Biomedical Engineering Reference
In-Depth Information
and the corresponding reflected magnetic field
jE
0
e
−
j
k
x
x
−
√
k
0
−
k
x
z
2
d
x
d
y
η
0
H
r
=
yx
k
x
z
. (3.11)
yx
k
0
−
k
x
x
xx
k
0
−
k
x
y
ee
ee
ee
×
−
α
+
α
−
α
Therefore, the transmission and reflection coe
cients for electric
fieldsduetotheinducedelectriccurrentdensityarecompactlygiven
by:
jk
0
cos
θ
2
d
x
d
y
jk
0
2
d
x
d
y
α
T
mm
=
1
−
ee
xx
;
T
em
=−
ee
yx
α
(3.12)
θ
jk
0
cos
jk
0
2
d
x
d
y
α
R
e
mm
=−
ee
xx
;
R
em
=−
ee
yx
,
α
2
d
x
d
y
k
0
−
θ
=
k
x
/
where cos
k
0
.
T
mm
(
R
mm
) and
T
em
(
R
em
) are the
transmission (reflection) coe
cients for TM incident polarization
radiating TM and TE polarizations, respectively.
Theelectricpotential
F
similarlygeneratesatransmittedelectric
field
jE
0
e
−
j
k
x
x
+
√
k
0
−
k
x
z
2
d
x
d
y
me
zx
k
x
y
,
E
t
=−
α
(3.13)
and a reflected field
jE
0
e
−
j
k
x
x
−
√
k
0
−
k
x
z
2
d
x
d
y
me
E
r
=−
α
zx
k
x
y
.
(3.14)
Therefore, the transmission and reflection coe
cients due to the
magnetic current density for TM excitationare
jk
0
sin
θ
2
d
x
d
y
α
T
mm
=
0;
T
em
=−
me
zx
(3.15)
jk
0
sin
θ
2
d
x
d
y
α
R
mm
=
0;
R
em
=−
me
zx
.
