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H
y
)
z
=
h
1
and find
S
1
from
(11.24). The problem is easily converted to the spectral domain. The Fourier spectra
for the electromagnetic field are
E
y
)
z
=
h
1
E
y
)
z
=
0
E
τ
(
E
x
,
=
E
τ
(
E
x
,
into
H
τ
(
H
x
,
∞
∞
e
y
)
z
=
h
1
=
E
y
)
z
=
h
1
e
i
(
k
x
x
+
k
y
y
)
dx dy
e
τ
(
e
x
,
E
τ
(
E
x
,
−∞
−∞
(11
.
25)
∞
∞
h
y
)
z
=
h
1
=
H
y
)
z
=
h
1
e
i
(
k
x
x
+
k
y
y
)
dx dy
h
τ
(
h
x
,
H
τ
(
H
x
,
,
−∞
−∞
where
k
x
,
k
y
are the spatial frequencies. Note that there exists the linear relation
between
h
and
e
(Berdichevsky and Dmitriev, 2002):
Y
xx
Y
e
Y
Y
xy
=
=
,
.
h
(11
26)
Y
yx
Y
yy
where
Y
is the spectral admittance tensor. Its components are
Y
TM
Y
TM
k
x
k
y
k
x
+
k
x
k
x
+
Y
xx
=−
Y
xy
=−
Y
TE
Y
TM
Y
TE
−
+
−
k
y
k
y
k
y
k
x
+
Y
TM
Y
TM
,
k
x
k
y
k
x
+
Y
xy
=
Y
yy
=
Y
TM
Y
TE
Y
TE
−
−
−
k
y
k
y
(11
.
27)
where
Y
TM
and
Y
TE
are the spectral admittances in the TM- and TM-modes defined
from the Riccati equations:
k
x
+
Y
TM
dY
TM
dz
2
i
o
1
k
y
−
−
=−
z
≥
h
1
(11
.
28)
k
x
+
dY
TE
dz
o
Y
TE
2
i
o
i
o
k
y
−
+
i
=−
z
≥
h
1
.
e
y
)
z
=
h
1
e
τ
(
e
x
,
Thus,
defining
the
spectum
of
the
known
electric
field
E
y
)
z
=
h
1
and determining the spectral admittance tensor
Y
, we can calcu-
late the spectrum
h
τ
(
h
x
,
E
τ
(
E
x
,
h
y
)
z
=
h
1
and compute the magnetic field
