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 finding a highly efficient numerical implementation. To this end, we choose all spatial approximations independent of frequency. In the first place, this concerns the inverse spatial Fourier transformation in the Sommerfeld representation of the fields. A suitable quadrature rule is obtained by introducing a normalized wave number, and identifying the result in terms of dual analytic signals. In the second place, this concerns the spectral fields for which a new integral equation is derived with a degenerate kernel. This integral equation is solved by a fully recursive procedure. Representative results are presented and discussed that can be understood from physical intuition