Time domain double diffraction at a pair of coplanar skew edges

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.