## 1. Introduction

[2] With the rapid development of communication systems whose operation is based upon the transfer of pulsed electromagnetic fields and the detection and subsequent interpretation of the pertaining digital signals, there is a need for mathematical analysis of model configurations where the influence of (a number of) the system parameters on the performance shows analytic expressions in analytic time domain that characterize the physical behavior. The present paper aims at providing such a tool with regard to the pulsed radiation behavior of a narrow slot antenna covered with a dielectric layer in a two-dimensional setting. The source exciting the structure is modeled as a prescribed distribution of the transverse electric field across a narrow slot of uniform width in a perfectly electrically conducting planar screen. The pulse shape of the exciting field is arbitrary. In front of this slotted plane, there is a homogeneous, isotropic dielectric slab of uniform thickness. The structure further radiates into free space. Using the combination of a unilateral Laplace transformation with respect to time and the spatial slowness representation of the field components that is known as the modified Cagniard method (Cagniard-DeHoop method), analytic time domain expressions are obtained for the electric and the magnetic field as a function of position and time. The representation appears as the superposition of a number of propagating, reflecting, and refracting wave constituents in the slab and is, within any finite time window of observation, exact. It is immediately clear that the pulse shapes of these constituents (that successively reach a receiving observer) are distorted versions of the activating source signature. Parameters in this respect are the pulse shape of the excitation (characterized by the pulse risetime and the pulse time width of a unipolar pulse), the thickness and the dielectric properties of the slab, as well as the position of observation relative to the exciting slot.

[3] The analytic expressions are readily evaluated numerically. Results are presented for vanishing slot width and field pulse shapes at the dielectric/free space interface for a variety of parameters, all chosen such that the pulse time width is smaller than the travel time needed to traverse the slab. In this way, the study can focus on the changes in pulse shape that occur in the individual successive wave constituents. In line with the International Electrotechnical Vocabulary (IEV) of the International Electrotechnical Committee (IEC 60050–IEV) (http://www.electropedia.org), the signature of the excitation is taken to be a unipolar pulse characterized by its pulse amplitude, pulse risetime, and pulse time width. The power exponential pulse provides a convenient mathematical model to accommodate these parameters.

[4] Apart from this, the obtained expressions can serve the purpose of benchmarking the performance of purely computational techniques that have to be called upon in the more complicated configurations met in practice, in particular the ones in patch antenna design, where the field calculated in the present paper represents the field “incident” on the geometry of the patches.