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

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.