Stokes transition

The resulting spectmm is illustrated in Figure 5.15, and Figure 5.16 shows in detail the processes involved in the first Stokes and anti-Stokes transitions and in the Rayleigh scattering. 

Richardson (1971) summarises a mefhod of predicting minimum fluidizing velocify as a function of the terminal falling velocify of a particle. This requires the terminal falling velocify Ut to be expressed in terms of fhe Galileo number. Thus, treating the Stokes, transition and Newton regions in turn ... 

Suppose that a compound has a Raman-active vibration at vM. If it is illuminated by a probe laser (v) simulataneously with a pump continuum covering the frequency range from v to v + 3,500 cm-1, one observes an absorption at v + vM in the continuum together with emission at v. Clearly, the absorbed energy, h(v + vM), has been used for excitation (/zvM) and emission of the extra energy (hv). This upward transition is called the inverse Raman effect since the normal anti-Stokes transition occurs downward. Because the inverse Raman spectrum can be obtained in the lifetime of the pulse, it may be used for studies of shortlived species (Section 3.5). It should be noted, however, that the continuum pulse must also have the same lifetime as the giant pulse itself. Thus far, the inverse Raman effect has been observed only in a few compounds, because it is difficult to produce a continuum pulse at the desired frequency range. 

Figure 6.1-5 Stokes transition for continuum resonance Raman scattering in from the initial vibrational state />= 0> to the final state f >= 6> via electronic state B( 77o+). (A) Absolute value of the time overlap < 6 0(t) > as a function of time, (B) excitation profile of this transition [square of the half Fourier transform of < f i t) > as a function of energy] (Ganz and Kiefer, 1993 a).

Euler Navier-Stokes Navier-Stokes Transition Molecular... 

Loo investigated Raman scattering of electrogenerated iodine on a titanium oxide electrode. He reports signals at 181, 190, and 360 (weak overtone) cm" Also the anti-Stokes transition is seen. The signals were not seen at 488- or 514.5-nm excitation, but only for excitations between 530.9 and 647.1 nm. This strongly indicates resonance scattering. However, that of free iodine is at 515 nm, and the band gap of the oxide is 3 eV (415 nm). Thus one must conclude that the interaction of the iodine with the solid shifts the resonance to lower frequencies. 

The first term on the right-hand side is zero unless i = j. This term is responsible for Rayleigh scattering. The second term determines the activity of fundamental vibrations in Raman scattering it vanishes for a harmonic oscillator unless j = i l (Sec. 1.10). If we consider a Stokes transition, u —> u + 1, Eq. 1.204 is written as [3]... 

The extraction of temperatures from SpRS spectra can happen by following a number of different strategies. One is based on the deduction of the number density of all the main molecular species resident in the interaction volume and responsible for rovibrational lines or pure rotational spectra. Another strategy focuses on the details of the whole spectral shape that usually contains a considerable number of lines. Finally, a third approach is rooted in the ratio of integrated line intensities of Stokes and anti-Stokes transitions. 

In the classical model, equation (11) indicates no difference in the expected intensities of Stokes and anti-Stokes transitions, since the coefficients of the two... 

The vibrational selection rules are the same for Raman spectroscopy as for infrared spectroscopy. In the Stokes process, the intense, monochromatic radiation t es a molecule from the v = 0 state to a virtual state, VO, from which it falls back to the v = 1 state. Similarly, in the anti-Stokes process, the virtual state VI is involved in the overall transfer of the molecule from the v = 1 to the v = 0 state. The Stokes and anti-Stokes transitions lie on the low and high wavenumber sides, respectively, of the exciting radiation. The intensity of the anti-Stokes line, relative to the Stokes transition is very low because of the lower population of the v = 1 state, compared to that of the v = 0 state. Consequently, Raman spectroscopy uses only the Stokes transitions. 

CARS can be resonantly-enhanced electronically when either the pump, Stokes or the CARS frequency Itself coincides with an electronic transition in the probed species. Stokes resonances are weighted by the excited vibrational state involved in the Raman resonance and this enhancement is generally weak even at flame temperatures. More typically one tries to achieve primary resonance with the pump laser. In so doing, Stokes resonances are automatically satisfied. The strength of the resonance scales as the product of the four dipole matrix elements Involved with each field in the wave mixing process. Thus only certain transitions tend to be enhanced leading in most cases to a simplification of the CARS spectrum. In the case of the combustion relevant OH molecule under study in our laboratory, a simple triplet spectrum is predicted since each Raman-resonant, downward Stokes transition must satisfy the appropriate dipole selection mles for strong electronic enhancement as shown in Fig. 10. ... 

Fig. 10. Energy level diagram for electronic resonance enhancement in the CARS spectrum of hydroxyl, OH, in which the pump laser is tuned into resonance. Strong enhancement occurs only for allowed downward Stokes transitions leading to a triplet spectrum.

The IR light from the remote controller can be aimed at an infrared sensor card, in a dark room, or in a darkened space under an overcoat. The IR is made visible by a special kind of fluorescence called an "anti-Stokes transition."... 

Stokes with slip correotion Stokes Transition ... 

Raman line intensities are proportional to the number density N of molecules in the initial state /c>, which is in turn proportional to the pertinent Boltzmann factor for that state at thermal equilibrium. Consequently, the relative intensities of a Stokes transition /c> - m> and the corresponding anti-Stokes transition m> -> /c> are 1 and exp — hoj kjkT), respectively. (The factor coicol varies little between the Stokes and anti-Stokes lines, because the Raman frequency shifts are ordinarily small compared to cui.) Hence the anti-Stokes Raman transitions (which require molecules in vibrationally excited initial states) are considerably less intense than their Stokes counterparts, particularly when the Raman shift (o k is large. In much of the current vibrational Raman literature, only the Stokes spectrum is reported (cf Fig. 10.1). 

A FIGURE 6.17 Raman transitions. An incident photon with frequency may result in a Raman transition to a higher eneigy state (Stokes transition) or a lower energy state (anti-Stokes transition) by way of an intermediate virtual (non-stationary) state. The difference in eneigy between states 3 and 5 shown would be obtained by measuring Vq and the frequency of the emitted radiation and calculating A s 3 =/t(fo — fa). 

In Raman scattering, photons striking a sample are redirected with energies either greater (anti-Stokes transition) or less (Stokes transition) than the original photon energy. 

Fig. 12.8 In coherent Raman spectroscopy, a beam of electromagnetic radiation with frequency Vp and wavevector kp, and a second beam with frequency Vj and wavevector are focused on the sample. Radiation emitted with frequency v = 2Vp — Vj and wavevector kf= 2kp — k, is collected. Stokes Raman transitions of the ground electronic state are stimulated when Vp — v, = v, where hv is a vibrational mode of the sample anti-Stokes transitions are stimulated when Vp — v = —v... 

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