702
14 Electromagnetism II
ω mn = π c
m
a
2 +
n
b
2
1/2
(8)
which is identical with (11) of prob. (14.104).
(c) Thus the features which are identical for the TM and TE modes are
(i) ω − k plot
(ii) Phase
(iii) Group velocity
(iv) Cut-off frequency
However the important difference is that when either m = 0 or n = 0, the
TM mode fails to exist. On the other hand H z does not vanish for m = 0
or n = 0 (see (6)). Because of this fact the TE 10 is the mode which has the
lowest cut-off frequency. Here we have assumed that a > b. The cut-off
frequency for TE 10 mode is given by
ω 10 =
π c
a
(9)
the free space wavelength being 2a.
The small dimension (b) has no bearing on the cut-off frequency for this
mode. The other advantage is that single mode operation is feasible over a
wide range of frequencies.
14 Electromagnetism II
ω mn = π c
m
a
2 +
n
b
2
1/2
(8)
which is identical with (11) of prob. (14.104).
(c) Thus the features which are identical for the TM and TE modes are
(i) ω − k plot
(ii) Phase
(iii) Group velocity
(iv) Cut-off frequency
However the important difference is that when either m = 0 or n = 0, the
TM mode fails to exist. On the other hand H z does not vanish for m = 0
or n = 0 (see (6)). Because of this fact the TE 10 is the mode which has the
lowest cut-off frequency. Here we have assumed that a > b. The cut-off
frequency for TE 10 mode is given by
ω 10 =
π c
a
(9)
the free space wavelength being 2a.
The small dimension (b) has no bearing on the cut-off frequency for this
mode. The other advantage is that single mode operation is feasible over a
wide range of frequencies.