Multiphoton principle

The Goeppert-Mayer two- (or multi-) photon absorption, mechanism (ii), may look similar, but it involves intennediate levels far from resonance with one-photon absorption. A third, quasi-resonant stepwise mechanism (iii), proceeds via smgle- photon excitation steps involvmg near-resonant intennediate levels. Finally, in mechanism (iv), there is the stepwise multiphoton absorption of incoherent radiation from themial light sources or broad-band statistical multimode lasers. In principle, all of these processes and their combinations play a role in the multiphoton excitation of atoms and molecules, but one can broadly... 

In contrast to the ionization of C q after vibrational excitation, typical multiphoton ionization proceeds via the excitation of higher electronic levels. In principle, multiphoton ionization can either be used to generate ions and to study their reactions, or as a sensitive detection technique for atoms, molecules, and radicals in reaction kinetics. The second application is more common. In most cases of excitation with visible or UV laser radiation, a few photons are enough to reach or exceed the ionization limit. A particularly important teclmique is resonantly enlianced multiphoton ionization (REMPI), which exploits the resonance of monocluomatic laser radiation with one or several intennediate levels (in one-photon or in multiphoton processes). The mechanisms are distinguished according to the number of photons leading to the resonant intennediate levels and to tire final level, as illustrated in figure B2.5.16. Several lasers of different frequencies may be combined. 

The general principle of detection of free radicals is based on the spectroscopy (absorption and emission) and mass spectrometry (ionization) or combination of both. An early review has summarized various techniques to detect small free radicals, particularly diatomic and triatomic species.68 Essentially, the spectroscopy of free radicals provides basic knowledge for the detection of radicals, and the spectroscopy of numerous free radicals has been well characterized (see recent reviews2-4). Two experimental techniques are most popular for spectroscopy studies and thus for detection of radicals laser-induced fluorescence (LIF) and resonance-enhanced multiphoton ionization (REMPI). In the photochemistry studies of free radicals, the intense, tunable and narrow-bandwidth lasers are essential for both the detection (via spectroscopy and photoionization) and the photodissociation of free radicals. 

The field of laser lithography (also often called laser microfabrication) branched out from multiphoton excitation microscopy and has become established during the last decade. The principles of two-photon microscopy, which has enabled high-resolution 3D imaging [3,4] and optical memory [5], were gradually adapted for 3D laser hthography [6]. A relevant collection of seminal papers on the field can be found in [7]. 

The H2 molecule is a system for which quite recently it has been possible to measure in unprecedented detail state-selected vibrationally and rotation-ally resolved photoionization cross sections in the presence of autoionization [27-29]. The technique employed has been resonantly enhanced multiphoton ionization. The theoretical approach sketched above has been used to calculate these experiments from first principles [30], and it has thus been possible to give a purely theoretical account of a process involving a chemical transformation in a situation where a considerable number of bound levels is embedded in an ensemble of continua that are also coupled to one another. The agreement between experiment and theory is quite good, with regard to both the relative magnitudes of the partial cross sections and the spectral profiles, which are quite different depending on the final vibrational rotational state of the ion. 

Figure 8.28 illustrates the principle of multiphoton IR dissociation with a simplified potential energy diagram. There are in principle two ways to reach the dissociation limit from the zeroth vibrational level of the ground state. 

Figure 7. Schematic energy level diagram showing the principle of the ionization method for detecting electron transfer in gas-phase adducts. Naphthalene cation (the hole donor) is formed by resonance-enhanced two-photon ionization of the neutral. A hole acceptor, whose ionization potential is lower than that of naphthalene, is not ionized, since its S level is not resonant with the UV photons used (vi). The vibrational levels of the ionic form of the acceptor are resonant with the naphthalene cation, and accept the hole easily. Detection is by photodissociation, using photons of different frequency (V2) that dissociate the naphthalene cation in a resonance-enhanced multiphoton absorption process. Charge transfer is detected by the diminution of the product ion signal in the presence of a suitable acceptor. Adapted from Ref. [32].

