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Fluorescence of coumarins and xanthenes after two-photon absorption with a pulsed titanium–sapphire laser A. Fischer, C. Cremer, and E. H. K. Stelzer Fluorescence emission after two-photon absorption of coumarins and xanthenes in an alcoholic solution was measured in the tuning range of a femtosecond-pulsed titanium–sapphire laser 1750–840 nm2. Xanthenes, which have a low one-photon absorption in the near UV, show a higher fluorescence signal after two-photon absorption than the UV-excitable coumarins. When fluxes of 1028 photons@1cm2 s2 are used, the two-photon absorption cross sections for xanthenes are 1 order of magnitude higher than the two-photon absorption cross sections of the coumarins. Absolute cross sections have been estimated for three coumarins and three xanthenes. For the xanthenes a significant wavelength-dependent departure from the expected fluorescence intensity square law was observed. The coumarins follow the square-law dependence. The consequences of the findings are discussed for analytic and diagnostic methods. An especially important result is that the resolution in two-photon microscopy of xanthenes is worse than expected. Key words: Fluorescence, two-photon, spectroscopy. 1. Introduction Shortly after the experimental verification of twophoton absorption1 by Kaiser and Garret with a CaF2:Eu21 crystal in 1961, the first measurements were made with organic dye solutions.2 The first two-photon absorption measurements for xanthenes were published in 1966 by Schäfer and Schmid,3 who investigated Rhodamine B in ethanol and suggested a simple geometric model for the explanation of their measurements. The expected quadratic dependence1 of the fluorescence intensity on the excitation intensity after two-photon absorption cannot be expected under all circumstances. Quenching can occur and, to our knowledge, was first reported by Galanin et al.4 for an aqueous solution of fluorescein when a ruby A. Fischer is with the Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 253, D-69120 Heidelberg, Germany. C. Cremer is with the Institut für Angewandte Physik, Universität Heidelberg, Albert-Überle Strasse 3-5, D-69120 Heidelberg, Germany. E. H. K. Stelzer is with the Cell Biophysics Programme, European Molecular Biological Laboratory, Meyerhofstrasse 1, Postfach 10.2209, D-69012 Heidelberg, Germany. Received 3 June 1994; revised manuscript received 8 September 1994. 0003-6935@95@121989-15$06.00@0. r 1995 Optical Society of America. laser was used as a light source. Stimulated emission from the first excited state S1 to a highly excited vibrational level of the ground state S0 was believed to be responsible. A similar behavior was also observed for Rhodamines by Bradley et al.5 and Hermann and Ducuing6 at ruby and neodymium frequencies for which results of the two-photon cross sections were given.6,7 Two-photon absorption is of interest in spectroscopy because two-photon transitions are governed by different selection rules than one-photon absorption transitions.8 Therefore transitions between singlet states can be excited by two-photon absorption, but they are forbidden for one-photon absorption because of the symmetry of their initial and final singlet states.6 In applications such as two-photon fluorescence microscopy it is possible to excite fluorophores in the near UV with near-infrared light. It has therefore been proposed that the enhanced resolution that is available through UV light can be achieved without the need for special UV optics.9 This has been proven for confocal fluorescence microscopy, showing that two-photon absorption leads to a confinement of the illumination volume.10 In these contributions9,10 it was only reported that it is possible to observe UV-excitable dyes 1e.g., coumarins2 with a pulsed infrared laser. 