We present absolute two-photon absorption (2PA) spectra of 15 commercial organic dyes covering an extended range of excitation wavelengths, 550–1600 nm. The 2PA is measured with an estimated accuracy ±10% using a femtosecond fluorescence excitation method. The data are corrected for the variations of the pulse duration and the beam profile with the excitation wavelength, and are applicable as reference standards for 2PA measurements.
©2008 Optical Society of America
Simultaneous two-photon absorption (2PA) is a nonlinear optical process, which finds an increasing use in fluorescence microscopy , 3D optical memory [2,3], nanofabrication , optical power limiting , and photodynamic therapy [6,7]. These applications crucially rely on the development of new materials with well-characterized and optimized 2PA properties (see, e.g. [4,5,7–9]).
Measuring the 2PA cross sections and spectra of new compounds in a broad range of wavelengths is usually a tedious task, especially when careful characterizations of the laser pulse and other experimental conditions are required. On the other hand, if there were some reference compounds with well-characterized 2PA spectra, then one could determine the unknown 2PA cross section by comparing the two-photon excited fluorescence intensity to that of the reference, and thus automatically correct for the temporal- and spatial beam profile variations of the excitation pulse. Furthermore, if the reference compound is chosen such that its fluorescence spectrum overlaps with that of the new sample, one can record the signal at the same wavelength and thus overcome the necessity of knowing the detector spectral sensitivity.
Previously, Webb and co-authors [10, 11] published 2PA spectra of a number of commercial dyes in the spectral range 690–1050 nm. Evaluation of the absolute cross section from the data requires, in most cases, the knowledge of fluorescence quantum yield, which is not always available, and often varies from solvent to solvent. The 2PA cross sections of common organic dyes, such as Anthracene, Fluorescein, and some Rhodamines, have been reported in the literature at selected wavelengths [12–32]. However, these previous results vary by a large margin, which means that there is still a need for accurate 2PA cross section reference data.
Here we present an improved set of reference 2PA data, based on an extended collection of commercial organic dyes. The reference compounds are selected such that their 2PA spans the range 550–1600 nm, and the fluorescence emission spectra span from 375 to 900 nm, i.e. most of the visible, as well as near-IR range of wavelengths. The absolute 2PA spectra are corrected for the variations of the laser photon flux, pulse duration, and beam spatial profile.
2. Methods and experimental details
2.1 Measurement of 2PA cross section at selected wavelength
Our experimental setup is shown in Fig. 1. We use a 1-kHz repetition rate Ti:Sapphire femtosecond regenerative amplifier (Coherent Legend-HE), which is seeded by a Ti:Sapphire femtosecond oscillator (Coherent Mira 900). The oscillator is pumped by a Coherent Verdi cw frequency-doubled Nd:YAG laser. The amplifier output is down-converted with an optical parametric amplifier (OPA) (Quantronix TOPAS-C). For two-photon excitation we use either the fundamental of signal (1100–1600 nm) or second harmonic of either idler (790–1100 nm) or signal (550–790 nm) beam. A polarizer selects the signal (or idler). The residual fundamental after the frequency doubling crystal is cut with color filters. The pulse energy is 100–300 µJ (5–30 µJ with SHG). For one-photon excitation, the second harmonic of the Ti:Sapphire amplifier or second harmonic of signal at 550 nm are used. The polarization of the excitation beam is controlled with a λ/2 plate, and is set vertical for both one- and two-photon excitation.
The fluorescence method [13–17, 33] takes advantage of the direct comparison between the intensities of two- and one-photon excited fluorescence, where the last is used to calibrate the fluorescence quantum yield of the sample and the efficiency of the fluorescence detection. The 2PA cross section is then evaluated based on the relative intensity of the two-photon excited fluorescence, provided that the registration is carried out under exactly the same conditions.
