Biomedical Engineering Reference
In-Depth Information
and a normal magnetic surface current density
ω
j
m
00
d
x
d
y
z
[
V
/
m
].
K
m
=
(3.5)
We have indicated the units of
K
e
and
K
m
in these formulas for
clarity.
3.2.1
Transverse-Magnetic Excitation
For transverse-magnetic (TM) polarized excitation, without loss of
generality
η
0
e
−
j
√
k
0
−
k
x
z
e
−
jk
x
x
E
0
=
y
,
H
inc
(3.6)
where
k
0
is the wave number in free-space. The associated incident
electric field is
k
0
−
k
x
k
0
⎛
⎞
E
inc
=
e
−
j
√
k
0
−
k
x
z
e
−
jk
x
x
E
0
k
x
k
0
z
⎝
⎠
.
x
−
(3.7)
The induced averaged surface currents radiate plane waves de-
scribed by the vector potentials
e
−
j
√
k
0
−
k
x
z
K
e
,
−
j
μ
0
2
k
0
−
k
x
A
=
(3.8)
and
e
−
j
√
k
0
−
k
x
z
K
m
.
0
2
k
0
−
k
x
−
j
=
F
(3.9)
From these expressions, it is easy to calculate the transmitted
and reflected fields. First, by combining all the previous equations,
we find the total transmitted magnetic fields associated with the
magnetic potential
A
:
jE
0
e
−
j
k
x
x
+
√
k
0
−
k
x
z
2
d
x
d
y
η
0
H
t
=
H
inc
+
e
yx
k
x
z
, (3.10)
e
yx
k
0
−
k
x
x
−
α
e
xx
k
0
−
k
x
y
−
α
×
α