20 April 1995 @ Vol. 34, No. 12 @ APPLIED OPTICS 1989 Unlike the researchers whose studies are described above, we also investigated the well-known dyes fluorescein, Rhodamine 6G, and Rhodamine B, which absorb strongly in the visible region but show a poor one-photon absorption in the near UV. With the advent of the titanium–sapphire laser an extraordinary light source has become available for applications of two-photon absorption. To our knowledge these are the first data for two-photon cross sections of coumarins and xanthenes in this wavelength range; until now only measurements for the wavelengths of the ruby laser 1694 nm2 and the neodymium laser 11064 nm2 have been published 1see Table 5, below2. 2. Experimental Arrangement The experimental setup is shown in Fig. 1. A titanium–sapphire laser 1Tsunami, Spectra Physics2 pumped by an argon–ion laser 1Model 2030, Spectra Physics2 generates 80–130-fs pulses at a repetition rate of 82 MHz, with peak powers up to 46 kW. The laser beam with a diameter of 2.6 mm is focused with an achromatic lens 1 f 5 44 mm2 into the middle of a cuvette holder. When sech2-shaped pulses are assumed, a flux of up to 5.5 3 1028 photons@1cm2 s2 is achievable in the focus. The intensity of the titanium–sapphire laser is reduced with metal-coated neutral density filters 1Jobin–Yvon, Grasbrunn, Germany2. The fluorescence light is detected at a right angle as it passes a telecentric system of two biconvex UV lenses 1 f 5 40 mm2 and the entrance slit 1d 5 2 mm2 of the monochromator 1H20, Jobin–Yvon2. The grid 11200 lines@mm2 is moved by a stepper motor that is controlled by a computer. The step width for each spectrum was 1 nm. The fluores- Fig. 1. Experimental arrangement for the measurement of fluorescence spectra after one- and two-photon absorption. The same sample can be excited with either the light from an argon–ion laser 1476, 488, or 514 nm2 or the light from a titanium–sapphire laser 1750–850 nm2. The spectra are recorded under computer control and are available as a digital data set. HV, high voltage. 1990 APPLIED OPTICS @ Vol. 34, No. 12 @ 20 April 1995 cence light is detected behind the exit slit 1d 5 2 mm2 by the use of a photomultiplier 1Hamamatsu R928, side on2. The spectral bandwidth is 8 nm. Since the natural bandwidth of the fluorescence spectra is 30–50-nm error in determining the true peak height is less than 5%.11 The signal of the photomultiplier tube 1PMT2 was amplified 1Hamamatsu C 1053-12 and measured with an analog-to-digital–digital-to-analog 1ADDA2 board 1DAS-1600, Keithly, Germering, Germany2, which was also used for the control of the high-voltage supply 1Hamamatsu C 1305-42 of the PMT. Because of dynamic reasons12 the detector was operated in the analog mode. The spectrum S1l2 is proportional to the intensity of the fluorescence. To obtain a quantity that is proportional to the flux of the fluorescence photons, one has to multiply S1l2 by the wavelength of the fluorescence light, l. We also took the spectral response of the photocathode 3whose values k1l2 are available134 into account. Furthermore, to correct the fluorescence spectra for self-absorption we used the results of the absorption measurements in which the optical density OD1l2 was measured with 1 cm 3 1 cm cuvettes. Taking into account a path length of the fluorescence light in the solutions of 0.5 cm, we show that the fluorescence signal has to be multiplied by the factor 10OD1l2@2. The integral of the fluorescence peak is then regarded as the fluorescence signal: Fl 5 e lk 211l2S1l210OD1l2@2dl. 112 The cw power of the titanium–sapphire laser was measured by the use of a photometer 1IL 1700, International Light, Newburyport, Mass.2 with a detector head SED 100@F@W and a neutral density filter QNSD1 for intensities up to 2 W@cm2. Please note that high peak powers are reached when a pulsed laser is used, although the cw power is quite low. To prove that one can conclude that the peak power of the laser pulses is from the cw power, we performed a simple experiment. The cw power of the titanium–sapphire laser was measured 3 times with different metal-coated filters for attenuation of the laser beam. In experiment 1a2 the full power was measured. In experiments 1b2 and 1c2 we measured the cw power, which reached the detector after one or two reflections from a microscope slide