Two-photon transitions

A good example is the spectnun of naphthalene. The two lowest excited states have 62 and synnnetries and are allowed for one-photon transitions. A weak transition to one of these is observable in die two-photon spectnun [33], presumably made allowed by vibronic effects. Much stronger two-photon transitions are observable at somewhat higher energies to a and an A state lying quite close to the energies predicted by theory many years earlier [34]. 

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. 

Nevertheless, 1,4-difluorobenzene has a rich two-photon fluorescence excitation spectrum, shown in Figure 9.29. The position of the forbidden Og (labelled 0-0) band is shown. All the vibronic transitions observed in the band system are induced by non-totally symmetric vibrations, rather like the one-photon case of benzene discussed in Section 7.3.4.2(b). The two-photon transition moment may become non-zero when certain vibrations are excited. 

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... 

The detection probability for a given trajectory depends on the fragment orientation (its Mj value) and the nature of the probe transition. All of these images were obtained via the two-photon Ilg XAS) transition. Five rotational branches are thus possible O, P, Q, R and S. The amplitudes for each of these two-photon transitions can be obtained from a sum of paired, Mj-dependent, one-photon amplitudes.37 The O branch, for example, consists of a contribution from a parallel P-type transition to a 7A virtual state, followed by a perpendicular P-type transition to the final 1ffs Rydberg (which is assumed to be ionized promptly). The product of those two transition amplitudes must be summed with another product in which the first transition is perpendicular and the second is parallel. The P and R branches consist of four contributions each and the Q branch has six such terms in its transition amplitude. The required one-photon amplitudes are taken from Ref. 37. 

Two-photon absorption occurs when the energy of a molecular transition matches the combined energy of two photons. Quantum mechanically, the absorption probability is proportional to the two-photon transition moment from the ground state, g, to the excited state, n, via intermediate state, m, and can be expressed as follows (Boyd 1992 Abe 2001) ... 

Hornung, T., Meier, R., Zeidler, D., Kompa, K. L., Proch, D., and Motzkus, M. 2000. Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback. Appl. Phys. B-Lasers Opt. 71(3) 277-84. 

Meshulach, D., and Silberberg, Y. 1998. Coherent quantum control of two-photon transitions by a femtosecond laser pulse. Nature 396(6708) 239 2. 

The two-photon transition operator is a tensor whose components may be nonzero. Thus an important reason for doing two-photon spectroscopy is that it allows us to observe the transitions directly as allowed transitions instead of indirectly as forbidden transitions as are all one-photon spectra of transition metal ions. 

Comprehensive experimental investigations of 2PA processes in fluorene derivatives were performed by Hales et al. [53,56-59] with open aperture Z-scan [26], two-photon induced fluorescence [60] and femtosecond white-light continuum pump-probe methods [61]. For degenerate two-photon excitation, the experimental 2PA spectra of symmetrical and asymmetrical fiuorenes are presented in Figs. 15 and 16. These spectra were obtained with the combination of open aperture Z-scan and two-photon fluorescence methods [57]. For centrosymmetric molecules, two-photon transitions from... 

To complete the two-photon transition, the two photons must arrive at the absorber within the virtual state lifetime r. For classical uncorrelated photons the probability of accidental overlap increases with photon flux density. Therefore excitation by short, tightly focused laser pulses is needed for the TPA. Probabilistic analysis gives the two-photon transition rate ... 

Javanainen J, Gould PL (1988) Linear intensity dependence of a two-photon transition rate. Phys Rev A 41 5088-5091... 

Figure 2. Transient two-photon spectra recorded at an excitation wavelength of 834 nm (pump) for (a)39,39 K2 and (b)39,41 K2. The ionization step (probe) was achieved by a delayed two-photon transition of the same wavelength. Despite their great similarity both molecules exhibit quite individual oscillatory behavior [7],...

Even in a molecule the size of benzene the resolution achieved in this way is sufficient to investigate the dynamic behavior of individual rotational states. For this it is necessary to eliminate the Doppler broadening of the rovibronic transitions. Two methods have been applied (i) the elimination of Doppler broadening in a Doppler-free two-photon-transition and (ii) the reduction of Doppler broadening in a molecular beam. Measurements of the dynamic behavior have been performed in the frequency [3] and time domain [4]. We will briefly summarize the results from high-resolution measurements and discuss the conclusions on the intramolecular decay mechanism. Then it will be discussed how the intramolecular dynamics is influenced by the attachment of an Ar or Kr atom to the benzene molecule, leading to a weakly bound van der Waals complex. 

From the point of view of optimizing selectivity, this transition, which shows well-resolved P, R, and S branches, is most likely to be a preferable starting point compared to the B-X or C-X bands of this molecule the two-photon transition intensity for the latter bands would be completely concentrated in the O -branch lines, which would not be well resolved. 

The fact that the single photon transitions require so little power prompts us to consider two photon transitions. Consider the Na 16d — 16g transition via the virtual intermediate 16f state which is detuned from the real intermediate 16f state as shown by the inset of Fig. 16.3. If the detuning between the real and virtual intermediate states is A and the matrix elements between the real states arefxx and fi2, the expression analogous to Eq. (16.5) for a two photon transition is... 

Recently, Brewer et al. (11,12) have reported on the use of lasers to induce the two photon transition in iodine and sulfur atoms, so that these atoms may be detected by fluorescence. 

The nonlinear absorption between two states separated by energy 2h(o is better known as two-photon absorption. Two-photon transitions are highly allowed only if the initial and final states of the transition arc the same parity. Two-photon... 

Another possible means of distinguishing electronic from vibronic lines is two-photon spectroscopy. The relevant matrix element for a single beam two-photon transition is... 

Chu, S. and Mills Jr., A.P. (1982). Excitation of the positronium l3Si-23Si two-photon transition. Phys. Rev. Lett. 48 1333-1337. 

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