Four-photon process

This tensor corresponds to the four-photon process of scattering of light by light, for which the conservation law... 

Three-photon processes Four-photon process... 

This quantity plays an important role in other multi-photon processes, such as two-photon absorption, second harmonic generation and hyper-Raman scattering as three-photon processes, and coherent anti-Stokes Raman scattering (CARS), a four-photon process (Table 1.5). The two-photon absorption can be treated theoretically from Eq. (1.115) in the same way as the Raman scattering process discussed above. Thus, the transition rate for two-photon absorption is given by Eq. (1.161). 

The term third harmonic generation, THG, refers to the generation of a light beam that consists of photons having three times the energy of the photons of the input beam. THG can be easily detected and is, therefore, widely employed in the third-order nonlinear characterization of newly developed materials [28]. THG is a four-photon process, in which three incident photons with angular frequency co create a photon with frequency 3virtual excited states, as shown by the dashed lines in Fig. 3.4. 

This is done explicitly for two-photon processes in Chapter 10, where two-photon absorption and Raman spectroscopy are discussed. This formalism becomes increasingly unwieldy when applied to three- and four-photon processes, and diagrammatic techniques then become useful for organizing the calculation of the pertinent transition probabilities (Chapter 11). 

Figure 11.4 Energy level diagrams for third-harmonic generation uj +0) +uj - 3 t/i (left) and frequency summing +uj +W2- 2uj + w ) (right), two of the four-photon processes which are possible in a material subjected to two intense beams at frequencies cu and uj -...

Figure 19 Schematic representation of saturation absorption as a degenerate four photon process.

Figure 20 Schematic representation of photoinduced absorption as a four photon process...

As the name XPS implies, the analytical sample is irradiated with x-ray light and the energy distribution of the emitted photoelectrons is recorded. Fig. 1 shows a comparison between the four different processes which are caused by the interaction between x-ray photons and matter, and which can be observed by four different spectroscopic techniques 17,I8). 

This rule is analogous for any number of photons thus, in a three-photon absorption process the allowed states are the p and f states, which allows even-to-odd or odd-to-even parity. This means that transitions can be divided between states of either the same or different parity corresponding to absorption of either even or odd numbers of photons. Hence the selection rules are the same for one and three photons and for two and four photons, respectively [49]. 

However this new realization of the lesser efficiency of the photosynthetic process in living plants opens up new possibilities of explanation. Hypotheses need no longer be handicapped by this high efficiency requirement. It is now worth while to examine the possibility that in a very complex molecule of special structure many photons may be absorbed, and, in the resulting rearrangements, the energy equivalent of four photons may be delivered in one unit at a particular part of the molecule to produce the photosynthetic union of carbon dioxide and water. 

Figure 1 Schematic representation of a time-resolved coherent Raman experiment, (a) The excitation of the vibrational level is accomplished by a two-photon process the laser (L) and Stokes (S) photons are represented by vertical arrows. The wave vectors of the two pump fields determine the wave vector of the coherent excitation, kv. (b) At a later time the coherent probing process involving again two photons takes place the probe pulse and the anti-Stokes scattering are denoted by subscripts P and A, respectively. The scattering signal emitted under phase-matching conditions is a measure of the coherent excitation at the probing time, (c) Four-photon interaction scheme for the generation of coherent anti-Stokes Raman scattering of the vibrational transition.

Nafie (1992) has given a review about the latest VOA instrumentation. Until 1988, the only measured form of ROA was incident circular polarisation (ICP) ROA, but as the process observed in Raman spectroscopy is a two-photon process, there are four possibilities for measuring Raman optical activity. ICP ROA is the unpolarized measurement of the Raman radiation emitted upon excitation with alternating right and left circularly polarized light. It is shown in Fig. 6.3-12, following the sketches of Nafie. As the first of the other possibilities scattered circular polarisation (SCP) ROA was measured. This... 

The reduction of each CO2 to the level of a hexose requires 2 moles of NADPH. The reduction of NADP+ is a two-electron process. Hence, the formation of 2 moles of NADPH requires the pumping of four photons hy photosystem... 

Reaction (16) is the sum of reactions (17) and (18). Clearly, if each photon harvested by the system can lead to the transfer of one electron, then a minimum of four photons are required for the conversion of each CO2 molecule. Experimental measurements of the quantum yield indicate that eight photons are actually needed, suggesting that two photons are used for each electron transfer and that a two-step process is taking place with long-lived intermediates coupling the steps. 

The avoidance of swelling during processing is a necessary but not sufiScient characteristic of a viable resist system for use in micrometer and submicrometer lithography. For such systems to have practical utility, they must also function with extremely high sensitivity to maximize productivity. The efiSciency of crucial photochemical transformations is characterized by the quantum yield for the process expressed as molecules transformed per photons absorbed. The quantum yield of typical diazonaphthoquinones is from 0.2 to 0.3. Thus, three or four photons are required to transform a single molecule of sensitizer. This places a fundamental limit on the photosensitivity of such systems. 

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