oriented at an angle of 45° relative to the direction of the laser beam. Calculation of the cw-power ratios in experiments 1a2, 1b2, and 1c2 for each filter position yields a constant value that proves that the photometer responds linearly. An autocorrelator 1Model 409, Spectra Physics2 was used to measure the pulse width with a precision of 5%. For the calibration of the fluorescence intensity after two-photon absorption we measured the fluorescence signal with the same optical setup after onephoton absorption of Rhodamine 6G excited by the 514.5-nm of the argon–ion laser. A cw power of 1 W was coupled out of the beam of the argon–ion laser into a polarization-preserving fiber 1Physik Instrumente, Waldbronn, Germany2 after the beam passed an appropriate interference bandpass filter 1Instruments SA, Omega Opticals, München, Germany2. The light that left the fiber was collimated. The beam, now with a diameter of 5.25 mm, was attenuated by a metal-coated neutral density filter of optical density 1.6. Because near-infrared or visible light was used for excitation the fluorescence measurements were carried out in 1 cm 3 1 cm cuvettes made from optical glass 1OS 101, Hellma, Mühlheim@Baden, Germany2. The absorption spectra were recorded with 1 cm 3 1 cm cuvettes made from fused silica suprasil 1QS 101, Hellma2 in an absorption spectrophotometer 1Uvikon 930, Kontron Instruments, München, Germany2 with a precision of 4 mAbs. For a comparison of the fluorescence spectra after two-photon absorption with the fluorescence spectra after one-photon absorption by the use of the equivalent excitation wavelengths 1375–425 nm2 we used a luminescence spectrometer 1Series 2, SLM-Aminco, Urbana, Illinois2. Measurements with a commercially available spectrograph on loan from Oriel 1InstaSpec IV, Oriel, Darmstadt, Germany2 with a CCD array to replace the H20 monochromator in the two-photon fluorescence spectrometer produced identical results. 3. mined by comparison of the relative fluorescence signals produced by one- and two-photon absorption.17 Since the depth of field is quite large and of approximately the same size as the entrance slit, the spatial beam profile is conformal with a cylinder. The fluorescence signal Fl1 after one-photon absorption is given by Fl1 5 KF1n1slF1, 122 where F1 is the quantum yield, n1 is the fluorophore number density, s is the one-photon absorption cross section measured in squared centimeters, l is the length of the path in which the photons are absorbed, F1 is the flux of incident photons 3in photons per squared centimeters times seconds 1photons@cm2 s24 and K is a dimensionless constant that depends on the optical setup. The unquenched fluorescence signal Fl2 after twophoton absorption is given by Fl2 5 K F2 2 n2dlF22, 132 where F2 is the quantum yield, which has to be divided by two since two photons have to be absorbed for each photon emitted. n2 is the fluorophore number density, d is the two-photon absorption cross section in centimeters to the fourth power times seconds 1cm4 s2, l is the path length, and F2 is the flux of incident photons in photons@1cm2 s2. The constant K in Eq. 122 is equal to the constant K in Eq. 132 since basically the same optical setup is used. When Eqs. 122 and 132 are combined, the Chemicals All dyes 1a-NPO; Coumarin 1, 120, 138, 151, and 152; fluorescein; Nilblue A; Oxazine 4 and 170; PBBO; POPOP; Rhodamione 6G and B2 were purchased from Kodak Eastman and initially dissolved in methanol pro analysi 1Merck, Darmstadt, Germany2. The final measurements were carried out with solutions of Coumarin 1, 120, and 151; Rhodamine 6G and B; and fluorescein in ethanol pro analysi 1Merck2. The fluorescein was a basic 12% NaOH2 solution. All stock solutions had a concentration of 1023 M. Diluting all solutions by a factor of 100, we got approximately 1025-M solutions. From these solutions, the exact concentrations were determined by measurement of the optical density in the spectrophotometer with the molar extinction coefficients available through the manufacturers’ catalogs.14,15 4. Theory The transition probability in two-photon absorption is proportional to the square of the flux of the incident photons.16 For low intensities and low excited-state absorption coefficients the intensity square law will also hold for the fluorescence signal. The twophoton absorption cross section can then be deter- Fig. 2. Jablonski diagram for two-photon absorption of nearinfrared light 1750–850 nm2 in xanthenes, whose first singlet state S1 absorbs around 500 nm. 20 April 1995 @ Vol. 34, No. 12 @ APPLIED OPTICS 1991 important result is Fl2F1n1sF1 d52 . 