Two photon process

Up to now, we have been primarily concerned with one-photon absorption and emission processes, whose probability amplitudes are given by the first-order term 

The frequencies co — co of the Raman lines in Fig. 10.1 prove to be independent of the excitation laser frequency co, and analysis shows that they are equal to vibrational energy level separations in Sq p-difluorobenzene. This is an example of the energy conservation law h (o — co ) = E — in Raman spectroscopy An incident photon with energy hoj interacts with the molecule a transition occurs from level k to level m , and a scattered photon emerges with a shifted energy hco that compensates for the energy gained or lost by the molecule (Fig. 10.2). When co co, the process is called a Stokes Raman 

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We will now look at two-photon processes. We will concentrate on Raman scattering although two-photon absorption can be handled using the same approach. In Raman scattering, absorption of an incident photon of frequency coj carries... 

Jent F, Paul H and Fischer H 1988 Two-photon processes in ketone photochemistry observed by time-resolved ESR spectroscopy Chem. Phys. Lett. 146 315-19... 

Figure B2.5.18 compares this inter molecular selectivity with intra molecular or mode selectivity. In an IR plus UV, two-photon process, it is possible to break either of the two bonds selectively in the same ITOD molecule. Depending on whether the OFI or the OD stretching vibration is excited, the products are either IT -t OD or FIO + D [24]- hr large molecules, mirmnolecular selectivity competes with fast miramolecular (i.e. unimolecular) vibrational energy redistribution (IVR) processes, which destroy the selectivity. In laser experiments with D-difluorobutane [82], it was estimated that, in spite of frequency selective excitation of the...

In the discussion in Section 9.1.6 of harmonic generation of laser radiation we have seen how the high photon density produced by focusing a laser beam into certain crystalline materials may result in doubling, tripling, etc., of the laser frequency. Similarly, if a laser beam of wavenumber Vl is focused into a cell containing a material which is known to absorb at a wavenumber 2vl in an ordinary one-photon process the laser radiation may be absorbed in a two-photon process provided it is allowed by the relevant selection rules. 

The similarity between a two-photon absorption and a Raman scattering process is even closer. Figure 9.27(a) shows that a Raman transition between states 1 and 2 is really a two-photon process. The first photon is absorbed at a wavenumber to take the molecule from state 1 to the virtual state V and the second photon is emitted at a wavenumber Vj,. 

Because Raman scattering is also a two-photon process the selection rules for two-photon absorption are the same as for vibrational Raman transitions. For example, for a two-photon electronic transition to be allowed between a lower state j/" and an upper state... 

Figure 9.50 Processes involved in obtaining (a) an ultraviolet photoelectron spectrum, (b) a zero kinetic energy photoelectron (ZEKE-PE) spectrum by a one-photon process and (c) a ZEKE-PE spectrum by a two-photon process in which the first photon is resonant with an excited electronic state of the molecule...

More commonly, the resonant two-photon process in Figure 9.50(c) is employed. This necessitates the use of two lasers, one at a fixed wavenumber Vj and the other at a wavenumber V2 which is tunable. The first photon takes the molecule, which, again, is usually in a supersonic jet, to the zero-point vibrational level of an excited electronic state M. The wavenumber of the second photon is tuned across the M to band system while, in principle, the photoelectrons with zero kinetic energy are detected. In practice, however, this technique cannot easily distinguish between electrons which have zero kinetic energy (zero velocity) and those having almost zero kinetic energy, say about 0.1 meV... 

The application of nonlinear optical recording techniques for reversible optical data storage based on the excitation of photochromic molecules by two-photon processes also has been described (154). 

However, as Raman scattering is a two-photon process, the probability of the Raman scattering process is lower than that of fluorescence and IR absorption processes. The cross section of Raman scattering is 10 cm, which is much smaller than that of fluorescence ( 10 cm ) and IR absorption ( 10 °cm ). When we detect Raman scattering at the nanoscale, the number of photons obtained is less than with the usual micro-Raman spectroscopy due to reduction in the detection area or the number of molecules. To overcome this problem, we need to devise a method for amplification of Raman scattering. 

Using a perturbative analysis of the time-dependent signal, and focusing on the interference term between the one- and two-photon processes in Fig. 14, we consider first the limit of ultrashort pulses (in practice, short with respect to all time scales of the system). Approximating the laser pulse as a delta function of time, we have... 

