Two-photon absorptive processes

In a two-photon absorption process the first photon takes the molecule from the initial state 1 to a virtual state V and the second takes it from V to 2. As in Raman spectroscopy, the state V is not an eigenstate of the molecule. The two photons absorbed may be of equal or unequal energies, as shown in Figures 9.27(b) and 9.27(c). It is possible that more than two photons may be absorbed in going from state 1 to 2. Figure 9.27(d) illustrates three-photon absorption. 

The population of level 2 occurs after a two-step, two-photon absorption process. The first step populates level 1 and the second step populates level 3, which feeds the emitting level 2. 

Instead, Kroger ct al. suggest consecutive two-photon absorption process, that is, process (VII-134) followed by... 

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. 

In the field of optical limiting based on two-photon absorption there exists some confusion with the convention of different physical processes. We refer here to the two-photon absorption process based on a2 OC -to,to,-to,to) and... 

Fig. 11. Schematic of the excellent three-dimensional spatial resolution of the two-photon absorption process...

To understand why control over the total cross section is lost and how the backward-forward symmetry is broken, we analyze in some detail the simplest case in this class, namely the interference between a one-photon and a two-photon absorption process [78], Consider irradiating a molecule by a field composed of two modes, o>2 and a)h with a)2 = 2coh for which the light-matter interaction is... 

In a composite material, as described here, the effective third-order nonlinear susceptibility should depend linearly with the concentration of the inclusions in a low filling fraction regime. In that way, the nonlinear absorption coefficient of the medium, associated to the Im[ (ru)] and consequently to the two-photon absorption processes, should also be a function of the inclusions concentration. 

Similar quenching was also observed when the colloid was excited by a two-photon absorption process. The decrease in the fluorescent peak intensity as a function of the colloid filling factor is shown in figure 18.6, for one and two-photon excitation. The fluorescence intensity was normalized to the case of no NPs in the solution. Each solid line in figure 18.6 is a two exponential decay fitting. Same decay parameters were used to fit the experimental data, indicating that the NP-Tryptophan interaction is similar for one and two-photon excitation. 

The photoinduced polar order results from the redistribution of molecules following their repeated selective polar excitation. Polar excitation involves simultaneous one- and two-photon absorption processes on highly coherent electronic excited states. The excitation probability can be written as the sum of three terms two axial terms related to one- and two-photon absorption, respectively, and the polar term corresponding to the interference betwem one- and two-photon absorption. Practically, in addition to molecular orientational diffusion, polar ordering also results from the competition between polar and axid excitations. 

The dyncimics of the photoreactive systems were investigated by two-photon absorption processes. The photopolymerizable a-DSP system was investigated by two-photon absorption process. For this process a dye-laser pumped by the second harmonic of a Nd-Yag laser was used to provide a tunable wavelength range from 600 to 700 nm. Even at... 

Such a mechanism would be consistent with the absence of reaction by a two-photon absorption process, because such a process does not produce excitons in high concentration and, therefore, reduce blexcitonic process. The temperature effect is simply a manifestation of reduced exciton hopping at lower temperature. 

For a degenerate two-photon absorption process (absorbing two photons of the same frequency), Eq. (9) can be transformed into the following expression [6] ... 

The basic idea of this method is to investigate the dependence of the fluorescence intensity on the excitation intensity because this relation determines the order of the non-linearity [8, 38-40]. For example, a quadratic dependence corresponds to a two-photon absorption process and a cubic dependence refers to a three-photon absorption. By means of a tunable excitation light source, one can also map the dispersion of the multi-photon transition, the resulting multi-photon excitation... 

In the present contribution the discussion of the NLO response is restricted to off-resonant case. The only exception is the purely resonant quantity, namely imaginary part of second-order hyperpolarizability in the resonant regime (Im-y(-tt> tu, —w, w)). This quantity describes the process of simultaneous absorption of two quanta. The two-photon absorption (TPA) process is much better understood than the three-photon absorption. The basic quantity associated with the two-photon absorption process is the two-photon absorption tensor (S ). In the most general case referring to two different photons (different polarizations and different energies is given by [75, 81] ... 

So, for two chemically distinct molecules or cliromophores A and B, with well-characterized vibronic excited states a and /S, a proximity-induced two-photon absorption process can be induced by tuning the exciting laser to a frequency equivalent to a mean of molecular excitation frequencies for the two molecules. 

The first two terms in Eq. (5.13) arise from the cooperative mechanism, while the distributive mechanism gives rise to the third and fourth terms. Deriving the general rate for a proximity-induced two-photon absorption process from the square modulus of the result is an elaborate procedure producing sixteen terms, including cross-terms associated with quantum mechanical interference between the cooperat ve and distributive mechanisms. However, in view of the selection rules discussed earlier, it is not generally necessary to perform this calculation since each of the four specific mechanisms for two-photon absorption under consideration can, at most, have only two terms of Eq. (5.13) contributing to the matrix element. 

The rate of a general, proximity-induced, two-photon absorption process can be calculated by combining the Fermi Golden rule, Eq. (5.6), with Eq. (5.13). For each of the four specific cases to be studied, the selection rules normally dictate that only two of the four terms in Eq. (5.13) arise for any given mechanism, thus reducing the number of terms in the rate equation to just four. A brief derivation of the rate of absorption for each case is presented below. 

Two-photon absorption process Near-zone Far-zone... 

The direct photoexcitation of water molecules by ultrashort laser pulses is used for the investigation of primary events occurring from 10 s (thermal orientation of water molecules and ultrafast proton transfer) to 10" s (primary reactions of a solvated electron with protic species) (57,58,61-65). The nonlinear interaction of ultrashort UV pulses (typically less than 100 fs in duration and having a power of 10 W cm" ) with water molecules triggers multiple electron photodetachment channels within a hydrogen bond network (see equations 4-7). An initial energy deposition via a two-photon absorption process (2 X 4 eV) leads to the formation of nonequilibrium states of an excess electron... 

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