Transient solutions for a class of diffraction problems

Abstract

The study of the fields excited by impulsive sources in layered media has been facilitated by a technique employed originally by Cagniard and Pekeris, and simplified subsequently by de Hoop. The procedure involves a reformulation of the time-harmonic solution so as to permit the explicit recovery of the transient result by inspection. In the present paper, it is shown that this method may be applied conveniently to the inversion of a certain Sommerfeld-type integral which occurs frequently in diffraction theory, thereby unifying the analysis of a class of pulse diffraction problems. Illustrative examples include the transient response to a line source in the presence of a dielectric half space, a perfectly absorbing and perfectly reflecting wedge, and a unidirectionally conducting infinite and semi-infinite screen. The latter applications illuminate the role of surface waves in the impulsive solution. It is found, in contrast to the time-harmonic case, that a different behavior characterizes the surface waves excited on a unidirectionally conducting half plane by the incident field and by the edge discontinuity, respectively.