Transient excitation of a layered dielectric medium by a pulsed electric dipole

In this paper, we consider the transient excitation by a pulsed vertical or horizontal dipole of a continuously layered lossy dielectric slab embedded in between two dielectric half-spaces. The focus of the paper is on findin g a highly efficient numerical implementation. To this end, we choose all s patial approximations independent of frequency. In the first place, this co ncerns the inverse spatial Fourier transformation in the Sommerfeld represe ntation of the fields. A suitable quadrature rule is obtained by introducin g a normalized wave number, and identifying the result in terms of dual ana lytic signals. In the second place, this concerns the spectral fields for w hich a new integral equation is derived with a degenerate kernel. This inte gral equation is solved by a fully recursive procedure. Representative resu lts are presented and discussed that can be underdstood from physical intui tion.