142 Fl1F2n2F22 Taking into account the sech2 shape of the pulses, we show that the fluorescence signal Fl2 after two-photon absorption becomes Fl2 5 K 5K 5 4 3 F2 2 K n2dlw e e 3 F 21t2dt 2` F2 2 1` 1` n2dlw 2` F2 2 n2dlw 1.76t 2 1 t 24 dt Fmax sech2 t 1.76 Fmax2, 152 where Fmax is the maximum flux during the pulse, w is the repetition rate of the laser pulses, and t is the pulse width. When a laser beam of diameter d and wavelength l is focused by a lens of focal length f, the Airy disk in the focus has the diameter Dx: Dx 5 1.22 l NA 5 2.44 lf . 162 d The flux in the focus is given by F5 Il hc 5 Pl , 172 p1Dx22hc where I is the intensity and P is the power of the laser Table 1. Relative Fluorescence Signals after Two-Photon Absorption of the 1023-M Solutions in Methanola Substance labs* 1nm2 lem* 1nm2 E 1L mole21 cm212 Fluorescence Signal 1%2 Coumarin 120 Coumarin 1 Coumarin 138 Coumarin 151 Coumarin 152 Coumarin 153 Fluorescein Rhodamine 6G Rhodamine B Chresyl-Violett Oxazine 4 Oxazine 170 Nilblue A 352 374 365 377 394 423 498 528 545 593 610 620 627 428 450 447 479 496 532 518 555 565 615 625 637 660 1.70 3 104 2.54 3 104 2.23 3 104 1.70 3 104 1.94 3 104 1.47 3 104 6.39 3 104 11.6 3 104 10.6 3 104 8.3 3 104 10.3 3 104 8.3 3 104 7.68 3 104 1.6 11.7 8.7 15.9 3.6 10.2 3.2 100 28.3 0 0 0 0 lem 1nm2 429 455 457 483 510 536 532 579 605 aFluorescence signal of Rhodamine 6G is set equal to 100%. The excitation wavelength of the titanium–sapphire laser was 784 nm. labs* and lem* are taken from the literature.14,15 The measured value lem is shifted to longer wavelengths because of self-absorption. For the bottom four dyes no fluorescence emission could be found. 1992 APPLIED OPTICS @ Vol. 34, No. 12 @ 20 April 1995 Fig. 3. Normalized fluorescence signals after two-photon absorption of the coumarins versus the peak flux of the titanium– sapphire laser for the excitation wavelength 770 nm. A power function was fitted to the experimental values. The measurements agree with a slope of 2. beam. When sech2-shaped pulses are assumed, one can determine the maximum of the flux by Fcw 5 Fmax w e 1` 2` ⇒ Fmax 5 Fcw 1.76t 1t2 sech2 0.88 wt , tion describes the two-photon absorption coefficient: d 5 20.3 hcp dt 182 where Fcw is the cw flux, Fmax is the maximum flux, w is the repetition rate of the laser, and t is the laser’s pulse width. With Eqs. 142–182, the following rela- F1Fl2n2 Pcw,1 d12l22 F2 Fl2n2 Pcw,22d24l1 f 2wts. 192 The error in determining d through Eq. 192 can be reduced if the second harmonic is used for one-photon excitation and if the same solution is used in both measurements. In this case it can be assumed that the quantum efficiencies F1 and F2 are equal, since the same final state is excited by one- and two-photon absorption.18 Furthermore, the number densities n1 Fig. 4. Normalized fluorescence signals after two-photon absorption of the xanthenes versus the peak flux of the titanium–sapphire laser for the two different excitation wavelengths, 770 and 825 nm. The xanthenes show a departure from the usually expected intensity square law. The sum N11t2 1 N21t2 of the model 1132 was fitted with s2n as a parameter and the constant values t21 5 1 ps for the relaxation time and t 5 100 fs for the pulse duration. The resulting values for s2n are presented in Table 4. For the excitation wavelength of 825 nm, the fit with the simple model 1132 shows a significant deviation at lower light fluxes. 