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In
the
presence
of
lateral
inhomogeneities,
the
anomalous
field
E z z = 0 =
E A ( E x ,
E y ,
E z
H A ( H x ,
H y ,
H z
)
,
),
0
appears.
Subtracting
(I.5)
of (I.4), we arrive at equations for the anomalous field:
curl H A
N E A
=
+
j
,
(1
.
6)
curl E A
o H A
=
i
.
From these equations we deduce the integral representations for the anomalous
field:
G E ( r
r v ) j ( r v ) dV
E A ( r )
=
|
,
V
(1
.
7)
G H ( r
r v ) j ( r v ) dV
H A ( r )
=
|
,
V
where [ G E ] and [ G H ] are the electric and magnetic Green tensors for horizontally
layered medium:
G xx
G xy
G xz
G xx
G xy
G xz
G yx
G yy
G yz
G yx
G yy
G yz
[ G E ]
[ G H ]
=
,
=
.
(1
.
8)
G zx
G zy
G zz
G zx
G zy
G zz
The Green tensors satisfy the equations
curl [ G H ( r
|
N [ G E ( r
|
r v )]
=
r v )]
+
[
( r
r v )]
,
(1
.
9)
curl [ G E ( r | r v )]
=
ω o [ G H ( r | r v )]
,
i
where [
] is the diagonal matrix consisting of the scalar Dirac
-functions:
.
( r
r v )
0
0
0
( r
r v )
0
[
( r
r v )]
=
0
0
( r
r v )
Here we should clarify how the curl of Green's tensor is calculated. Let us write
[G] in the form
=
,
[ G ]
[ G x
G y G z ]
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