In our setup (Fig. 1), we align the laser beam through two pinholes, placed 35cm apart, before and after the sample, which ensures that both 1PA and 2PA excitation beams pass through the exact same location, about 1 mm from the sample cell wall through which the fluorescence is collected. During the experiment the pinholes are open. The beam is slightly focused by an f=25cm lens, which is placed 14 cm before the sample. A spherical mirror (f=50 cm, diameter d=10 cm) collects the fluorescence at 90° with respect to the laser beam direction, and focuses the horizontally-elongated image of fluorescence track on the entrance plane of a grating spectrometer (Jobin-Yvon, Triax 550). The height of the vertical spectrometer slit is much larger than the height of the fluorescence image. The spectral dispersion on a two-dimensional CCD detector (Spectrum One) occurs in the horizontal direction, while the signal in the vertical direction is integrated over the whole slit height. The slit width is much smaller than the horizontal dimension of the fluorescence image and is kept the same in both 1PA and 2PA signal measurements. While recording the fluorescence spectrum, special care is taken to eliminate any spurious signals, such as scattered laser light, fluorescence of impurities, etc. The fluorescence spectra of the sample excited via 1PA and 2PA always had the same shape.
Here and below, lower indices 1 and 2 denote, respectively, one-photon and two-photon excitation. We assume that the excitation rate is always much below the saturation limit.
Consider first one-photon excitation. The fluorescence signal integrated over time, T, and wavelength interval, λmin-λmax, is:
where η(λ) is the differential detection efficiency (including efficiency of collecting fluorescence, finite slit width, diffraction grating efficiency, efficiency of the CCD detector, etc.), N 1 is the number of molecules in the sample excited per unit time. φ(λ) is the differential quantum efficiency of fluorescence, defined as, , where Q is the standard quantum yield, equal to the ratio of the radiative decay rate to the total decay rate of the S1 state. The number of molecules excited per unit time can be presented as follows:
where OD is the optical density of the sample at the excitation wavelength, ν 1 is the photon frequency (in Hz), I 1(x,y) is the incident intensity (in W/cm 2) in the x-y plane, perpendicular to the propagation direction, z. In the experiments, the optical density was, OD=0.05–0.1. The limits of integration in (2) are set from minus infinity to infinity because the slit height (y-direction) is much larger than the fluorescence spot’s height and because there is no re-absorption of fluorescence from the sample layers perpendicular to the observation direction (x-direction). The integral in (2) corresponds to the experimentally measured laser power (in w): . The one-photon fluorescence signal is,
Note that the one-photon excitation rate depends neither on the beam spatial profile nor on whether a pulsed or cw laser is used.
Consider now two-photon excitation. Assuming that the fluorescence collection- and detection conditions are the same as above, the intensity of the two-photon excited fluorescence is:
where g is the pulse repetition rate (in Hz) and N 2 is the number of molecules excited during one laser pulse,
where σ 2 is the 2PA cross section, C is the concentration (in cm-3), l is the beam path length inside the sample (1 cm in our experiment). Factor ½ in front of the expression (5) reflects the fact that two photons are needed to excite one molecule . The temporal and spatial profiles of the laser beam are well-described by Gaussians (see below), and, therefore, the intensity function can be presented as:
where I 2 (0) is the peak intensity (in W/cm 2), τ is the temporal pulse width (FWHM) and Δx and Δy are the spatial beam widths (FWHM). The average laser power (in W) is,
which gives the peak intensity:
Substitution of (6) and (8) into Eq. (5) gives:
As a result, the two-photon fluorescence intensity (4) reads:
By dividing the two fluorescence signals, and by substituting, lC=ln 10OD/σ 1, where σ 1 is the one-photon absorption cross section at one-photon excitation wavelength (λ 1), we find for σ 2:
The average laser power (W 1 and W 2) was measured with a calibrated optical power meter (OPHIR, Nova II). The one-photon excitation intensity was adjusted with neutral density filters, such that the F1 and F2 were of the same order. The fluorescence was integrated in a 40–60 nm interval around the emission peak. The signal was obtained by averaging 2–5 acquisition, where each acquisition included 0.5–5 s CCD integration time.
