Time domain double diffraction at a pair of coplanar skew edges

Abstract

Abstract-This study aims at describing the field propagation in terms of pulsed rays, that are particularly advantageous when dealing with short-pulse excitations. In the framework of the Geometrical Theory of Diffraction we augment Geometrical Optics and uniform singly diffracted field solutions available in the time domain (TD), by TD doubly diffracted (DD) rays, that are expressed in simple closed forms. Impulsive double diffraction at a pair of coplanar edges is here formulated directly in the TD, as a double superposition of impulsive spherical waves. Nonuniform and uniform wavefront approximations for TD-DD fields are determined in closed form, defining two novel TD transition functions. The scalar case with either hard or soft boundary conditions is analyzed first, and then used to build an electromagnetic dyadic DD coefficient for a pair of coplanar edges with perfectly conducting faces. Particular attention is given to the definition of TD transition regions, i.e., the elliptical regions where the TD-DD field does not exhibit a ray optical behavior. The compensation mechanism by which the TD-DD fields repair the discontinuity introduced by singly diffracted fields at their shadow boundaries is also analyzed in detail. Our result for the TD-DD field excited by an impulsive spherical wave is valid only for early times, at and close to (behind) the DD ray wavefront. The TD-DD field response to a more general pulsed excitation is obtained via convolution, and if the exciting signal has no low-frequency components the range of validity of the resulting pulsed response is enlarged to later observation times behind the wavefront.

An Efficient Ray-Tracing Based Model Dedicated to Wireless Sensor Network Simulators for Smart Cities Environments

“…This solution gives good results but for separate wedges only, not for two joint wedges as found in a conventional building shape, and their iterative behavior leads to significant computation times as the number of wedges increases. Finally, Capolino and Albani [57], [58] proposed a closed-form solution for highfrequency diffraction problems from a perfectly-conducting thick screen. It is efficiently computable, strictly continuous in the transition region and still valid when the thickness becomes vanishingly small.…”

“…Although it needs the computation of generalized Fresnel integral, an efficient solution was provided in [70]. Finally, it was extended in [58] to handle 3D diffraction problems. This solution is used in this work, in combination with classical UTD coefficients when single wedge diffraction occurs (cf.…”

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

“…The pyramid is illuminated by an impulsive source, located in , which radiates a field with a spherical wavefront. In the following we use the analytic time transform (ATT) [6], [7], [14], [16], defined as…”

“…As shown in Appendix A, is the ATT of , where is the frequency-domain UTD vertex diffraction transition function used in [22]. Finally, in (8) (14) and (15) with round (16) ( round indicates the integer that is nearest to ), are the TD-UTD vertex transition function parameters (cf. [22]).…”

“…Furthermore, in [14], the authors derived their TD-UTD solution by adopting the analytic signal representation for the transient fields [6]- [8], which is particularly useful, since it provides a closed form (as opposed to numerical) expression for the convolution integral that must be calculated when the excitation is a realistic finite energy pulse. More recently, new TD-UTD solutions were introduced to describe single wedge slope diffraction [15], wedge double diffraction [16], the scattering from perfectly electrically conducting (PEC) smooth convex surfaces [17], and the radiation of a pulsed antenna placed on PEC smooth convex surfaces [18]. A preliminary expression for TD-UTD vertex diffraction was introduced in [19] for real time.…”