Two-photon and multiphoton absorption

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. 

Two-photon absorption has been observed in the microwave region with an intense klystron source but in the infrared, visible and ultraviolet regions laser sources are necessary. 

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 

Then Equation (9.20) is seen to be analogous to Equations (6.64) and (6.65) for vibrational Raman transitions. 

Because two-photon selection mles are different from one-photon (electric dipole) selection mles, two-photon transitions may allow access to states which otherwise could not be reached. We shall consider just one example in detail - a two-photon electronic absorption specfrum. 

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The inclusion of only two Bom-Oppenheimer states in our derivation is warranted if the one-photon absorption process is resonant with the electronic transition frequency. (Two-photon and multiphoton absorption processes are assumed to be nonresonant.) However, at the same time the pulse must be broad enough in frequency to include the spread of Franck-Condon-allowed vibrational levels. 

Figure 9.27 Multiphoton processes (a) Raman scattering, (b) absorption of two identical photons, (c) absorption of two different photons and (d) absorption of three identical photons. V and V are virtual states...

Thus far, we have examined vibrational spectroscopy using IR absorption spectroscopy, what we called in Ch. 3 one photon method , a general type that encompasses most experiments in spectroscopy. There exist, however, other types of spectroscopy to observe vibrations. These are for instance Raman spectroscopy, which is also of a current use in chemical physics and may be considered a routine method. Other less known methods are modem time-resolved IR spectroscopies. All these methods are two-photon or multiphoton spectroscopies. They do not involve a single photon, as in absorption, but the simultaneous absorption and emission of two photons, as in Raman and in other scattering experiments, or the successive absorption(s) and emission(s) of photons that are coherently delayed in time, as in time-resolved nonlinear spectroscopies. By coherently , we assume the optical waves that carry these two photons keep a well-defined phase difference. In this latter type of spectroscopy, we include all modem set-ups that involve time-controlled laser spectroscopic techniques. We briefly sketch the interest of these various methods for the study of H-bonds in the following subsections. 

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... 

Multiphoton Absorption and Ionization. High laser powers can induce the simultaneous absorption of two or more photons that together provide the energy necessary to excite a transition this transition may be one that is forbidden as a single-photon process (8,297). Such absorption can be made Doppler-free by propagating two laser beams of frequency V in opposite directions, so the Doppler shifts cancel and a two-photon transition occurs at 2v for any absorber velocity. The signal is strong because aU absorbers contribute, and peak ampHtudes are enhanced by, which may... 

Figure 8.2e shows the dependence of the fluorescence intensity on the excitation power of the NIR light for the microcrystals measured with a 20x objective. In this plot, both axes are given in logarithmic scales. The slope of the dependence for the perylene crystal is 2.8, indicating that three-photon absorption is responsible for the florescence. On the other hand, slopes for the perylene and anthracene crystals are 3.9 for anthracene and 4.3 for pyrene, respectively. In these cases, four-photon absorption resulted in the formation of emissive excited states in the crystals. These orders of the multiphoton absorption are consistent with the absorption-band edges for each crystal. The four-photon absorption cross section for the anthracene crystal was estimated to be 4.0 x 10 cm s photons by comparing the four-photon induced fluorescence intensity of the crystal with the two-photon induced fluorescence intensity of the reference system (see ref. [3] for more detailed information). 

A technique that has been used in laboratory studies for oxides of nitrogen and shows promise for field measurements is resonance-enhanced multiphoton ionization (REMPI) (Guizard et al., 1989 Lemire et al., 1993 Simeonsson et al., 1994). For example, Akimoto and co-workers (Lee et al., 1997) have reported a REMPI system in which a (1 + 1) two-photon absorption of light at 226 nm by NO results in ionization (vide supra). They report a detection limit of 16 ppt in their laboratory studies. Other oxides of nitrogen such as NOz and HN03 can also photodissociate in the... 

The structure-property relationships are affected by three main structural elements-coordination and hence packing, which determines some of the nonlinear harmonics the degree of conjugation along the backbone and the effects of the substituents-all of which have previously been reported to affect two-photon absorption processes thus it is proposed that the same applies for other higher-order systems. However, it is rare for reports of these high-order multiphoton absorption processes displayed by organic metal complexes to be accompanied with detailed molecular structure to show the correlation between the photoproperties. 

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