The one-photon cross section, σ 1(λ 1), was obtained from the molecular extinction measured with Perkin-Elmer Lambda 900 spectrophotometer. The peak extinction coefficient was evaluated from the linear part of the Lambert-Beer plot, obtained for a series of solutions with gradually decreasing concentrations.
A LabView routine was used to check the quadratic dependence of the 2PA at selected wavelengths, especially if the laser approached the long-wavelength edge of linear absorption. The excitation intensity was changed using an automated neutral density filter wheel, placed before the beam splitter (Fig. 1). A thin glass plate directed a small part of the excitation beam to the reference detector (Molectron J3-02), and a digital oscilloscope (Tektronix TDS 3052) transferred the detector output reading to the PC. The fluorescence signal was then measured as a function of the excitation intensity, and a linear fit to the log-log plot was applied. The quadratic law was verified, if the linear fit showed exponential factor, α=1.9–2.1, with a standard deviation less than 0.1.
The pulse duration was measured in the whole wavelength region, 550–1600 nm, with SHG auto-correlator (Clark MXR AC-150). For comparison, the same measurement was performed with FROG (Newport/Swamp Optics, Grenouille 8–50) in the 700–1000 nm range. Both measurements gave similar result. Figure 2(a) shows the pulse width (FWHM) measured with the auto-correlator in the signal (red symbols), second harmonic of idler (orange symbols) and second harmonic of signal (green symbols) range of wavelengths.
The beam spot size at the sample location was measured with a CCD camera (Xillix, PMI1400) using Air Force Resolution Chart for calibration. In the 550–1150 nm range, the beam spot was imaged directly, whereas at longer wavelengths, 1150–1600 nm, the camera detected the fluorescence spot created in a thin polymer film, activated with a two-photon (three-photon) absorbing fluorophore . In the latter case, the actual Δx and Δy values are obtained by multiplying the fluorescence spot diameters with factor √2 (√3). As a check, the edge-blade method was used to measure the beam diameter in both x- and y-directions. Both methods gave similar results. Figure 2(b) shows the variation of the beam width (FWHM) as a function of OPA wavelength. The data shows that the beam spatial profile is slightly elliptic. These data are used below for the evaluation of the absolute 2PA cross section (at one or two selected wavelengths for each OPA tuning region), and also for the calibration of relative 2PA spectra, as described in the next section. Figure 2(c) shows the combined correction function, which accounts for both temporal as well as spatial variations of the excitation beam.
2.2. Measurement of 2PA spectra
The measured two-photon excited fluorescence signal, detected as a function of the excitation wavelength, is (cf. (10)):
where constant A includes all the parameters that are independent of λ. The corrected 2PA spectrum (in relative units) is obtained, if we take into account the measured average power, W(λ), the pulse duration τ(λ) and the beam size, Δx(λ) and Δy(λ):
The correction function, shown in Fig. 2(c), corresponds to the last three terms in (13):
The absolute 2PA spectrum was obtained by calibrating the relative spectrum with respect to the absolute cross section, which was measured at one or several selected wavelengths. This procedure was repeated for each of the three OPA tuning regions.
We note that some common solvents (including water) absorb in the near-IR region, and may cause artifacts, if a thick sample cell is used. In our measurement, for molecules dissolved in chloroform, a 1-mm spectroscopic cell was used instead. In other cases, carbon tetrachloride, which is transparent at least up to 1600 nm, was used.
3. Results and discussion
Figure 3 shows the fluorescence spectra of the compounds studied.
Figures 4(a)–4(p) present the 2PA cross section (left vertical scale) and molar extinction (right vertical axis) spectra of the dyes. The bottom axis represents the transition wavelength (1PA wavelength), and the top axis represents the 2PA laser wavelength. The 2PA cross section values are summarized in Table 1. (See also detailed Tables in Appendix). We estimate that the experimental uncertainty in the absolute cross sections is about 10%. The main contributing factors are the relative fluorescence signals (F 1 and F 2 ~5% each), absolute pulse duration (~5%), and absolute beam diameter (Δx and Δy ~4% each). Experimental factors contributing to the ~10% error of determining the relative 2PA spectra, include the fluorescence signal error and an error in the relative pulse duration value.
