  An electromagnetic truncated Gaussian pulse propagates through a waveguide
with piecewise different dielectric constants. The waveguide contains a
barrier, namely a region of a lower dielectric constant compared to the
neighboring regions. This set-up yields a purely imaginary wave vector in the
region of the barrier ('electromagnetic tunneling'). We exactly calculate the
time-dependent Green's function for a slightly simplified dispersion relation.
In order to observe the plain tunneling effect we neglect the distortions
caused by the wave guide in obtaining the transmitted pulse. The wave front of
the pulse travels with the vacuum speed of light. Nevertheless, behind the
barrier, the maximum of the transmitted pulse turns up at an earlier time than
in the case without an barrier. This effect will be explained in terms of the
energy flow across the barrier. The solutions obtained reproduce the shape of
the pulses measured in the tunneling experiments of Enders and Nimtz [J. Phys.
(France) I2, 1693 (1992); Phys. Rev. E48, 632 (1993); Phys. Rev. B47, 9605
(1993); J. Phys. (France) I3, 1089 (1993); 4, 565 (1994)].
