Stokes lines

The next two temis (Lorentzians) arise from the mechanical part of the density fluctuations, the pressure fluctuations at constant entropy. These are the adiabatic sound modes (l/y)exp[-FA t ]cos[co(A) t ] with (D(k) = ck, and lead to the two spectral lines (Lorentzians) which are shifted in frequency by -ck (Stokes line) and +ck (anti-Stokes line). These are known as the Brillouin-Mandehtarn, doublet. The half-width at... 

It is well known that the intensity of scattered light varies as the fourth power of the frequency, and based on this alone one would predict the Stokes lines to be less intense than the anti-Stokes by a factor of... 

The first three Stokes lines in the rotational Raman spectrum of 02 are separated by 14.4 cm, 25.8 cm and 37.4 cm from the exciting radiation. Using the rigid rotor approximation obtain a value for tq. 

Antistatic coatings Antistatic finishes Antistatic yarns Antistatin D Antisterility vitamin Antistick agents Antistick applications Anti-Stokes lines... 

The third common level is often invoked in simplified interpretations of the quantum mechanical theory. In this simplified interpretation, the Raman spectrum is seen as a photon absorption-photon emission process. A molecule in a lower level k absorbs a photon of incident radiation and undergoes a transition to the third common level r. The molecules in r return instantaneously to a lower level n emitting light of frequency differing from the laser frequency by —>< . This is the frequency for the Stokes process. The frequency for the anti-Stokes process would be + < . As the population of an upper level n is less than level k the intensity of the Stokes lines would be expected to be greater than the intensity of the anti-Stokes lines. This approach is inconsistent with the quantum mechanical treatment in which the third common level is introduced as a mathematical expedient and is not involved directly in the scattering process (9). 

The energy of the scattered radiation is less than that of the incident radiation for the Stokes line of the Raman spectrum and the energy of the scattered radiation is more than that of the incident radiation for the anti-Stokes line. The energy increase or decrease from the excitation is related to the vibrational energy spacing... 

Figure 3.6. A simplified energy diagram illustrating the origins of Rayleigh scattering and of the Stokes and anti-Stokes lines in the Raman spectrum.

Since the Raman scattering is not very efficient (only one photon in 107 gives rise to the Raman effect), a high power excitation source such as a laser is needed. Also, since we are interested in the energy (wavenumber) difference between the excitation and the Stokes lines, the excitation source should be monochromatic, which is another property of many laser systems. 

Figure 2.52 Schematic representation of the transitions giving rise to the Raman effect. GS = ground electronic state, ES = excited electronic state, VS = virtual electronic stale, R = Rayleigh scattering, S = transitions giving rise to Stokes lines, AS = transitions giving rise to Anti-Stokes lines, RRS = transitions giving rise to resonance Raman.

The ratio of the intensity of anti-Stokes and Stokes lines is primarily determined by the Boltzmann population of the excited vibrational states. For mid-IR frequencies this fractional population is very low (seIO-4 at 2000cm-1). As a result, Raman spectra are usually taken from the Stokes side of the Rayleigh line as these are generally very much more intense and are not broadened by emissions from hot states. 

Figure 3. Energy schemata of transitions involving vibrational states (a excitation of 1st vibrational state - mid-IR absorption b excitation of overtone vibrations - near-IR absorptions c elastic scattering - Rayleigh lines d Raman scattering - Stokes lines e Raman scattering - Anti-Stokes lines f fluorescence).

Raman spectra are usually represented by the intensity of Stokes lines versus the shifted frequencies 12,. Figure 1.15 shows, as an example, the Raman spectrum of a lithium niobate (LiNbOs) crystal. The energies (given in wavenumber units, cm ) of the different phonons involved are indicated above the corresponding peaks. Particular emphasis will be given to those of higher energy, called effective phonons (883 cm for lithium niobate), as they actively participate in the nonradiative de-excitation processes of trivalent rare earth ions in crystals (see Section 6.3). 

Stokes line spect A spectrum line in luminescent radiation whose wavelength is greater than that of the radiation which excited the luminescence, and thus obeys Stokes law. stoks, ITn ... 

Through interaction of the Stokes lines with the laser line, stimulated anti-stokes lines can be produced 223),... 

Higher order Stokes or anti-Stokes lines have been observed to occur at exact harmonics of the first vibrational 724) or rotational 723) shifts. 

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