3.1. Comparison with literature data
First of all, we note that in some previous works [15–20], the 2PA cross section is defined without factor ½ in Eq. (5). For proper comparison to our results, we multiply the 2PA cross sections presented in those articles by factor 2. Table 2 presents our and literature data for the three most frequently studied dyes, Fluorescein, Rhodamine 6G and Rhodamine B. Our results agree reasonably well with the majority of the earlier measurements carried out with the fluorescence method, and, above all, if short pulses <10-11 s were used for excitation. Excluded from the list are the reports, which failed to confirm the quadratic dependence of fluorescence signal on the excitation power.
There is a close quantitative agreement between our results and the data of Webb and co-authors [10, 11, 25] on Fluorescein in alkaline water solution, especially in the region 700–900 nm. Song, et al., obtained σ2=54 GM at 800 nm , which also agrees well with our measurement, σ2(800)=36 GM. The cross section obtained by Bradley, et al., with picosecond laser at 1064 nm  is ~2 times larger than our value, which is probably because neutral ethanol solution, used by the authors, results in different spectral forms of the dye. The cross sections reported by Webb  for Rhodamine 6G in methanol agree with our values within the error margins in the 920–960-nm region. However, our values appear systematically smaller at 690–700 nm and larger at 720–900 nm.
There are numerous reports on the 2PA cross section of Rhodamine 6G measured by various methods around 800 nm. Oulianov, et al.,  obtained σ2(800)=134 GM, which is 2 times larger than our measurement. However, the fluorescence quantum yield of Rhodamine B, Q=0.71, obtained from , and which was used as reference, is probably overestimated. More recent data [37, 38], as well as our own measurements give, Q=0.45. If we account for this correction, then we get, σ2(800)=85 GM, which is in a fair agreement with our result, 65±9 GM. Other measurements performed by femto- and picosecond nonlinear transmission (NLT) techniques, report values that are systematically 2.5–5 times lower than those obtained by the fluorescence method. This discrepancy was explained  by contributions from possible spurious effects, such as stimulated emission, Raman scattering, self-phase modulation, etc., which may cause the incident intensity to be overestimated, and, thus, lead to underestimated σ2 values.
There are further reports on the σ2 values of Rhodamine 6G measured at selected wavelengths. The data by Hermann and Ducuing  agree well with ours at 765 and 870 nm, but are ~2.7 times higher at 976 and 1060 nm. The fluorescence results by Bradely, et al.,  at λ=1060 nm (both ps and ns) compare well to our measurement, however, the values obtained by other authors [19, 20] using nanosecond pulses and cw lasers are also about 2 times higher. Hermann and Ducuing  used as a reference the nonlinear-optical coefficient of quartz, which was 1.6 times larger than currently accepted value . This may explain why their cross section at 976 and 1060 nm is 2.6 times larger than our value. With the updated value for the quartz, the results of  coincide well with ours. On the other hand, the results of the same paper , obtained at 765 and 870 nm, become overestimated (compared to ours) after the same correction. This could be due to other reasons, e.g. different beam properties at these excitation wavelengths. Mode-beating [17, 26] could have caused two fold overestimation of σ2 in [19,20]. A corrected σ2 would match rather well our values. Note also that the value of Penzkofer and Leupacher  obtained with NLT method at 1054 nm, while taking into account the effects of amplified spontaneous emission, excited-state absorption, and dimer formation, corresponds very well to our result.
