WOLFRAM|DEMONSTRATIONS PROJECT

Electromagnetic Waves in a Parallel-Plate Waveguide

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mode
TM
TE
mode number n
0
1
2
3
4
5
channel width b (m)
0.25
0.5
0.75
1.
1.25
frequency f (GHz)
0.2
time in ω t (degree)
0
f >
f
c
= 0.15 (GHz) ⟶ wave passes through.
displayed fields
electric field
magnetic field
Poynting vector
(power density)
values
1000 V/m
2.654 A/m
2000 W/
2
m
displayed
0.2 m length
in red arrow
0.2 m length
in blue arrow
1 m length in
horizontal graph
Electromagnetic waves can propagate through a parallel-plate waveguide under appropriate conditions. This Demonstration determines the corresponding fields, energy distributions, and energy transport. The parallel plates support transverse magnetic (TM) and transverse electric (TE) waves. Specifying one of those modes, the mode number
n
, channel width
b
, and frequency
f
, the instantaneous fields and energy density distribution are determined for the designated time or phase
ωt
. The maximum electric field is fixed at 1000 V/m in all cases. The frequency has to be higher than the cut-off frequency
f
c
, which is determined by
b
and
n
. Taking the wave propagation direction as the
z
axis, the fields are function of
y
,
z
, and
t
. The energy flows along the channel (in the positive
z
direction).
The electric and magnetic fields are shown by red and blue arrows, respectively. The energy density is represented by color variation. The energy transport or power density equals the averaged Poynting vector, whose magnitude depends on the
y
position, as indicated by the curve on the right. The magnitudes of the fields are shown, as described in the table.