Like Raman scattering, fluorescence spectroscopy involves a two-photon process so that it can be used to determine the second and the fourth rank order parameters. In this technique, a chromophore, either covalently linked to the polymer chain or a probe incorporated at small concentrations, absorbs incident light and emits fluorescence. If the incident electric field is linearly polarized in the e direction and the fluorescent light is collected through an analyzer in the es direction, the fluorescence intensity is given by... 

Light intensity at the usual levels seldom has an effect on the primary photochemical step if all other variables are kept constant, although it may affect overall results considerably since it may control the concentrations of reactive intermediates. However, it will affect the outcome of a competition between primary one-photon and two-photon processes. The latter are still somewhat of a rarity but may be more important than is commonly realized, namely in rigid media where triplets have long lifetimes and quite a few of them are likely to absorb a second photon. The additional available energy may permit motion to new minima in Ti and thus give new products. 

Two-photon fluorescence microscopy has also been used with good effect in the near-IR. For example, Ferguson et al.r24> at the University of Strathclyde have used 270 fsec pulses from a titanium sapphire (Ti sapphire) laser at 790 nm to observe visible fluorescence from dyes in zebra fish larvae and erythrocytes. The high depth and lateral definition afforded by the two-photon process and confocal microscopy are useful here. Also, the use of near-IR excitation minimizes photobleaching. 

Because of the low energy of a ruby-laser photon (X = 6940 A A 1.8 eV), most of the photolysis experiments with ruby laser sources either use frequency doubling or proceed by two-step excitation or two-photon processes. 

Polymerization of styrene and p-isopropylstyrene could be photo-initiated with radiation from the ruby laser in the absence of photosensitizers and oxygen Since ordinarily no unsensitized photoinitiation of styrene is detected for wavelengths longer than 4000 A, the results of this experiments must be due to two-photon processes. 

TWO-PHOTON EXCITATION TWO-PHOTON PROCESS TWO-PROTONIC-STATE ELECTROPHILES AFFINITY LABELING Two-site ping pong mechanism,... 

Fig. 6.10 Z-scheme system for water splitting by a two-photon process with visible light response [149],...

The use of two-photon processes is also being extensively studied in the use of photochromies in 3D data storage (Chapter 1, section 1.2.8.3) and in the holographic storage of data, which is covered in Chapter 5 (section 5.4). 

A two-photon process at 435 nm to generate O( D) has been observed in laboratory studies (Crowley and Carl, 1997). However, the combination of relatively low light intensities and high pressures which quench excited NOz make this unimportant in the atmosphere. 

Photofragmentation-laser-induced fluorescence (PD-LIF). This spectroscopic method is based on the photofragmentation of NH-, in a two-photon process using 193-nm radiation, followed by laser-induced fluorescence of the NH fragment (Schendel et al., 1990). The processes are as follows ... 

Two-photon processes caused by absorption of photons by reaction intermediates and excited states are common under condition of high-power laser excitation. The consequence of two-photon excitation can include the formation of new reaction intermediates (electron photoejection is common) and the partial depletion of intermediates formed in monophotonic processes. To minimize this problem, do not use higher laser power then required to obtain a good signal/noise ratio, and do not focus the laser too tightly. There are in fact techniques used to obtain a more diffuse and homogenous laser beam (see below). 

Cyclohexene, upon excitation through a two-photon process providing 186 kcal/ mol, gives two species detected through ionization by a probe pulse and mass spectrometry a species at 82 amu, the parent stmcture or the drradical species formed through p-cleavage, and at 54 amu, a mass corresponding to butadiene. An ion at M-15, at 67, is also recorded. The femtosecond transients show that the 82 amu... 

Figure 3.18 Schematic representation of transition moment integral for monophotonic and biphotonic transitions in naphthalene. (A) Transition forbidden by one photon process (B) Allowed by two photon process.

The high intensity of laser light (lots of photons per cm3) gives significant probability to transitions in which two photons, rather than one, are absorbed. Such two-photon processes are a field of active study. 

Figure 7. Ratio of Na+ and Na2+ ion signals as a function of pump-probe delay for the two-photon process depicted in Fig. 6.

For a three-photon and a two-photon process we have shown that vibrational wavepacket propagation excited by an ultrashort laser pulse can be used to drive a molecule to a nuclear configuration where the desired product formation by a second probe pulse is favored (Tannor-Kosloff-Rice scheme). In both cases the relative fragmentation and ionization yield of Na2 was controlled as a function of pump-probe delay. By varying the delay between pump and probe pulses very slowly and therefore controlling the phase relation between the two pulses, additional interference effects could be detected. 

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