The 2PA spectrum of Rhodamine B in methanol published by Webb and co-authors  shows two different sets of data, which diverge in the 800–850-nm region by as much as two-fold. Our results are in agreement with the higher values in the region 690–850 nm, and with the lower ones in 880–1030 nm. As in the case of Rhodamine 6G above, most of the NLT data obtained for Rhodamine B in the 780–880 nm region with femto- and picosecond pulses appear to be underestimated, probably because of experimental artifacts . At 1060 nm, the fluorescence results of Refs. [16–18, 20] correlate, within error margins, with our data.
There is also a number of data published on molecules closely related to some of those presented here. Webb and co-authors reported σ 2 Q=19±5.5 GM for Coumarin 307 (7-Ethylamino-6-methyl-4-trifluoromethylcoumarin) at 776 nm . Assuming that the quantum yield value is, Q=0.56 , this translates into, σ 2(776)=34±10 GM. This correlates very well with our result, σ 2(776 nm)=33 GM±4.6 GM for Coumarin 485 (7-Dimethylamino-4-trifluoromethylcoumarin). Taking into account the corrected nonlinear coefficient of quartz (see above), the value reported by Hermann and Ducuing for 7-Diethylamino-4-methylcoumarin, σ2 (694)=11±4.6 GM , is again in good agreement with our result for Coumarin 485, σ2 (694)=8±1 GM. The absolute 2PA spectrum of Coumarin 151 (7-amino-4-trifluoromethylcoumarin), σ2 max(754)=47 GM, obtained in , also correlates well with our data for Coumarin 485, showing σ2 max(754)=35±5 GM.
Our cross section of 9-Chloroanthracene, σ2 (694 nm)=0.28±0.04 GM, is in good agreement with several previous fluorescence results for Anthracene in solution: 0.18 GM , 0.32±0.1 GM , 0.18±0.08 GM (corrected with the factor of 2.6, see above) , 0.14±0.04 GM , and in gas phase: 0.18 GM . The Perylene cross section measured in gas phase (2.4 GM at 694 nm)  also agrees with our result (1.1±0.2 GM). Absolute 2PA cross section of 4,4’-Bis-(diphenylamino)stilbene (BDPAS) was measured in toluene with picosecond fluorescence excitation, σ2 max(690)=190±30 GM, , and correlates with our data (σ2 max(687)=330±45 GM here and 320±65 in ). Femtosecond NLT result reported for BDPAS in THF solution, σ2(800)=33 GM  is ~2 times less than our value, which may be caused by artifacts similar to those mentioned above.
In , the authors report σ 2 Q=0.95±0.3 GM at 860 nm for Lucifer Yellow in water. With the assumed quantum yield value, Q=0.21 , one obtains, σ 2=4.5±1.4 GM, which compares to our result in methanol, σ 2=2.4±0.34 GM. More recent result, σ2(860 nm)=2.8±0.8 GM , is in even better agreement with ours.
The 2PA spectrum of Tetraphenyl-porphine in toluene reported in [33, 45] may be slightly distorted because of the solvent absorption in a thick cell. This did not, however, alter the absolute cross section, σ2(1205)=3.3±0.7 GM, which agrees well with our current value in CCl4, σ2(1205)=2.8±0.4 GM. Recently, Morone, et al.,  and Ishi-I, et al., , reported 2PA cross sections of Tetraphenyl-porphine in chloroform measured at 800–810 nm by femtosecond open aperture z-scan method. The value of Morone, et al., σ2=16±4 GM, agrees well with our measurements in toluene (10±2 GM) [33, 45] and in CCl4, 8±1 GM (Fig. 4(i)). The smaller value reported in , σ2=2.2 GM, may be due to similar reasons as discussed above for other NLT measurements.
The 2PA spectra of Zn-tetra-tert-butyl-phthalocyanine and Zn-tetrakis-(phenylthio)-phthalocyanine previously obtained in dichloromethane in the 800–1100 nm region  coincide within experimental errors with those obtained here in CCl4 with 1% pyridine.
