Nonlinear Raman Spectroscopy
Previously we had assumed that the dipole moment of
the molecule, p, in an electric field is:
p = μ 0 + α~ ⋅ E
where μ0 is the permanent dipole moment, α is the
polarizability, and E is the electric field of the light
wave.
However, when the intensity of the incident light is
sufficiently large, the induced oscillation of the dipole
moment becomes nonlinear:
~
~
p = μ 0 + α ⋅ E + β ⋅ E ⋅ E + γ~ ⋅ E ⋅ E ⋅ E
where β is the hyperpolarizability and γ is the second
hyperpolarizability.
Nonlinear effects only become evident in very intense
light, i.e., large E.
Consider two nonlinear Raman techniques:
1. Stimulated Raman Scattering
2. Coherent Anti-Stokes Raman Scattering (CARS)
1. Stimulated Raman Scattering
Normal Raman spectroscopy → typically observed
perpendicular to incident beam
Stimulated Raman Scattering → observed in same
direction as incident beam or at small angle to it.
Observe concentric rings of different colours.
virtual
level
ν0
ν0
νS
ν1
Ei
Stokes
νA= ν0 + ν1
Anti-Stokes
Differences between linear (spontaneous) and nonlinear
(induced) Raman effect:
- Intensity of spontaneous Raman is proportional to
incident pump intensity, but smaller by many orders of
magnitude; intensity of stimulated Raman depends
nonlinearly on incident intensity, but intensities can be
comparable to the pump intensity.
- Threshold intensity for stimulated Raman effect
- Most substances only show Stokes lines from
vibrations with the most intense Raman scattering
Applications of stimulated Raman scattering include:
1. Measurement of molecular parameters
2. Raman lasers or Raman shifting to generate intense
radiation at different wavelengths (cf. DIAL and
LIDAR) → access to different wavelengths from
fixed frequency lasers.
Scattering intensity at νS = ν0 – ν1 can be about 50%
of that of incident laser beam (at frequency ν0).
E.g.,
The H2 stretching frequency is 4160 cm-1.
Raman shifting a 308 nm XeCl (308 nm =
32 467 cm-1) with pressurised H2 would give a new
frequency at 32467 – 4160 =28308 cm-1, or 353 nm.
1. Coherent Anti-Stokes Raman Scattering (CARS)
In stimulated Raman scattering, the Stokes line gave rise
to other Raman frequencies.
In CARS, we use two lasers at ν1 and ν2 to achieve a
similar effect:
- νv = ν1 – ν2 matches a Raman-active vibration
- ν1 corresponds to the pump wave in SRS
- ν2 matches the Stokes wave in SRS
virtual
levels
New Stokes and
Anti-Stokes lines are
generated
Produces a high
population density
of vibrationally
excited molecules.
ν1
ν1
Ei
νA= 2ν1 – ν2
ν2
νv = ν 1 – ν2
A corresponding Stokes wave at 2ν2 – ν1 is also
produced, similar to the anti-Stokes line → CSRS.
The generated signal beam in CSRS is at lower
frequencies → fluorescence may interfere with signal →
CARS preferred to CSRS.
Experimental arrangement:
- typically use pump laser ν1 together with tunable laser
at ν2 at a small angle to each other
- anti-Stokes wave ν3 (= νA) emerges at different angle
→ allows spatial filtering
→ coherent beam, unlike in spontaneous Raman
2 2
S
∝
N
I1 I 2
- CARS signal,
- Focused beam → high spatial resolution
Advantages of CARS:
- signal levels are 104 – 105 times greater than in
spontaneous Raman spectroscopy
- higher frequency signal beam (νA > ν1 > ν2) allows
filtering to reject incident and fluorescent light
- small beam divergence allows detector to be
placed far away → better discrimination against
fluorescence or luminous backgrounds (e.g.,
flames, discharges)
- small sample volume and high spatial resolution
- high spectral resolution
Disadvantages:
- expensive equipment
- strong fluctuations in signal arising from
ƒ intensity fluctuations
ƒ alignment instabilities of incident beams