Multiphoton spectroscopy

The subject of multiphoton excitation spectroscopy began in 1931 when Goppert-Mayer [450] wrote a theoretical paper in which she calculated the transition rate for an atom in the presence of two photons rather than just one. At the time, the process seemed rather exotic, and it was reassuring that the calculated rate was so low as to guarantee that it could not readily be observed in the laboratory with conventional sources. This conclusion was reassuring because it implies that a simple perturbative theory (one photon per transition is the weak-field limit) is adequate for most purposes. 

The subject came to life with the advent of lasers, when it became easy to create intense beams of light. Since the probability of excitation by two photons grows as the square of the photon density, whereas the probability of single-photon excitation grows only linearly with photon density, two-photon transitions gain in relative strength with increasing intensity despite the small value of the rate coefficient. 

The development of multiphoton spectroscopy has followed that of lasers as the available power has increased, so has the number of photons involved in individual transitions. More significantly, it has become apparent that the physics of the interaction between radiation and matter is not the same at high laser powers as under weak illumination, i.e. that there is a qualitative change which sets in at strong laser fields. This is normally expressed by saying that perturbative approximations break down. A more direct (and equally accurate) statement is that new effects are observed, which are not present in conventional spectroscopy, even where the latter is extended to include, say, two- and three-photon transitions. 

We begin with a brief summary of some aspects of multiphoton physics 

In this section we consider the simultaneous absorption of two or more photons by a molecule that undergoes a transition Ei Ef with ( / — ,-) = The 

The first detailed theoretical treatment of two-photon processes was given in 1929 by Gbppert-Mayer [237], but the experimental realization had to wait for the development of sufficiently intense light sources, now provided by lasers [238,239]. 

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All the previous discussion in this chapter has been concerned with absorption or emission of a single photon. However, it is possible for an atom or molecule to absorb two or more photons simultaneously from a light beam to produce an excited state whose energy is the sum of the energies of the photons absorbed. This can happen even when there is no intemrediate stationary state of the system at the energy of one of the photons. The possibility was first demonstrated theoretically by Maria Goppert-Mayer in 1931 [29], but experimental observations had to await the development of the laser. Multiphoton spectroscopy is now a iisefiil technique [30, 31]. 

Ashfold M N R and Howe J D 1994 Multiphoton spectroscopy of molecular species Ann. Rev. Phys. Chem. 45 57-82... 

Fig. 1.9. Potential energy curves of 2 1 showing the symmetric and asymmetric dissociation channels. Also shown is an example of transient pump-probe multiphoton spectroscopy, discussed in Sect. 1.3.2...

The theoretical background of multiphoton spectroscopy and a discussion of experiments published up to November 1966 has been given in a review article by Peticolas HD. 

Multiphoton ionization (MPI) has become an important technique for the study of highly excited electronic states (e.g., Rydberg states in polyatomic molecules) or states not accessible by one-photon absorption. Some studies that have made use of simultaneous absorption of more than one photon by the species of interest have already been mentioned in previous sections, particularly if the non-linear absorption leads to fluorescence. Table 6 provides details of remaining articles dealing with multiphoton spectroscopy and MPI. 

Nonlinear Raman scattering spectroscopy is a multiphoton spectroscopy that enables access to vibrationally excited molecular levels. Through nonlinear optical processes, this technique allows us to study rich molecular information which cannot be reached by linear optical method. 

Time-resolved measurements are also one of the advantages in multiphoton spectroscopy. In the case of nanomaterials, physical and chemical properties are largely affected by interaction with surrounding environments. Therefore, the dynamical study should be useful for characterizing nanomaterials from the viewpoints of nanodevice applications. 

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. 

In this chapter, Wigner s scattering theory has been presented and applied to a wide variety of effects which occur when Rydberg series of au-toionising resonances interact with one another. Overlapping resonances occur in many atomic spectra they become more and more frequent as the number of subshells increases. They can also be manufactured by multiphoton spectroscopy, a theme we return to in the following chapter. The effects we have described (symmetry reversals, width fluctuations and disappearances of structure) are also expected to occur in photoelectron spectroscopy [449]. 

Fig. 9.3. The Q-reversal effect in multiphoton ionisation. Note that Q stands for the generalised asymmetry parameter in multiphoton spectroscopy, as opposed to q in single-photon spectroscopy. The choice of parameters corresponds to REMPI of K (see text - after J.-P. Connerade and A.M. Lane [385]).

J.W. Borst, M.A. Hink, A. van Hoek, A.J.W.G. Visser, Multiphoton spectroscopy in living plant cells, Proc. SPIE 4963, 231-238 (2003)... 

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