
97Waveguides
2. If {(m
π
/a)
2
+ (n
π
/b)
2
} >
ω
2
με
,
γ
is purely imaginary (i.e.,
γ
= j
β
), the
wave progresses (theoretically) without attenuation. The phase shift
constant of the wave is
β γ ω µε
π π
β ω µε= = −
+
= −
2
2 2
2 2 2
m
a
n
b
h
nm
or
(3.22b)
3. Lastly, if {(m
π
/a)
2
+ (n
π
/b)
2
} >
ω
2
με
, the angular frequency
ω
=
ω
c
(= 2
π
f
c
), where f
c
is referred to as the cutoff or critical frequency and
is given by
f
m
a
n
b
c
=
+
1
2
2 2
π µε
π π
(3.22c)
3.3.4 Possible and Impossible Modes
In view of Equations 3.19 and 3.21, the following conclusions can be drawn:
3.3.4.1 Lowest Possible TM Mode
In case of the TM wav