Biomedical Engineering Reference
In-Depth Information
frequency
ω
0
, the molecule (treated as a classic electric dipole) will
irradiate at the Raman shifted frequency
ω
with a dipole moment
ωα ω
; (11.1)
where
α
M
is the molecular Raman polarizability. The primary ield at
p
pd
(,)= (, )
E d
Mp 0
Ed
ω
is composed of two parts.
p
(, )
0
Ed
(, )= (, )+ (, )
ω
Ed
ω
E
d
ω
;
(11.2)
0
i
0
LM0
Ed
ω
the elastically
scattered ield derived from Lorenz-Mie theory. The electric ield
associated with the Raman-shifted radiation at an observation point
r
is given by
R
(,)
Ed
ω
being the incident ield and
LM
with
i
(, )
(, )
0
0
Er
ω
which also composed of two components.
ω ω ω
; (11.3)
where
E
DIP
is the ield of the oscillating dipole
p
in the absence of the
metal NP and
E
sc
is the ield scattered by the sphere at the Raman-
shifted frequency
ω
. The Raman scattering intensity,
I
R
, is the square
of the far-ield amplitude of
E
R
and the SERS enhancement factor
G
is deined as
Er
(,)= (,)+ (,)
E
r
E r
R
DIP
sc
=
I
R
0
R
G
I
(11.4)
0
is the Raman intensity in the absence of the metal NP.
In the regime where the size of the NP is suficiently small
compared to the excitation wavelength
λ
0
, the NP will exhibit a
dipole moment,
p
0
where
I
R
3
00i
pgaEd
ω
(11.5)
where
g
0
=
(
ε
0
−
1)/(
ε
0
+
2) and is essentially the ield enhancement
averaged over the surface of the particle brought on by the incident
light excitation of the metal NP. This dipole moment,
p
0
, is also
responsible for the surface enhanced Rayleigh radiation. A molecule
located at a distance
d
away from the metal NP exhibits a dipole
moment,
p
1
which is induced by
E
p
1 Mp
=
( , )
0
p E
α ω
(11.6)
The secondary scattered ield
E
sc
also induces a dipole moment
=
( , )
0
3
p aE d
ω
(11.7)
where
g
= (
ε
− 1)/(
ε
+ 2) and thus represent the ield enhancement
of the Raman scattered radiation in the presence of the metal NP. In
the coniguration with a molecule on the surface of the NP and the
=
( , )
2
DIP
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