Absolute measurement of molecular two-photon absorption cross-sections using a fluorescence saturation technique

We have developed a fluorescence saturation technique for accurate measurements of the absolute molecular two-photon absorption (TPA) cross-section of fluorescent dyes. We determine the TPA crosssection both from measurements at excitation intensities well below saturation onset (in the square power-law regime) and from data obtained near the onset of saturation. The two estimates have different sensitivities to potential sources of errors. Using the square power-law regime requires calibration of the overall collection efficiency of the detection channel, including the quantum yield of the dye. In the saturation regime, the two key requirements are a good knowledge of the excitation profile and an adequate model of the two-photon excitation transition. To fulfill the former requirement, we developed diagnostic tools to characterize the tightly focussed excitation beam. To satisfy the latter requirement, we included the correct polarization dependent averaging over molecular orientations in our model. We measured the TPA cross-section of Rhodamine B (RhB) and Rhodamine 6g (Rh6g) in methanol at 798 nm for linear and circular polarization. For RhB we observed excellent agreement between the TPA cross-section estimate < sigma2 > obtained from the square power-law regime and that obtained from the saturation regime, < sigma2 >(sat). For the case of linear polarization we found: < sigma2 > = 12 +/- 2 GM and < sigma2 >(sat) = 10.5 +/- 2 GM. For the case of circular polarization we obtained: < sigma2 > = 8.4+/-2 GM and < sigma2 >(sat) = 7.5+/-2 GM. The results obtained with linear polarization are in good agreement with previously published non-linear transmission data (delta= 2sigma = 20.4 GM at 800nm). For Rh6g the difference between < sigma2 > and < sigma2 >(sat) is larger, but still considerably smaller than the variance of sigma2 values found in the literature.