The Two-Photon Absorption Process

The probabihty of a molecule absorbing one photon is proportional to the intensity of the excitation beam  

The 2PA process is very weak relative to one-photon excitation, in the sense that the ratio (from Eqs. 1 and 2) is typically small for intensities be- 

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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...

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. 

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] ... 

Figure Bl.22.7. Left resonant second-harmonic generation (SHG) spectrum from rhodamine 6G. The inset displays the resonant electronic transition induced by the two-photon absorption process at a wavelength of approximately 350 nm. Right spatially resolved image of a laser-ablated hole in a rhodamine 6G dye monolayer on fused quartz, mapped by recording the SHG signal as a function of position in the film [55] SHG can be used not only for the characterization of electronic transitions within a given substance, but also as a microscopy tool.

We have already discussed the two-photon absorption process [9.187] (Sect. 9.1.3c). Normally, the signals are Doppler broadened, and high resolution is not obtained even if narrow-band lasers are used. However, a very important observation was made as early as 1970 by Chebotayev and co-workers [9.188]. The Doppler broadening can be eliminated if the two photons are extracted in such a way that one is supplied from one of two counter-propagating laser beams and one from the other beam. For a certain atom with a velocity component v along one direction of propagation, the energy in-... 

As it has been already mentioned in the introduction, the most important consequence of the two-photon absorption process is the possibility of exciting the molecule with the help of a pair of photons of two times larger wavelength than in the case of IPA. Another important aspect of the 2PA phenomenon is related to the fact that for the one-and two-photon transitions (in the case of centrosymmetric molecules), different selection rales apply (see Figure 10.3.1). 

Formally, at a microscopic level, the two-photon absorption process can be described by the imaginary part of second hyperpolarizability, y(-co co, -ro, ro), charaeterizing the interaction of the molecule with an optical field of high intensity at a frequency co. As it was already mentioned in the introduction, the most frequently used parameter quantifying the two-photon absorption of the atomic or molecular system is the 2PA cross-section ( 2pa)> usually presented in the GM units (1 GM = 10-50 cm s photon ). Referring to the semi-classical approximation for the degenerate 2PA process, C2PA can be defined as fol-... 

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. 

The absorption cross sections of the Sn Si transition are determined from the kinetic analyses based on the two-photon absorption measurement. In contrast, tetraphenylporphin scarcely show the S2 state fluorescence. In order to elucidate the effect of the imino hydrogens on the radiationless transitions, deuterium isotope effect on the relaxation processes from the lowest excited singlet state of metal free porphyrins has been investigated. 

The two-photon absorption spectroscopy can overcome the symmetry barrier imposed by the selection rule for angular momenta in the one-photon process. Thus, the technique is able to identify and assign molecular and atomic states which are not accessable to one-photon spectroscopy. 

The difference between the RSA process and two-photon absorption is that the two-photon absorption is virtually instantaneous whereas processes involving intermediate absorbing states exhibit certain kinetic behavior,... 

The transition to the C B- state of H 0 was achieved by a two photon absorption of KrF laser light near 248 nm (32). The OH(A-X) fluorescence excitation spectrum in the 247.9-248.5 nm range follows the rotational structure of the C B -+ X A transition. However, (i) the OH(A-X) fluorescence spectrum produced by the two photon dissociation of H 0 has a maximum population at N = 14, while single photon absorption near 124 nm generates OH fluorescence spectrum with a maximum population at N = 20 (ii) only absorption to Ka= 1 (and not Ka= 0 where K is the rotational angular momentum about the a axis) of the ClB-L state predissociates into 0H(a2%) + H probably through the B A state. Apparently, the two-photon absorption near 248 nm predominantly populates the c b state, while the single photon process populates the B A near 124 nm. 

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. 

Some authors are using the same relations between the third-order susceptibility and the nonlinear refractive index and the two-photon absorption coefficient for the self- and cross-phase modulation process. 

If some of the involved frequencies are degenerate the above expressions for 2D-molecules can be further simplified due to the permutations symmetry of the nonlinearities. The two-photon absorption is frequently characterized with a coefficient <5 defined as the loss of photons through the two-photon process upon propagation along the z-direction... 

Concerning the chemical stability, oxidation by the ambient oxygen is of major concern [18]. Sealing and encapsulation of the material improves the lifetime. For photostability any absorption process has to be strongly avoided [19, 20]. Not only the linear absorption a0 but also the two-photon absorption a2 is of concern. The prevention of any absorption is therefore not only important for the figures of merit but also for the photostability. 

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... 

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