3.2. Application notes for using the 2PA standards
The data presented here can be used as a reference for determining absolute 2PA cross sections and spectra. First, one needs to select a reference, which has a fluorescence maximum close to that of the sample under study (Fig. 3). The signal should be integrated over a narrow 1–3 nm wavelength interval. The unknown 2PA cross section can then be determined from the relation:
where F2 is the fluorescence intensity, λ reg, is the fluorescence registration wavelength. Indices r and s stand, respectively, for the reference and the sample under study, and other symbols are described earlier. The differential quantum efficiency, φ(λ reg), can be obtained with a regular spectrofluorimeter, if it is set at the same registration wavelength, λ reg. The detector spectral response is nearly constant in narrow wavelength interval. This means that even though different spectral instruments are used, the detector response cancels in both ratios, F 2(λ reg)/F 2,r(λ reg) and φ r(λ reg)/φ(λ reg). For the same reason, there is no need for correction to a difference in solvent refraction indexes of reference and sample solutions in this case. The corrected relative 2PA spectrum is obtained as,
where F 2,s(λ) and F2,r(λ) are the non-corrected fluorescence excitation spectra, and A2PA,r(λ) is the corrected reference 2PA spectrum (in relative units).
We present absolute two-photon absorption spectra of 15 commercially available dyes in a broad range of excitation wavelength, 550–1600 nm, measured with high fidelity and high wavelength resolution. The 2PA cross sections were evaluated by comparing the fluorescence signals, obtained upon one- and two-photon excitation. Our σ2 values have the estimated accuracy ±10% and are in good agreement with literature data at selected wavelengths, especially those measured with fluorescence technique. Our data can be used as a reference for determining absolute 2PA cross sections and spectra, while avoiding tedious characterization of the excitation laser parameters.
This work was supported by AFOSR Grant No. FA9550-05-1-0357. We thank Yuryi Stepanenko for helping with the LabView applications.
References and links
3. G. W. Burr, “Volumetric storage” in Encyclopedia of Optical Engineering, R. B. Johnson and R. G. Driggers, eds., (Marcel Dekker, New York, 2003), and references therein.
4. B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–53 (1999). [CrossRef]
5. C. W. Spangler, “Recent development in the design of organic materials for optical power limiting,” J. Mater. Chem. 9, 2013–2020 (1999), and references therein. [CrossRef]
6. J. D. Bhawalkar, N. D. Kumar, C. F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15, 201–204 (1997). [PubMed]
7. A. Karotki, M. Kruk, M. Drobizhev, A. Rebane, E. Nickel, and C. W. Spangler, “Efficient singlet oxygen generation upon two-photon excitation of new porphyrin with enhanced nonlinear absorption,” IEEE J. Sel. Top. Quantum Electron. 7, 971–975 (2001). [CrossRef]
8. N. S. Makarov, A. Rebane, M. Drobizhev, H. Wolleb, and H. Spahni, “Optimizing two-photon absorption for volumetric optical data storage,” J. Opt. Soc. Am. B 24, 1874–1885 (2007). [CrossRef]
9. M. Drobizhev, Y. Stepanenko, Y. Dzenis, A. Karotki, A. Rebane, P. N. Taylor, and H. L. Anderson, “Extremely strong near-IR two-photon absorption in conjugated porphyrin dimers: quantitative description with three-essential-states model,” J. Phys. Chem. B 109, 7223–7236 (2005). [CrossRef]
10. C. Xu and W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13, 481–491 (1996). [CrossRef]
11. M. A. Albota, C. Xu, and W. W. Webb, “Two-photon fluorescence excitation cross sections of biomolecular probes from 690 to 960 nm,” Appl. Opt. 37, 7352–7356 (1998). [CrossRef]
12. W. L. Peticolas, R. Norris, and K. E. Rieckhoff, “Polarization effects in the two-photon excitation of anthracene fluorescence,” J. Chem. Phys. 42, 4164–4169 (1965). [CrossRef]
13. M. D. Galanin and Z. A. Chizhikova, “Effective cross sections of two-photon absorption in organic molecules,” JETP Lett. 4, 27–28 (1966).
