraction, time-domain (TD) uniform theory of diffraction, transient propagation, transient scattering, vertex diffraction. Giorgio Carluccio was born in 1979 and grew up in Ortelle, . His research interests are focused on asymptotic high-frequency techniques for electromagnetic scattering and propagation, complex source and Gaussian Beam electromagnetic field diffraction.Recently, he also worked on the development of algorithms for the analysis and design of dielectric lens antennas and of reflectarray antennas.
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