Stokes process

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). 

Auzel F (2004) Upconversion and anti-stokes processes with f and d Ions in solids. Chem Rev 104 139-174... 

According to classical theory, in Eq. (16.16), the first term represents an oscillating dipole that radiates light of frequency v0, that is, Rayleigh scattering. The second term is associated with the Raman scattering of frequency v0 - vm (Stokes process) and v0 + vm (anti-Stokes process). If (daldq)0 is zero, the vibration is not Raman active (Ferraro and Nakamoto, 1994). 

Up-conversion is a process by which two photons of lower energy are subsequently converted into a luminescence photon of higher energy (typically, two IR photons giving rise to one visible photon, e.g. in Er111-containing compounds). This anti-Stokes process is usually observed for ions embedded in solids and is made possible by various mechanisms, such as the now classical excited state absorption mechanism (ESA), or sequential energy transfers (ETU for... 

Figure 3.16. A few interactions contributing to the Raman-Stokes process (with creation of one phonon). The propagators are labeled with the notation of the text. The process a is of the first order b could be included by renormalization of the created exciton c would require the renormalization of the interaction (or the vertex).

Fig. 11.1 Schematics of vibrational Raman process. Stokes process gives scattered lights that are lower in energy than the incident light, and anti-Stokes process gives scattered lights that are higher in energy than the incident light...

For Stokes processes involving phonons, the intensity I of scattered light is given by [6] ... 

Here the and -f signs correspond to those Raman processes in which an elementary excitation is created or annihilated (Stokes and anti-Stokes processes, respectively). In crystalline solids, the quasi-momentum conservation gives the following relation between the wave vectors k, of the incident light, kj of the scattered light, and q of the elementary excitation ... 

In this case one ion at Site-1 spin-couples to another ion at Site-2, In the above diagram, i refers to the initial state of each and f is the final state. Thus, the "2-ion" goes from the "B" level to the "A" level, while the "1-ion" simultaneously transforms fi"om the "B" level to the "C" level. Thus, from two excited Ions, we end up with one in the ground state and the other in an energy state double that of the tnltial state. This process has been observed in rare earth activated phosphors which can absorb infrared radiation and convert it to visible light (an Anti-Stokes process). 

As should be apparent by now, the rare earths are one of the few cases where such Stokes processes can be studied at room temperature. If we were to study phonon processes using other activators, we would find that we must study them at 4.2 K. We would also find that the phonon spectra were rather complex and difficult to interpret, instead of being simple. Now we will address the so-called "Anti-Stokes phosphors where the dominant mechanism is absorption of several phonons to produce a single photon of higher energy. We will find that only certain trivalent lanthanides eire suitable when combined with a selected host lattice if we wish to have high efficiency, i.e.- "brightness". 

By irradiation of the sample with monochromatic radiation a small proportion of the radiation is re-emitted (scattered) with the wavelengths differing by frequencies corresponding to the vibrational modes of the sample. Frequencies smaller (Stokes process) or higher (anti-Stokes process) than the excitation frequency are observed. The strength of the effect is determined by the derivative of the molecular polaris-ability of the sample with respect to the vibrational coordinates. 

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. 

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