20 April 1995 @ Vol. 34, No. 12 @ APPLIED OPTICS 1993 and n2 are also equal. If wavelengths other than the second harmonic are used for one-photon absorption, one has to know the quantum efficiencies F1 and F2. Absolute values of quantum yields are difficult to measure19 with an accuracy below 65%. It is easier to measure the quantum efficiencies relative to a known standard. An alkaline solution of fluorescein in ethanol is known to have a quantum efficiency of 90 6 5%, and a solution of Rhodamine 6G in ethanol has a quantum efficiency of 95 6 5% if it is excited into the S1 singlet state.19 By the use of a titanium– sapphire laser, the xanthenes are excited to a singlet state above S1, whereas the coumarins are excited into the S1 singlet state. There are very few measurements of the quantum efficiency of fluorescence dyes excited into higher singlet states. It has been shown for Rhodamine B that its quantum efficiency should be constant for excitation wavelengths down to 250 nm.20 Following Drexhage, this should also be true for other Rhodamines.21 More recent measurements that were done for Rhodamine 6G and B indicate that the ratio between the quantum efficien- Fig. 5. Fluorescence after two-photon absorption of the 1025-M solutions in ethanol: C, coumarin; F, fluorescein; R, Rhodamine for different excitation wavelengths. The fluorescence spectra are corrected for self-absorption and sensitivity of the PMT. The spectra are normalized by the square of the cw power of the titanium–sapphire laser. 1994 APPLIED OPTICS @ Vol. 34, No. 12 @ 20 April 1995 cies at the excitation wavelengths l 5 256 nm and l 5 530 nm is 0.95 6 0.05 for Rhodamine 6G and 0.7 6 0.05 for Rhodamine B.22 We therefore assumed that the quantum efficiency of Rhodamine 6G has the constant value 0.95 for excitation wavelengths between 375 and 515 nm and used this as a standard for determination of the relative quantum efficiencies between 375 and 515 nm. If the one-photon absorption cross section s of the excitation wavelength l1 is known, the following relation becomes useful: Fli 5 e Fli 1l2dl 5 KFi 1li 2F01l12exp32nsi1l12x4nisi 1l12l ⇒ Fi 1l12 5 1 Fli exp3nsi 1l12x4 K F01l12ni si 1l12l 5. Theory of the Behavior of Xanthenes at High Intensities A striking phenomenon is the deviation of the fluorescence signals of xanthenes from the intensity square law at high laser intensities.4–6 For an explanation we tried the simplest model that takes into account the excited-state absorption of the singlet S2 state excited by the titanium–sapphire laser. Accordingly one has to solve the rate equations 1122, below, which can be done analytically if squared pulses are assumed.5 Normally the absorption maximum around 350 nm is termed the S2 state, if the two lower weakly absorbing singlet states are ignored.23 Stimulated emission as a depletion process can be ruled out because the fluorescence spectra of the investigated xanthenes do not overlap with the tuning range of the titanium–sapphire laser. The processes are depicted in Fig. 2. dN2 . 1102 dt dN1 K is a dimensionless constant that depends on the optical setup, x is the length of the path to the middle of the cuvette, and l is the length of the path in which the light is absorbed. The same equation for two different dyes 1i 5 a, b2 leads to a ratio of the quantum efficiencies as a function of the excitation wavelength l1: Frelative1l12 5 Fa1l12 Fb1l12 5 Fla exp3nasa1l12x4nbsb1l12 Flb exp3nbsb1l12x4nasa1l12 . 1112 If the quantum efficiency Fb1l12 is known, one can calculate the quantum efficiency Fa1l12 with Eq. 1112. dt 5 N0d02 F 2 2 N2s2n F 2 5 N2 N2 , t21 . t21 1122 where N1 and N2 are the population densities of the excited singlet states S1 and S2, d02 is the two-photon absorption cross section, s2n is the one-photon absorption cross section from the excited state S2, t21 is the relaxation time between the excited states S2 and S1, and F is the flux of incident photons. Only the term 2N2s2n F leads to quenching because the two terms 6N2@t21 cause a rearrangement of the electrons in the excited states S1 and S2. The fluorescence signal is proportional to the sum of the populations of the levels N1 and N2 after the pulse has passed. The solution of the