14. A. P. Aleksandrov and V. I. Bredikhin, “Measurement of the absolute value of the cross-section for twophoton absorption in anthracene molecules,” Opt. Spectrosc. 30, 37–38 (1971).
15. J. P. Hermann and J. Ducuing, “Absolute measurement of two-photon cross sections,” Phys. Rev. A 5, 2557–2568 (1972). [CrossRef]
16. J. P. Hermann and J. Ducuing, “Dispersion of the two-photon cross section in rhodamine dyes,” Opt. Commun. 6, 101–105 (1972). [CrossRef]
17. D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, “Interactions of picosecond laser pulses with organic molecules. II. Two-photon absorption cross-sections,” Proc. R. Soc. Lond. A 329, 105–119 (1972). [CrossRef]
18. I. M. Catalano and A. Cingolani, “Absolute two-photo fluorescence with low-power cw lasers,” Appl. Phys. Lett. 38, 745–747 (1981). [CrossRef]
20. S. Li and C. Y. She, “Two-photon absorption cross-section measurements in common laser dyes at 1.06 µm,” Opt. Acta 29, 281–287 (1982). [CrossRef]
21. S. M. Bachilo and S. L. Bondarev, “Spectral and polarization features of two-photon absorption in retinal and retinyl acetate,” J. Appl. Spectrosc. 45, 1078–1083 (1987). [CrossRef]
22. A. P. Blokhin, A. V. Povedailo, and V. A. Tolkachev, “Polarization of two-photon excited fluorescence of vapors of complex organic molecules,” Opt. Spectrosc. 60, 60–64 (1986).
23. P. Sperber and A. Penzkofer, “S0-Sn two-photon absorption dynamics of rhodamine dyes,” Opt. Quantum Electron. 18, 381–401 (1986). [CrossRef]
24. A. Penzkofer and W. Leupacher, “S0–S1 two photon absorption dynamics of organic dye solutions,” Opt. Quantum Electron. 19, 327–349 (1987). [CrossRef]
25. C. Xu, J. Guild, W. W. Webb, and W. Denk, “Determination of absolute two-photon excitation cross sections by in situ second-order autocorrelation,” Opt. Lett. 20, 2372–2374 (1995). [CrossRef] [PubMed]
26. P. Kaatz and D. P. Shelton, “Two-photon fluorescence cross-section measurements calibrated with hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 16, 998–1006 (1999). [CrossRef]
27. J. M. Song, T. Inoue, H. Kawazumi, and T. Ogawa, “Determination of two photon absorption cross section of fluorescein using a mode locked titanium sapphire laser,” Anal. Sci. 15, 601–603 (1999). [CrossRef]
28. P. Sengupta, J. Balaji, S. Banerjee, R. Phillip, G. R. Kumar, and S. Maiti, “Sensitive measurement of absolute two-photon absorption cross sections,” J. Chem. Phys. 112, 9201–9205 (2000). [CrossRef]
29. D. A. Oulianov, I. V. Tomov, A. S. Dvornikov, and P. M. Rentzepis, “Observations on the measurement of two-photon absorption cross-section,” Opt. Commun. 191, 235–243 (2001). [CrossRef]
30. P. Tian and W. S. Warren, “Ultrafast measurement of two-photon absorption by loss modulation,” Opt. Lett. 27, 1634–1636 (2002). [CrossRef]
31. R. Kapoor, C. S. Friend, and A. Parta, “Two-photon-excited absolute emission cross-sectional measurements calibrated with a luminance meter,” J. Opt. Soc. Am. B 20, 1550–1554 (2003). [CrossRef]
32. M. Kauert, P. C. Stoller, M. Frenz, and J. Rička, “Absolute measurement of molecular two-photon absorption cross-sections using a fluorescence saturation technique,” Opt. Exp. 14, 8434–8447 (2006). [CrossRef]
