Wave Propagation in Linear Media | re-examined

0.5
-0.5
I/I0
-1
3Wave propagation in electromagnetic transmission lines
100 125 150 175 200 225 250 275
Figure 3.20: Current due to a short pulse spanning two signal periods (n = 2) with = 0:2 far away
from the signal source (at X = 100).
greater than that of light. Its speed is a maximum immediately behind the entrance and
decreases as it approaches the wave front. This mirrors in fact the phase velocity of a locally
dominating frequency. In an experiment where no sharp wave front is present, however, a
su ciently narrow-band wave packet could likely be mistaken to move at a superluminal
velocity.
Fig. 3.20 nally shows what a short current pulse looks like at a considerable distance from the
tunnel entrance. The twowave fronts are clearly marked by sharp needle-like pulses. Note that
after switch-o , the residuary oscillations following the two wave fronts have slightly di erent
temporary frequencies and consequently form wave packets due to interference. Dispersion,
however, has rendered the original pulse nearly unrecognisable.
3.8 Turn-on e ects in a wave guide
As we have seen in the last section, the wave front of a TEM wave in a lossless plasma
propagates at the velocity of light. With a view to the microwave experiments carried out in
search of superluminality, we stress that the results obtained for the unbounded plasma also
hold for the TE modes of a rectangular wave guide because of the identical dispersion relation.
While the strictly causal wave front motion may seem plausible for a purely transverse wave,
there is still the open question as to how a more general mode reacts to a disturbance. In
this context, it is of particular interest how a eld component in the direction of propagation
evolves. We will thus explore the turn-on of such a mode.
The TE01 or H01 mode in a rectangular wave guide ( g. 3.21) is characterised by a longitudinal
component of the magnetic eld. The eld components perpendicular to that direction are
60
T