The nonlinear phenomena in intense magnetic and laser fields are given some prominence in this volume. Two chapters deal with multiphoton processes and time-dependent phenomena in atoms. In another chapter it is emphasized that the process of multi-electron dissociative ionization of molecules offers considerable challenges both for modeling and for the study of first-principles. The dynamics of molecules in such intense laser fields is an area of great interest, both at the time of writing and for future studies. In all these chapters the interplay between theory and experiment is demonstrated. 

The chapter is organized as follows. The principle of the coupled-channel method is reviewed in detail in Section 2. The results are discussed in connection to higher order terms in Section 3. The application to multiphoton ionization is described in Section 4. Comparisons with measurements are provided in Section 5. A simple model for the electronic energy loss is... 

The dependence of multiphoton absorption cross sections on entanglement times and path delayes may, in principle, be used for the determination of spectrum and dipol moments of the absorbing material (for two-photon (three-photon) absorption, see Ref. 95 (Ref. 94). 

From the results in the last section it is clear that for particular applied radiative frequencies or frequency multiples, close to resonance with particular molecular states, each molecular tensor will be dominated by certain terms in the summation of states as a result of their diminished denominators—a principle that also applies to all other multiphoton interactions. This invites the possibility of excluding, in the sum over molecular states, certain states that much less significantly contribute. Then it is expedient to replace the infinite sum over all molecular states by a sum over a finite set—this is the technique employed by computational molecular modelers, their results often producing excellent theoretical data. In the pursuit of analytical results for near-resonance behavior, it is often defensible to further limit the sum over states and consider just the ground and one electronically excited state. Indeed, the literature is replete with calculations based on two-level approximations to simplify the optical properties of complex molecular systems. On the other hand, the coherence features that arise through adoption of the celebrated Bloch equations are limited to exact two-level systems and are rarely applicable to the optical response of complex molecular media. 

The selection rules for multiphoton transitions are clearly different from the usual dipole selection rules, since each photon carries an angular momentum 1 Thus, for two-photon transitions, one rule is A J = 0 2, but further control can be exercised by selecting the polarisation of the light the A J = 0 transitions are only possible if the laser light is linearly polarised (i.e. contains both circular polarisation), while the choice of either circular polarisation results in an increase or a decrease of J. Detailed discussion of the selection rules for two-photon transitions can be found in several papers [453, 455, 459]. For multiphoton transitions, the same principles apply, and the role of polarisation is still more significant. A general reference is [460], in which selection rules are derived from first principles, and a list of selection rules for two-photon transitions is given in table 9.1. 

Various forms of radiation have been used to produce ions in sufficient quantitites to yield neutral products for subsequent analysis. In principle, it should be possible to use intense beams of UV below ionization threshold for this purpose. To date, however, efforts to collect neutrals from resonant multiphoton ionization (REMPI) have not succeeded. In one experiment, 1 mbar of gaseous -propyl phenyl ether was irradiated at room temperature with a 0.1 W beam of 266 nm ultraviolet (from an 800 Hz laser that gives 8 n pulses) concurrent with a 0.5 W beam at 532 nm. The beams were intense enough not only to ionize the ether in the mass spectrometer, but also to excite it so that it expels propene. After several hours of irradiation < 10% of the starting material remained. Production of carbon monoxide and acetylene (decomposition products of the phenoxy group) could be detected by infrared absorption spectroscopy, but the yield of neutral propene (as measured by NMR spectroscopy) was infinitesimal. 

Laser-scanning microscopes can be classified by the way they excite and detect fluorescence in the sample. One-photon microscopes use a NUV or visible CW laser to excite the sample. Two-photon, or Multiphoton , microscopes use a femtosecond laser of high repetition rate. The fluorescence light can be detected by feeding it back through the scanner and through a confocal pinhole. The principle is termed confocal or descanned detection. A second detection method is to divert the fluorescence directly behind the microscope objective. The principle is termed direct or nondescaimed detection. 

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