Nonlinear effects only become evident in very intense light, i.e., large E. Consider
two nonlinear Raman techniques: 1. Stimulated Raman Scattering. 2.
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 intensity fluctuations alignment instabilities of incident beams
