Biomedical Engineering Reference
In-Depth Information
polarization of the incident and scattered radiation perpendicular
to the scattering plane, the SERS enhancement factor is given by
Kerker
et al.
6
as
2
G g g gg
(11.8)
The quantity
g
or
g
0
becomes large when Re(
ε
) approaches −2 which
occurs at the surface plasmon resonance. Under this condition,
2
=51+2 +2 +4
0
0
8
G g
≈
. Thus, for a low-wavenumber Raman vibrational band
where
g
~
g
0
, the enhancement factor
G
is proportional to the fourth
power of the enhancement of the local incident near ield, i.e., |
g
|
4
or |
E
L
|
4
. Experimentally, Van Duyne
et al.
7
has deine the SERS
enhancement factor
G
as
0
I
()/
ω
ω
N
R
surf
(11.9)
G
=
0
R
I
()/
N
vol
where
N
surf
is the number of molecules bound to the enhancing
metallic substrates and
N
vol
is the number of molecules in the
excitation volume. The enhancement factor is often used as a gauge
to assess the enhancing ability of various SERS active substrates.
In summary, there are three oscillating induced dipoles,
p
0
,
p
1
,
and
p
2
; where
p
0
arises from the collective oscillation of the NP with
frequency
ω
0
while
p
1
and
p
2
are both induced dipoles oscillating with
a Raman shifted frequency
ω
. The observed Raman scattering from a
molecule positioned near a spherical NP is associated with the two
oscillating dipoles
p
1
and
p
2
both related to the induced molecular
dipole. The
p
1
dipole induces its own new local dipolar ield
E
DIP
which in turn induces a dipole
p
2
in the sphere. The readers who are
interested in a more comprehensive overview of the EM mechanism
are encouraged to a number of excellent reviews by Moskovits
8-10
and the original report by Kerker.
6,11
11.1.2
Consequences of Electromagnetic Enhancement
The EM enhancement mechanism has led to the understanding
of many characteristic SERS effects. We outline a few of the direct
consequences of the EM enhancement mechanisms in this section.
According to the EM model, the largest SERS signals are expected
when both the frequency of the incident and Raman scattering
frequency approach the surface plasmon resonance conditions, e.g.,
Re(
ε
) approaches -2 if the ambient medium is vacuum. The metals
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