set of differential equations 1122, which is only valid for a period of time equivalent Fig. 6. Comparison between fluorescence after two-photon absorption of the 1025-M solutions in ethanol and the fluorescence after one-photon absorption of the 1025-M solution of Rhodamine 6G in ethanol excited with the 514.5-nm line of the argon–ion laser used for calibration. The spectra are corrected for self-absorption and sensitivity of the PMT. Identical scales are used for both plots. The excitation wavelength at two-photon absorption was 784 nm at a cw power of 0.8 W and a pulse duration of 100 fs. The excitation wavelength for one-photon absorption was the 514.5-nm line of the argon–ion laser at a cw power of 3.4 3 1026 W. The spectra were recorded with the same optical setup described in Fig. 1. C, coumarin; F, fluorescein; R, Rhodamine. 20 April 1995 @ Vol. 34, No. 12 @ APPLIED OPTICS 1995 to the pulse duration with N1102 5 N2102 5 0, is given by N11t2 5 N21t2 5 Quenching will occur if Fs2nt21 : 0, so that the sum N11t2 1 N21t2 will not depend on the square of F but in N0d02 F 25t 2 t21 1 t21 exp32t1Fs2n 2 1@t2124 1 Fs2nt21 t6 , 11 1 Fs2nt2122 N0d02 F 2t2151 2 exp32t1Fs2n 2 1@t21246 1 1 Fs2nt21 . 1132 Fig. 7. Fluorescence after one-photon absorption of the 1025-M solutions in ethanol. C, coumarin; F, fluorescein; R, Rhodamine for different excitation wavelengths recorded with the fluorimeter. These spectra cannot be compared quantitatively with the results shown in Fig. 5. The fluorescence spectra are corrected for self-absorption and sensitivity of the PMT. 1996 APPLIED OPTICS @ Vol. 34, No. 12 @ 20 April 1995 the extreme becomes only linear. population N1t2 is given by The unquenched N1t2 5 N0d02 F 2t. N1t2 N11t2 1 N21t2 d 5 20.3 hcp 1142 The relative quenching D can then be calculated as a function of l, that combines 1Eqs. 132 and 1142: D1l2 5 Equation 192 can thus be written as . 1152 6. F1Fl2n1 Pcw,1 d12l22 F2 Fl1n2 Pcw,22d24l1 f 2wtsD1l22. 1162 Results Because two-photon absorption cross sections are very small 1<10248 cm4 s2, one requires high intensities and high dye concentrations to get a reasonable fluorescence signal. In a first step we tested a vari- Fig. 8. One-photon absorption cross sections calculated with the literature values of E in Table 1 and the measured optical densities of the 1025-M solutions in ethanol with s 5 3.824 3 10221 OD1l2@c, with c in moles@liter and s in squared centimeters. Note that different scales are used for coumarins and xanthenes. The precision of the spectrophotometer was 4 mAbs. Because the 1025-M solutions had an optical density of OD < 1, the error in the determination of the one-photon absorption cross section was approximately 1.5 3 10218 cm2. 20 April 1995 @ Vol. 34, No. 12 @ APPLIED OPTICS 1997 ety of fluorescence dyes with highly concentrated solutions 11023 M2 in methanol, although self-absorption can obviously not be neglected. The results are presented in Table 1. The coumarins, which are known to be very efficient laser dyes24 in the blue and green regions, all showed comparable fluorescence signals 1see also Table 12. Because the quantum efficiency of Coumarin 152 is low in polar solvents24 such as methanol, the low fluorescence signal of Coumarin 152 in comparison with other coumarins is explained. The green and orange-red emissions are covered by xanthenes. They all showed higher fluorescence signals than any other investigated class of dyes, although they have low one-photon absorption cross sections between 375 and 425 nm. The result for fluorescein in Table 1 was measured with a neutral solution. Afer 2% 1 M NaOH was added, the fluorescence efficiency was raised drastically to approximately the same level as the fluorescence signal of Rhodamine 6G after one- and two-photon absorption. The differences between fluorescence emission after one- and two-photon absorption are also striking for molecules that show very similar one-photon absorption maxima in the near UV. An example is POPOP and Coumarin 120. The one-photon absorption maxima are very similar 1358 and 352 nm2, but the strength