透過係数
透過波側の自由空間と誘電体の境界面を
z
=
0
にとると,導体素子がない場合の透過波の接線電界
E
t
,
tan
は,
(1)
E
t
,
tan
|
z
=
0
=
{
T
t
e
E
−
V
1
TE
−
(
u
t
×
u
z
)
+
T
t
m
E
−
V
1
TM
−
u
t
}
e
j
k
t
⋅
ρ
また,導体素子による散乱波の接線電界
E
s
,
tan
は,
(2)
E
s
,
tan
|
z
=
0
=
1
d
x
d
y
∑
m
,
n
G
¯
¯
~
T
(
d
o
)
E
J
(
k
t
m
n
)
⋅
J
~
s
(
k
t
m
n
)
e
j
k
t
m
n
⋅
ρ
この境界面での全透過波
E
t
,
tan
(
FSS
)
を,反射波と同様に次のようにフロケモードで展開する.
E
t
,
tan
(
FSS
)
=
E
t
,
tan
|
z
=
0
+
E
s
,
tan
|
z
=
0
(3)
=
∑
m
,
n
{
V
[
m
n
]
−
(
u
t
m
n
×
u
z
)
+
V
(
m
n
)
−
u
t
m
n
}
e
j
k
t
m
n
⋅
ρ
透過係数を求めるため,両者を等しくおき,両辺に
ψ
00
∗
(
ρ
)
=
e
−
j
k
t
00
⋅
ρ
を乗じ,単位セル
S
にわたり積分して,
∫
S
[
∑
m
,
n
{
V
[
m
n
]
−
(
u
t
m
n
×
u
z
)
+
V
(
m
n
)
−
u
t
m
n
}
e
j
k
t
m
n
⋅
ρ
]
e
−
j
k
t
00
⋅
ρ
d
S
=
∫
S
[
{
T
t
e
E
−
V
1
TE
−
(
u
t
×
u
z
)
+
T
t
m
E
−
V
1
TM
−
u
t
}
e
j
k
t
⋅
ρ
]
e
−
j
k
t
00
⋅
ρ
d
S
(4)
+
∫
S
[
1
d
x
d
y
∑
m
,
n
G
¯
¯
~
T
(
d
o
)
E
J
(
k
t
m
n
)
⋅
J
~
s
(
k
t
m
n
)
e
j
k
t
m
n
⋅
ρ
]
e
−
j
k
t
00
⋅
ρ
d
S
直交性より,
{
V
[
00
]
−
(
u
t
×
u
z
)
+
V
(
00
)
−
u
t
}
(5)
=
{
T
t
e
E
−
V
1
TE
−
(
u
t
×
u
z
)
+
T
t
m
E
−
V
1
TM
−
u
t
}
+
1
d
x
d
y
G
¯
¯
~
T
(
d
o
)
E
J
(
k
t
)
⋅
J
~
s
(
k
t
)
これより,
(
u
t
×
u
z
)
成分,
u
t
成分は,
(6)
V
[
00
]
−
=
T
t
e
E
−
V
1
TE
−
+
1
d
x
d
y
(
u
t
×
u
z
)
⋅
G
¯
¯
~
T
(
d
o
)
E
J
(
k
t
)
⋅
J
~
s
(
k
t
)
(7)
V
(
00
)
−
=
T
t
m
E
−
V
1
TM
−
+
1
d
x
d
y
u
t
⋅
G
¯
¯
~
T
(
d
o
)
E
J
(
k
t
)
⋅
J
~
s
(
k
t
)
したがって,主偏波成分の透過係数
T
[
00
]
TE
→
TE
(TE波),
T
(
00
)
TM
→
TM
(TM波)は,
T
[
00
]
TE
→
TE
=
V
[
00
]
−
V
1
TE
−
(8)
=
T
t
e
E
−
+
1
d
x
d
y
(
u
z
×
u
t
)
⋅
G
¯
¯
~
T
(
d
o
)
E
J
⋅
J
~
s
|
V
1
TE
−
=
1
,
V
1
TM
−
=
0
T
(
00
)
TM
→
TM
=
V
(
00
)
−
V
1
TM
−
(9)
=
T
t
m
E
−
+
1
d
x
d
y
u
t
⋅
G
¯
¯
~
T
(
d
o
)
E
J
⋅
J
~
s
|
V
1
TE
−
=
0
,
V
1
TM
−
=
1
また,交差偏波成分の透過係数
T
(
00
)
TE
→
TM
,
T
[
00
]
TM
→
TE
は,
T
(
00
)
TE
→
TM
=
V
(
00
)
−
V
1
TE
−
(10)
=
1
d
x
d
y
u
t
⋅
G
¯
¯
~
T
(
d
o
)
E
J
⋅
J
~
s
|
V
1
TE
−
=
1
,
V
1
TM
−
=
0
T
[
00
]
TM
→
TE
=
V
[
00
]
−
V
1
TM
−
(11)
=
1
d
x
d
y
(
u
z
×
u
t
)
⋅
G
¯
¯
~
T
(
d
o
)
E
J
⋅
J
~
s
|
V
1
TE
−
=
0
,
V
1
TM
−
=
1
ここで,
G
¯
¯
~
T
E
J
(
k
t
)
⋅
J
~
s
(
k
t
)
=
(
u
x
u
y
)
(
G
~
x
x
G
~
x
y
G
~
y
x
G
~
y
y
)
(
J
~
x
J
~
y
)
=
(
u
t
×
u
z
u
t
)
(
sin
ϕ
i
−
cos
ϕ
i
cos
ϕ
i
sin
ϕ
i
)
(
G
~
x
x
G
~
x
y
G
~
y
x
G
~
y
y
)
(
J
~
x
J
~
y
)
=
(
u
t
×
u
z
u
t
)
(
Z
~
TE
0
0
Z
~
TM
)
(
sin
ϕ
i
−
cos
ϕ
i
cos
ϕ
i
sin
ϕ
i
)
(
J
~
x
J
~
y
)
=
(
u
t
×
u
z
u
t
)
(
Z
~
TE
sin
ϕ
i
−
Z
~
TE
sin
cos
i
Z
~
TM
cos
ϕ
i
Z
~
TM
sin
ϕ
i
)
(
∑
p
,
q
B
~
x
p
q
I
x
p
q
∑
p
,
q
B
~
y
p
q
I
y
p
q
)
(12)
=
(
u
t
×
u
z
u
t
)
(
Z
~
TE
{
sin
ϕ
i
∑
p
,
q
B
~
x
p
q
I
x
p
q
−
cos
ϕ
i
∑
p
,
q
B
~
y
p
q
I
y
p
q
}
Z
~
TM
{
cos
ϕ
i
∑
p
,
q
B
~
x
p
q
I
x
p
q
+
sin
ϕ
i
∑
p
,
q
B
~
y
p
q
I
y
p
q
}
)
これより,
(
u
t
×
u
z
)
⋅
G
¯
¯
~
T
E
J
(
k
t
)
⋅
J
~
s
(
k
t
)
(13)
=
Z
~
TE
{
sin
ϕ
i
∑
p
,
q
B
~
x
p
q
I
x
p
q
−
cos
ϕ
i
∑
p
,
q
B
~
y
p
q
I
y
p
q
}
u
t
⋅
G
¯
¯
~
T
E
J
(
k
t
)
⋅
J
~
s
(
k
t
)
(14)
=
Z
~
TM
{
cos
ϕ
i
∑
p
,
q
B
~
x
p
q
I
x
p
q
+
sin
ϕ
i
∑
p
,
q
B
~
y
p
q
I
y
p
q
}
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