112
K. Kneipp et al.
The nonlinear polarization, which generates SRS is
P
SRS
∝ X
(3) E L (ν L ) E
∗
L (−ν L ) E S (ν S )
(2.12b)
Stimulated Raman spectroscopy can be used in an enhancing or depletion modus
by measuring an enhancement in the lower frequency “Stokes” laser field (stimulated
Raman gain), or a depletion in the higher frequency “anti-Stokes” laser field (stimulated Raman loss or inverse Raman scattering), respectively [11, 14]. Whereas CARS
requires additionally phase matching conditions between the interacting lasers, stimulated Raman spectroscopy always fulfills this momentum conservation automatically.
In the discussed coherent Raman processes, four interacting coherent optical fields
can benefit from plasmonic enhancement. The enhancement factor for the coherent
non-linear Raman processes can be written as
G SECARS =
(X
(3)
ads ) 2
(X
(3)
f ree ) 2
|A (ν L )|
4
|A (ν S )|
2
|A (ν aS )|
2
(2.13a)
G SESRS =
|X
(3)
ads | 2
|X
(3)
f ree | 2
|A (ν L )|
4
|A (ν S )|
4
(2.13b)
Here we consider that also the non-linear susceptibility can be different for
adsorbed and “free” molecules.
There are some reports on experimental demonstration of surface enhanced coherent Raman spectroscopy (SECARS) [45–50]. Silver nanoparticle aggregates, silver
films and nanostructured gold surfaces were used as plasmonic enhancing structures. SECARS enhancement factors exceeding five orders of magnitude have been
observed [49]. Recently, surface enhanced femtosecond stimulated Raman spectroscopy has been reported exploiting gold nanoantenna with embedded Raman
molecules. Using a picosecond Raman and femtosecond probe pulse, the time- and
ensemble averaged enhancement factor was estimated in the range from 10 4 − 10 6
[51].
Figure 2.3 summarizes different plasmon supported spectroscopic methods for
vibrational probing. Note that in incoherent probing, spectroscopic signals linearly
depend on the number of molecules while coherent Raman signals show a quadratic
dependence. In general, field enhancement factors A(v) depend on frequency. However, Raman shifts are relatively small and therefore, we can assume for SERS,
SEPAS and SECARS that A(v L ) ∼ A(v S ) ∼ A(v aS ) = A(v). SEIRA, SERS and
SEHRS depend on field enhancement factors A(v) to the power of two, four and six
respectively, while SEPARS, SECARS, and SESRS benefit from A(v) to the power
of eight.
For supporting different vibrational spectroscopic methods, field enhancement is
required within very different wavelength ranges including IR and THz frequencies
K. Kneipp et al.
The nonlinear polarization, which generates SRS is
P
SRS
∝ X
(3) E L (ν L ) E
∗
L (−ν L ) E S (ν S )
(2.12b)
Stimulated Raman spectroscopy can be used in an enhancing or depletion modus
by measuring an enhancement in the lower frequency “Stokes” laser field (stimulated
Raman gain), or a depletion in the higher frequency “anti-Stokes” laser field (stimulated Raman loss or inverse Raman scattering), respectively [11, 14]. Whereas CARS
requires additionally phase matching conditions between the interacting lasers, stimulated Raman spectroscopy always fulfills this momentum conservation automatically.
In the discussed coherent Raman processes, four interacting coherent optical fields
can benefit from plasmonic enhancement. The enhancement factor for the coherent
non-linear Raman processes can be written as
G SECARS =
(X
(3)
ads ) 2
(X
(3)
f ree ) 2
|A (ν L )|
4
|A (ν S )|
2
|A (ν aS )|
2
(2.13a)
G SESRS =
|X
(3)
ads | 2
|X
(3)
f ree | 2
|A (ν L )|
4
|A (ν S )|
4
(2.13b)
Here we consider that also the non-linear susceptibility can be different for
adsorbed and “free” molecules.
There are some reports on experimental demonstration of surface enhanced coherent Raman spectroscopy (SECARS) [45–50]. Silver nanoparticle aggregates, silver
films and nanostructured gold surfaces were used as plasmonic enhancing structures. SECARS enhancement factors exceeding five orders of magnitude have been
observed [49]. Recently, surface enhanced femtosecond stimulated Raman spectroscopy has been reported exploiting gold nanoantenna with embedded Raman
molecules. Using a picosecond Raman and femtosecond probe pulse, the time- and
ensemble averaged enhancement factor was estimated in the range from 10 4 − 10 6
[51].
Figure 2.3 summarizes different plasmon supported spectroscopic methods for
vibrational probing. Note that in incoherent probing, spectroscopic signals linearly
depend on the number of molecules while coherent Raman signals show a quadratic
dependence. In general, field enhancement factors A(v) depend on frequency. However, Raman shifts are relatively small and therefore, we can assume for SERS,
SEPAS and SECARS that A(v L ) ∼ A(v S ) ∼ A(v aS ) = A(v). SEIRA, SERS and
SEHRS depend on field enhancement factors A(v) to the power of two, four and six
respectively, while SEPARS, SECARS, and SESRS benefit from A(v) to the power
of eight.
For supporting different vibrational spectroscopic methods, field enhancement is
required within very different wavelength ranges including IR and THz frequencies