2 Plasmonics for Enhanced Vibrational Signatures
109
optical field strength
P ind = α E + β E E + · · ·
(2.5)
with β as hyper polarizability. The first linear term including α describes linear
Raman and Rayleigh scattering, the second term describes hyper Rayleigh and hyper
Raman scattering. Hyper Raman scattering follows symmetry selection rules different from Raman scattering. Therefore, it can probe vibrations hat are forbidden in
Raman scattering [8, 9].
As a non-linear, two-photon excited process, HRS depends on the excitation photon flux density n L to the power of two. In analogy to Eq. (2.1) , the number of
surface-enhanced hyper Raman Stokes photons n SEHRS can be calculated as
n
SEHRS
= N 0 σ
SEHRS n
2
L
(2.6)
where σ SEHRS is the effective cross section of the surface-enhanced hyper Raman
process.
HRS can be enhanced in an analogous fashion to normal Raman scattering by
a chemical effect and by enhancement of the optical fields when the molecule is
in close proximity of metallic nanostructures. The effective surface-enhanced hyper
Raman cross section can be written as
σ
SEHRS
= σ
HRS
ads |A (ν L )|
4
|A (ν hS )|
2
(2.7)
where σ HRS ads describes an “chemically” enhanced hyper Raman cross section compared to that of a “free” molecule, A(v) describe the enhancement of the optical fields
at the excitation and hyper Raman scattered wavelengths, respectively. We can write
an enhancement factor for SEHRS as
G SE H RS =
σ HRS
ads
σ HRS
f ree
|A(ν L )|
4
|A(ν H S )|
2
(2.8)
Strong surface enhancement corresponding to the field enhancement factor to the
power of six can overcome the inherently weak nature of hyper-Raman scattering
and enable to measure hyper Raman spectra also at the anti-Stokes side [35].
Figure 2.2 displays Stokes and anti-Stokes hyper Raman spectra and illustrates
the dependence of non-linear SEHRS signals on the excitation intensity to the power
of two. Effective cross sections of SEHRS have shown to be on the order of 10 −46 −
10 −45 cm 4 s, comparable or even better than the best cross sections for two-photon
fluorescence obtained so far. These cross sections enable the measurement of SEHRS
spectra at excitation intensities of 10 6 − 10 7 W / cm −2 , conditions that can be easily
achieved with mode-locked picosecond lasers under weak focusing conditions [36],
and also in tightly focused continuous wave (cw) [37] or low-energy pulsed lasers
[38].
109
optical field strength
P ind = α E + β E E + · · ·
(2.5)
with β as hyper polarizability. The first linear term including α describes linear
Raman and Rayleigh scattering, the second term describes hyper Rayleigh and hyper
Raman scattering. Hyper Raman scattering follows symmetry selection rules different from Raman scattering. Therefore, it can probe vibrations hat are forbidden in
Raman scattering [8, 9].
As a non-linear, two-photon excited process, HRS depends on the excitation photon flux density n L to the power of two. In analogy to Eq. (2.1) , the number of
surface-enhanced hyper Raman Stokes photons n SEHRS can be calculated as
n
SEHRS
= N 0 σ
SEHRS n
2
L
(2.6)
where σ SEHRS is the effective cross section of the surface-enhanced hyper Raman
process.
HRS can be enhanced in an analogous fashion to normal Raman scattering by
a chemical effect and by enhancement of the optical fields when the molecule is
in close proximity of metallic nanostructures. The effective surface-enhanced hyper
Raman cross section can be written as
σ
SEHRS
= σ
HRS
ads |A (ν L )|
4
|A (ν hS )|
2
(2.7)
where σ HRS ads describes an “chemically” enhanced hyper Raman cross section compared to that of a “free” molecule, A(v) describe the enhancement of the optical fields
at the excitation and hyper Raman scattered wavelengths, respectively. We can write
an enhancement factor for SEHRS as
G SE H RS =
σ HRS
ads
σ HRS
f ree
|A(ν L )|
4
|A(ν H S )|
2
(2.8)
Strong surface enhancement corresponding to the field enhancement factor to the
power of six can overcome the inherently weak nature of hyper-Raman scattering
and enable to measure hyper Raman spectra also at the anti-Stokes side [35].
Figure 2.2 displays Stokes and anti-Stokes hyper Raman spectra and illustrates
the dependence of non-linear SEHRS signals on the excitation intensity to the power
of two. Effective cross sections of SEHRS have shown to be on the order of 10 −46 −
10 −45 cm 4 s, comparable or even better than the best cross sections for two-photon
fluorescence obtained so far. These cross sections enable the measurement of SEHRS
spectra at excitation intensities of 10 6 − 10 7 W / cm −2 , conditions that can be easily
achieved with mode-locked picosecond lasers under weak focusing conditions [36],
and also in tightly focused continuous wave (cw) [37] or low-energy pulsed lasers
[38].