Biomedical Engineering Reference
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as the ratio of the transmitted intensity of the EM ield
T
metal
on the
opposite side of the metallic thin ilm to the transmitted intensity
without the metal
T
w
/
metal
.
G
is obtained using Fresnel's equation for
a three layer stacking of glass/metal/dielectric:
40
gm md
pp
tt
T
metal
(10.12)
G
=
=
(
)
gm md
T
+
1
rr
exp 2
kd
wmetal
pp
m
ij
(
g - glass; m - metal; d - dielectric)
are the
Fresnel's transmission and relection coeficients in
p
-polarization,
respectively, for the boundary between media
i
and
j
when light is
incident from
i
to
j
;
d
is the thickness of the metal thin ilm; and
k
zm
is
the component of the wave vector in the metal normal to the surface.
The resonant excitation of the SPP on one side of the metal thin ilm
induces a charge oscillation that results in an enhanced EM ield at
the metal-dielectric interface. The EM ield increases throughout
the ilm thickness to reach a maximum at the metal-dielectric
interface.
38
The calculated
G
values of the EM ield at
λ
= 634 nm for
an optimized ilm thickness of about
d
= 50 nm are 14.3 for Ag and
5.9 for Au.
ij
and
r
p
where
t
p
10.2.2.1.2
Corrugated surfaces
SPPs are usually nonradiative because their wave vector
(momentum) is greater than those of free photons of the same
frequency, resulting from the fact that the real part of the SPP
effective refractive index (
n
SPP
) is slightly larger than the refractive
index of the dielectric medium. We note that
(
)
n
εε ε ε
,
in which
ε
d
and
ε
m
are the relative permittivities of the medium
and that of the metal surface, respectively. Instead of a speciic
illumination condition, this momentum excess can be overcome
using a textured metallic surface.
Patterning the metallic surface with a periodic wavelength
scale corrugation provides an elegant solution for the excess of
the momentum. Breaking the translational invariance of a thin
ilm allows investigators to relax the momentum conservation
restriction. For a periodic modulation of period
z
, the momentum
conservation is now given by
k
SP
=
+
SPP
d m d m
′
=
k
SP
±
n g
B
where
g
B
is the grating
or Bragg wave vector that is equal to 2
π
/
z
and
n
is an integer.
Figure 10.6
shows a typical example of the effective enhancement
factor plotted as a function of the emission angle
θ
for a corrugated
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