Polarization Dependence of the Two-Photon Absorption of Tumbling Molecules with Application to Liquid 1-Chloronaphthalene and Benzene

Abstract

The two-photon absorption cross section δ for photons of any polarization (linear, circular, or elliptical) is averaged over all orientations of the absorbing molecule. The result is given by 〈δ〉 = δFF + δGG + δHH, where δF, δG and δH are molecular parameters and F, G, and H are simple functions of the polarization vectors. It is shown how the δ's may be calculated from theory and also how they may be measured by experiment. Experiments using only linearly polarized light are insufficient to determine all three δ's; hence, circularly polarized light will play an essential role in this spectroscopy. For absorption of two linearly polarized photons with angle θ between their polarization vectors, the angular dependence is 〈δ〉 = A + Bcos2θ, where A and B are simple combinations of the δ's. We obtain two exact symmetry rules which permit allowed two-photon transitions of different symmetries to be distinguished. For transitions from totally symmetric ground states the rules are: (1) If the excited state transforms like xy, yz, or zx, then δF = 0. (2) If the excited state transforms like x2, y2, or z2, then δG = δH. In cases of near resonance, when a single intermediate state dominates the formula for the cross section, we show that δF = δH, and that linearly polarized light suffices for a complete investigation. These results are applied to liquid 1-chloronaphthalene. We find two allowed two-photon transitions which are assigned Bb11g (perpendicular nodes) at 37 700 cm−1 and A1g (total symmetry) at 42 600 cm−1. This is in reasonable agreement with theoretical predictions of other authors. We have also examined the region of the second excited singlet of benzene, near 6.2 eV. We were not able to detect any two-photon absorption, setting an upper limit of about 10−51 cm4·sec/photon·molecule on its 〈δ〉. This leads to an unequivocal assignment of B11u for this state according to calculations of Jortner. In an Appendix we examine the effect of “hot spots” in the laser beam on the observed cross sections. We show that the elimination of the hot spots is of some importance, contrary to a statement of other authors.

Two-Color Two-Photon Excitation Using Femtosecond Laser Pulses

“…Here, in contrast to 1c2p experiments, it is possible to manipulate the polarization of each of the absorbed photons independently. Theoretical considerations 9,18 as well as 2c2p experiments conducted as absorption measurements 19 imply that there is a close relationship between the relative polarizations of the two photons and the symmetry of the involved electronic states. The absorption data published by McClain 18,19 lead to the assumption that it should be possible to discriminate chromophores possessing different symmetries by their different behavior toward different excitation polarizations.…”

“…Theoretical considerations 9,18 as well as 2c2p experiments conducted as absorption measurements 19 imply that there is a close relationship between the relative polarizations of the two photons and the symmetry of the involved electronic states. The absorption data published by McClain 18,19 lead to the assumption that it should be possible to discriminate chromophores possessing different symmetries by their different behavior toward different excitation polarizations. An additional indication for this assumption is given by the work of Lakowicz 10 et al where a different behavior of PTP and indole toward the excitation with perpendicularly polarized photons was found.…”

The photochemical event in rhodopsins

“…Transitions of the g t-t g type are allowed in two photon absorption spectroscopy. The ' A , state has been shown to be the lowest excited singlet state in long chain linear polyenes (41,(55)(56)(57)(58)(59)(60)(61)(62)(63)(64)(65). While actual visual chromophores do not have a center of inversion, they "remember" C 2 h symmetry sufficiently for transitions from the ground state to 'A,--like states to remain weak and transitions to 'Bu+-like states intense in one-photon spectra.…”

“…It became accessible to experimental research thanks to the rapid development of two photon spectroscopy (see refs. [52][53][54][55]. Transitions of the g t-t g type are allowed in two photon absorption spectroscopy.…”

Alternative selection rules for one- and two-photon transitions in tribenzotetraazachlorin: Quasi-centrosymmetrical π-conjugation pathway of formally non-centrosymmetrical molecule

“…To perform the orientational averaging we apply the classical method of Monson and MacClain. 49,50 According to Sec. III A, both molecules possess quasi-D 2h symmetry.…”