Biomedical Engineering Reference
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a
=
b
1.2
1.0
0.8
E
21΄
E
21
0.6
E
x
12΄
E
y
12
E
11΄
E
11
0.4
E
31΄
E
31
0.2
E
x
22΄
E
y
22
1
2
3
4
5
6
7
8
9
10
1/2
2
b
λ
n
1
-
n
4
FIGURE 5.9
Propagation cutoff curve for λ = 10.6 μm.
evanescent mode tails occurs. Figure 5.13 illustrates such a device. The elec-
trical properties and field penetrations
e
35
and
n
24
for the parallel guides
shown in Figure 5.13 are the same as those of the isolated channel. Such
a parallel channel directional coupler can transmit both the
E
pq
x
and
E
pq
y
modes.
Following the analysis of Marcatili [5], the coupling coefficient
K
between
the two guides and the length
L
(along the
z
-direction) necessary for com-
plete transfer of power from one to the other is given by
⎛
⎜
Kx
2
*
e e
−
c e
/
2 2
⎞
⎟
⎛
⎜
π
2
⎞
⎟
=
5
5
(5.14)
−
iK
=
2
*
L
k a
* (1
+
k e
)
z
x
5
A more-accurate expression for the coupling was published by Kuznetsov
[6]. This work indicated that the Marcatili analysis overestimates the cou-
pling coefficient, especially in the weaker-guiding cases, by as much as a
factor of 2. The design program used for channel guides was also written
to calculate the coupling length
L
for any separation
C
, for identical guides,
for the X-polarized electrical field. Both the Marcatili and the Kuznetsov
values of coupling length have been determined as a direct basis for
comparison.
Following are plots of the predicted coupling lengths versus channel sepa-
rations for several representative channel waveguide designs (Figure 5.14a
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