
122 Microwave Engineering
In view of these assumptions, the Maxwell’s equations in region O and I
can be written as follows:
Region O (Air Region) Region I (Dielectric Slab Region)
∂
∂
γ ωµ
E
y
E j H
z
o y o x
+ = −
(3.77a)
o x o y
H j E
(3.77b)
− =
∂
∂
ωε
H
y
j E
x
o z
(3.77c)
∂
∂
γ ωµ
E
y
E j H
z
i y i x
+ = −
(3.78a)
i x i y
H j E
(3.78b)
− =
∂
∂
ωε
H
y
j E
x
i z
(3.78c)
Equations 3.77 and 3.78 can be manipulated to yield
∂
∂
γ ω µ ε
2
2
2 2
0
H
y
H H
x
o x o o x
+ + =
(3.79a)
∂
∂
γ ω µ ε
2
2
2 2
0
H
y
H H
x
i x i i x
+ + =
(3.80a)
∂
∂
2
2
2
0
H
y
h H
x
o x
+ =
(3.79b)
∂
∂
2
2
2
0
H
y
h H
x
i x
+ =
(3.80b)
where
h
o o o o
2 2
= +γ ω µ ε
2
(3.79c)
h
i i i i
2 2 2
= +γ ω µ ε
(3.80c)
Solution to Equation 3.79b can b ...