Biomedical Engineering Reference
In-Depth Information
Summing Eq. (3.12) and Eq. (3.15), we find the total transmission
and reflection coe
cients for TM excitation:
jk
0
cos
θ
2
d
x
d
y
T
mm
=
T
mm
+
T
mm
=
1
−
e
xx
α
2
d
x
d
y
α
zx
jk
0
T
em
=
T
em
+
T
em
=−
ee
yx
me
+
sin
θα
(3.16)
jk
0
cos
θ
2
d
x
d
y
R
mm
=
R
e
mm
+
R
mm
=−
ee
xx
α
2
d
x
d
y
α
zx
jk
0
R
em
=
R
em
+
R
em
=−
ee
yx
me
+
sin
θα
The above equations compactly describe the interaction of the
metasurface with arbitrary TM impinging waves. Notice that the
relations
T
mm
=
1
+
R
mm
and
T
em
=
R
em
hold due to the continuity
of the tangential electric field on the surface, which was supposed
here to beinfinitesimally thin.
3.2.2
Transverse Electric Plane Wave Incidence
For transverse electric (TE) excitation, we can assume without
losing generality that theimpinging electric field is givenby
E
inc
=
E
0
e
−
j
√
k
0
−
k
x
z
e
−
jk
x
x
y
.
(3.17)
The radiated fields can be similarly calculated as in the previous
section, but now, also the normal component of the magnetic field
can contribute to induce transverse electric currents on the surface.
The transmitted electric field produced by the electric current
density is
⎛
k
0
−
k
x
k
0
⎞
k
x
α
xy
x
⎝
⎠
em
xz
ee
+
k
0
α
jE
0
e
−
j
k
x
x
+
√
k
0
−
k
x
z
2
d
x
d
y
k
x
α
yy
y
k
0
k
0
−
k
x
em
yz
ee
E
t
=
E
inc
−
+
+
k
0
α
,
k
0
k
x
α
e
xy
z
k
x
e
xz
−
+
k
0
α
(3.18)
