Biomedical Engineering Reference
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E y or E x
Constant e x 5
Constant e -x 3
x
a
ε 5
ε 3
y
Constant e - y 2
n 2
cos ( k y Y + B )
b
E y or H z
n 4
Constant e y 4
FIGURE 5.6
Field distribution of the fundamental mode 11 for a guide immersed in several dielectrics.
are E y and H x . Figure 5.6 shows the fundamental mode E 11 , characterized by
extinction coefficients n 2 , e 3 , n 4 , and e 5 in the regions where the mode is expo-
nential, and by propagation constants k x and k y in region 1. In cases where
n 3 = n 5 , the fields will be symmetric with respect to the x = 0 plane.
Quantitative expressions for k x , k y , n , and e are now determined.
Assuming that the plane wavelets that make a mode impinge on the inter-
faces at grazing angles, that is, 1/ n 1 ( n 1 n y ) ≪ 1, then k , e 3 , and h 2 are given by
1
p
a
π
A A
a
+
3
5
k
x =
+
(5.8)
1
π
1
q
b
π
2
2
1
+
n A n A
n b
+
2
2
4
4
(5.9)
k
y =
π
2
1
1
2
2
2
2
2
π
p
a
π
q
b
2
2
A A
a
+
n A n A
+
1
3
5
2
3
4
4
(5.10)
k
z =
k
+
+
1
1
1
π
π n b
1
2
 
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