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

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.