33. A. Karotki, M. Drobizhev, M. Kruk, C. Spangler, E. Nickel, N. Mamardashvili, and A. Rebane, “Enhancement of two-photon absorption in tetrapyrrolic compounds,” J. Opt. Soc. Am. B 20, 321–332 (2003). [CrossRef]
35. M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, “Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000). [CrossRef]
36. J. N. Demas and G. A. Crosby, “The measurement of photoluminescence quantum yields. A review,” J. Phys. Chem. 75, 991–1024 (1971). [CrossRef]
37. T. Karstens and K. Kobs, “Rhodamine B and Rhodamine 101 as reference substances for fluorescence quantum yield measurements,” J. Phys. Chem. 84, 1871–1872 (1980). [CrossRef]
38. O. S. Finikova, T. Troxler, A. Senes, W. F. DeGrado, R. M. Hochstrasser, and S. A. Vinogradov, “Energy and electron transfer in enhanced two-photon-absorbing systems with triplet cores,” J. Phys. Chem. A 111, 6977–6990 (2007). [CrossRef] [PubMed]
39. G. A. Reynolds and K. H. Drexhage, “New coumarin dyes with rigidized structure for flashlamp-pumped lasers,” Chem. Phys. Lett. 13, 222–225 (1975).
40. A. Fischer, C. Cremer, and E. H. K. Stelzer, “Fluorescence of coumarins and xanthenes after two-photon absorption with a pulsed titanium-sapphire laser,” Appl. Opt. 34, 1989–2003 (1995). [CrossRef] [PubMed]
41. M. Drobizhev, A. Karotki, Y. Dzenis, A. Rebane, Z. Y. Suo, and C. W. Spangler, “Strong cooperative enhancement of two-photon absorption in dendrimers,” J. Phys. Chem. B 107, 7540–7543 (2003). [CrossRef]
42. Z. Huang, X. Wang, B. Li, C. Lv, J. Xu, W. Jiang, X. Tao, S. Qian, Y. Chui, and P. Yang, “Two-photon absorption of new multibranched chromophores based on bis(diphenylamino)stilbene,” Opt. Mater. 29, 1084–1090 (2007). [CrossRef]
43. W. W. Stewart, “Synthesis of 3,6-disulfonated 4-aminonaphthalimides,” J. Am. Chem. Soc. 103, 7615–7620 (1981). [CrossRef]
44. A. Karotki, M. Khurana, J. R. Lepock, and B. C. Wilson, “Simultaneous two-photon excitation of photofrin in relation to photodynamic therapy,” Photochem. Photobiol. 82, 443–452 (2006). [CrossRef] [PubMed]
45. M. Kruk, A. Karotki, M. Drobizhev, V. Kuzmitsky, V. Gael, and A. Rebane, “Two-photon absorption of tetraphenylporphin free base,” J. Lumin. 105, 45–55 (2003). [CrossRef]
46. M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, “Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon β-functionalization with donor-acceptor substituents,” Org. Lett. 8, 2719–2722 (2006). [CrossRef] [PubMed]
47. T. Ishi-i, Y. Taguri, S. Kato, M. Shigeiva, H. Gorohmaru, S. Maeda, and S. Mataka, “Singlet oxygen generation by two-photon excitation of porphyrin derivatives having two-photon-absorbing benzothiadiazole chromophores,” J. Mater. Chem. 17, 3341–3346 (2007). [CrossRef]
48. M. Drobizhev, N. S. Makarov, Y. Stepanenko, and A. Rebane, “Near-infrared two-photon absorption in phthalocyanines: enhancement of lowest gerade-gerade transition by symmetrical electron-accepting substitution,” J. Chem. Phys. 124, 224701 (2006). [CrossRef] [PubMed]
49. R. Sailaja, P. B. Bisht, C. P. Singh, K. S. Bindra, and S. M. Oak, “Influence of multiphoton events in measurement of two-photon absorption cross-sections and optical nonlinear parameters under femtosecond pumping,” Opt. Commun. 277, 433–439 (2007). [CrossRef]