Time-domain three-dimensional diffraction by the isorefractive wedge

The extension of the Biot-Tolstoy exact time domain solution to the electromagnetic isovelocity or isorefractive wedge is described. The TM field generated by a Hertzian electric dipole can he represented by a vector potential parallel to the apex of the wedge and a scalar potential necessitated by the three dimensionality of the magnetic field. The derivation of the former is exactly that of the pressure in the corresponding acoustic situation [1], and a more efficient version of the lengthy details is presented herein. A Lorentz gauge determines the scalar potential from the vector potential, and the diffracted field contains impulsive and "switch-on" terms that cannot be evaluated in closed form. The ratio of arrival times, at a given point, of the geometrical optics and diffracted fields provides a convenient parameter, in addition to the usual metric-related variable, for graphically displaying this scalar potential.