Multiple photon process

We have in this way obtained a generalization of Einstein s theory of the interaction between matter and radiation including multiple photon processes and involving transition probabilities. But there is a basic difference. The operator definite positive. We no longer have a simple addition of transition probabilities. This corresponds exactly to the interference of probabilities discussed in Section IV. The process is not of the simple Chapman-Smoluchowski-Kolmogoroff type (Eq. (11)) the operator transition probability. As the result, the second of the two sequences discussed above may decrease the effect of the first one. It is very interesting that even in the limit of classical mechanics (which may be performed easily in the case of anharmonic oscillators) this interference of probabilities persists. This is in agreement with our conclusion in Section IV. 

The stochastization limit Agtoch and hence the necessary order of the multiple-photon process depend strongly on the number of atoms in the given molecule and the relationship between the frequency of the resonant mode and the frequencies of the other modes. For simple molecules, the stochastization limit lies high, and such molecules are therefore difficult to excite so that they rise to the... 

Some partial photoionization cross sections, derived in this way for neon, are shown in Fig. 2.11 as a function of photon energy. The uppermost curve is the total absorption cross section. At the onset of the ionization thresholds for the ejection of Is, 2s and 2p electrons this quantity shows the corresponding absorption edges (see the discussion related to equ. (2.11)). The partition of the total cross section into partial contributions cr(i) clearly demonstrates that the dominant features are due to main photoionization processes described by the partial cross sections satellite transitions from multiple photoionization processes are also present. If these are related to a K-shell ionization process, they are called in Fig. 2.11 multiple KL where the symbol KLX indicates that one electron from the K-shell and X electrons from the L-shell have been released by the photon interaction. Similarly, multiple I/ stands for processes where X electrons from the L-shell are ejected. Furthermore, these two groups of multiple processes are classified with respect to ionization accompanied by excitation, (e, n), or double ionization, ( ,e). If one compares in Fig. 2.11 the magnitude of the partial cross sections for 2p, 2s and Is photoionization at 1253.6 eV photon energy (Mg Ka radiation) and takes into account the different... 

The selection rules will be mentioned briefly here. In general, the process of multiphoton absorption is similar to that of single-photon absorption. The multiple photons are absorbed simultaneously to a real excited state in the same quantum event, where the energy of the transition corresponds to the sum of the energies of the incident photons. Thus selection rules for these transitions may be derived from the selection rules for one-photon transitions as they can be considered multiple one-photon transitions [20]. 

As large intensities are necessary to induce a nonlinear refractive index change, not only linear but also multiple photon absorption processes have to be considered. The intensity I and the induced nonlinear phase shift NL are coupled differential equations as a function of the propagation direction z. 

The photophysics and photochemistry of processes induced by multiple-photon i.r. laser excitation have been the subjects of a series of review articles by Letokhov and co-workers. Letokhov has also presented a more general review of photochemistry initiated by laser radiation, including singlephoton, multiple-photon vibrational, and multiphoton electronic photo-... 

Processes that are resonant at zero held (i.e., with a atomic Bohr frequency that is an integer multiple of the laser frequency) can be investigated through an effective Hamiltonian of the model constructed from a multilevel atom driven by a quasi-resonant pulsed and chirped radiation held (referred to as a pump held). If one considers an w-photon process between the considered atomic states 1) and 2) (of respective energy E and Ef), one can construct an effective Hamiltonian with the two dressed states 11 0) (dressed with 0 photon) and 2 —n) (dressed with n photons) coupled by the w-photon Rabi frequency (2(f) (of order n with respect to the held amplitude and that we assume real and positive) and a dynamical Stark shift of the energies. It reads in the two-photon RWA [see Section III.E and the Hamiltonian (190)], where we assume 12 real and positive for simplicity,... 

Laser-induced reaction has been widely used to stimulate gas-surface interaction. Lasers are also used to probe molecular dynamics in heterogeneous systems as well. In the applied area, the laser photochemical techniques are successfully applied to produce well defined microstructures and new materials for microelectronic devices (1). Enhanced adsorption and chemical reaction on surfaces can be achieved by a photoexcitation of gaseous molecules, adsorbed species as well as solid substrates. The modes of the excitation include vibrational and electronic states of the gaseous species and of the adsorbates surface complexes. Both a single and a multiple photon absorption may be involved in the excitation process. 

Vibrationally excited processes can be applied in the formation of semiconductor films. One of the examples to demonstrate the photoenhanced chemisorption and reaction due to the vibrational excitation is the interaction of SF molecules with silicon (2). In this case, SFg molecules can be chemically activated by multiple photon absorption of CO2 laser either in the gas phase or in the adsorbed state. Deposition of Si on quartz or glass surface can also be stimulated by the decomposition of SiH enhanced by the irradiation of CO2 laser to the gas phase (3). 

Thus it is not clear how much of the apparent difference in emission threshold for N2 and phenyl radicals in Fig. 44 is due to different emission intensities versus different detection probabilities. Since two N2 molecules must be emitted to release one phenyl radical, some difference in fluence dependence is expected. For both species, the intensity rises above the background in approximately power law fashion. Finally, at still higher fluences, the intensity rolls over, growing more slowly with increasing fluence. The slopes of the power-law portions of the two plots are 8 for N2 and 12 for the phenyl radical, respectively. Although we could suggest that this corresponds to an eight- and 12-photon process (either multiphoton or multiple photon) this seems totally unacceptable and unreasonable. Furthermore, it is inconsistent with a simple photodecomposition mechanism, where we... 

Photoionization also occurs in the already mentioned photoreactions between frans-anthole and fumarodinitrile. In this case, the electron is immediately scavenged by the solvent to give a monomeric or dimeric anion of acetonitrile, which constitutes the second radical of the pair. The precursor multiplicity is again singlet, and CIDNP experiments with varying laser intensity show the ionization to be a two-photon process. 

This modular system is very flexible with respect to the type of thin-film deposition process (different methods of PVD and CVD) and the means of laser ionization (one-, two- or multiple-photon ionization with fixed or tunable laser wavelengths). 

The carrier multiplication (CM) process generated as a result of a single photon absorption in a spherical quantum dot (QD) is explained as due to multiple,virtual band-to-band electron-photon quantum transitions. Only the electron-photon interaction is used as a perturbation without the participation of the Coulomb electron-electron interaction. The creation of an odd number of electron-hole (e-h) pairs in our model is characterized by the Lorentzian-type peaks, whereas the creation of an even number of e-h pairs is accompanied by the creation of one real photon in the frame of combinational Raman scattering process. Its absorption band is smooth and forms an absorption background without peak structure. It can explain the existence of a threshold on the frequency dependence of the carrier multiplication efficiency in the region corresponding to the creation of two e-h pairs. 

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