Time-Domain UTD Vertex Diffraction Coefficient for the Scattering by Perfectly Conducting Faceted Structures

Abstract

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.

Analysis on radiation of antenna mounted on perfectly conducting convex surfaces by using NURBS‐UTD method

“…According to (4), in order to achieve one point (u j + 2 , v j + 2 ) in the trajectory, two previous points (u j + 1 , v j + 1 ) and (u j , v j ) are needed; therefore, two start points are needed to apply the algorithm, the first one is obviously the source point…”

“…Uniform geometrical theory of diffraction (UTD) is an important method in computational electromagnetic (CEM) which is quite efficient for electrically large problems. The basic theory of UTD appeared in the 1970s [1,2] and basic study still attracts attention [3][4][5][6]. Theoretically, EM fields are supposed to be carried by EM rays and most factors used to calculate EM fields are related to geometrical parameters of the scatterers.…”

Analytic impulsive time-domain UTD coefficient for pyramid-vertex diffraction

“…In the last decade new TD-UTD solutions were developed to describe single wedge slope diffraction [4], double diffraction by a pair of coplanar skew edges [5], the scattering from perfectly conducting smooth convex surfaces [6], the radiation of a pulsed antenna placed on PEC smooth convex surfaces [7]. A preliminary expression for TD-UTD vertex diffraction was introduced in [8] for real time, whereas the formulation with complex time has been outlined in [9].…”