The design of surface ground-penetrating radar (GPR) antennas is inherently
difficult, primarily because the presence of the air-soil interface
greatly complicates both analytic and laboratory-based approaches
aimed at characterizing the antennas. Versatile numerical simulation
techniques capable of describing the key physical principles governing
GPR antenna radiation offer new solutions to this problem. We use
a finite-difference time-domain (FDTD) solution of Maxwell's equations
in three dimensions to explore the radiation characteristics of various
bow-tie antennas (including quasi-linear antennas) operating in different
environments. The antenna panels are either modeled as having an
infinite conductivity [i.e., a perfect electrical conductor (PEC)],
a constant finite conductivity, or a Wu-King finite-conductivity
profile. Finite conductivities are accommodated through a subcell
extension of the classical FDTD approach, with the model space surrounded
by highly efficient generalized perfectly matched layer (GPML) absorbing
boundary conditions. Our results show that input impedances, radiated
waveforms, and radiation patterns of bow-tie antennas with Wu-King
conductivity profiles are largely invariant when placed in free space
or above diverse half-space earth models. By comparison, antennas
with PEC or constant finite-conductivity panels have variable characteristics
that depend somewhat on their operating environment. Quasi-linear
antenna designs tend to be less sensitive in this respect, and hence
may be suitable for a somewhat larger variety of soil conditions
than planar bow-tie antennas characterized by large flare angles.
Antennas with constant finite-conductivity panels are considerably
more robust (i.e., less sensitive to their environment) than their
PEC analogs because the loss resistance is increased, and the range
over which a significant amount of current flow occurs is decreased
when the antenna panels are resistively loaded. For the extreme case
of Wu-King conductivity profiles, the current in the antenna panels
approaches that of a quasi-infinitesimal electric dipole. This is
shown by the surface-charge distributions on the various antennas
and by the corresponding energy radiation patterns. Unfortunately,
the favorable characteristics of the latter antennas are counterbalanced
by markedly lower radiation efficiency. For the antenna designs considered
in this study, we found that the peak energy radiated into earth
models from bow-tie antennas with Wu-King conductivity profiles is
about one order of magnitude lower than for antennas with PEC terminals.