of the fluorescence signals after twophoton absorption are not. POPOP showed poor fluorescence after two-photon absorption, which could hardly be distinguished from the background. Coumarin 120 was therefore chosen for further investigations. Unfortunately it was not possible to get a clear fluorescence signal after two-photon absorption from oxazines and Nilblue A. This is probably due to the overlap of the fluorescence spectra with the tuning range of the titanium–sapphire laser. As mentioned above, we also investigated several other UV-excitable dyes such as a 2 NPO, PBBO, and POPOP. After two-photon absorption they all showed very poor fluorescence, of the order of 91% compared with the fluorescence signal after two-photon absorption of Rhodamine 6G. Finally we chose Coumarin 1, 120, and 151 for further investigations because of the strength of their Table 2. Substance F 1375–425 nm2 @F 1515-nm2 F 1265 nm2 @F 1530 nm2 1Ref. 222 Rhodamine B Fluorescein 0.80 6 0.07 0.46 6 0.07 0.7 6 0.05 fluorescence signals and because their fluorescence spectra cover a wide wavelength range. The xanthenes Rhodamine 6G, Rhodamine B, and fluorescein were chosen for the final measurements for similar reasons. The two-photon absorption processes of these dyes had been investigated at the wavelengths of the neodymium laser 11064 nm2 and the ruby laser 1693 nm2.3–7 For the final measurements 1025-M solutions in ethanol were produced from the original 1023-M stock solutions. We confirm the significant departure from the intensity square law for the xanthenes reported by other authors.4–6 However, contrary to these earlier measurements performed with giant-pulse lasers, we observed the deviation from the intensity square law at different wavelengths and pulse widths. The results for coumarins and xanthenes are presented in Figs. 3 and 4, respectively. For all coumarins the intensity square law holds. The fluorescence spectra recorded at six different excitation wavelengths of the titanium–sapphire laser for the 1025-M solutions in ethanol are presented in Fig. 5. The fluorescence spectra are corrected for self-absorption and for the sensitivity of the PMT. For the sake of comparability the spectra are also normalized by the use of the square of the cw power of the titanium–sapphire laser, even though the xan- Quantum Efficiencies AQE’sB Relative to Rhodamine 6G for Excitation Wavelengths between 375 and 425 nma Substance QE Absolute Error Relative Error 1%2 Rhodamine 6G Rhodamine B Fluorescein Coumarin 1 Coumarin 120 Coumarin 151 0.95 0.499 0.496 0.529 0.514 0.582 — 0.038 0.074 0.034 0.096 0.032 — 7.6 14.9 6.4 18.6 5.5 aValues were calculated from the fluorescence signals after one-photon absorption at six excitation wavelengths between 375 and 425 nm shown in Fig. 7. The one-photon absorption cross sections for these excitation wavelengths are presented in Fig. 8. 1998 Table 3. Ratio of the Quantum Efficiencies for Excitation Wavelengths 375–425 nm and 514.5 nm Compared with Values Found by Other Authors APPLIED OPTICS @ Vol. 34, No. 12 @ 20 April 1995 Fig. 9. Quenching factors for the fluorescence emission after two-photon absorption D calculated according to Eq. 1152 for three measured excited-state absorption coefficients s2n . The constant values t21 5 1 ps for the relaxation time and t 5 100 fs for the pulse duration were assumed. The three curves belong to the following excited-state absorption coefficients: 1, s2n 5 2 3 10216 cm2; 2, s2n 5 5 3 10216 cm2; 3, s2n 5 8 3 10216 cm2. For measurements of the two-photon absorption coefficient 1Fig. 10, below2 fluxes of 12.7 6 12 3 1028 photons@cm2 s were used. The quenching factors of the fluorescence after two-photon absorption for the xanthenes are therefore around 1.8. thenes showed a departure from the expected intensity square law at higher excitation wavelengths. To calibrate the fluorescence signals after twophoton absorption, we took the fluorescence spectra of Rhodamine 6G excited with the 514.5-nm line of the argon–ion laser with the same spectrometer 1Fig. 62. 7. Discussion A comparison of the results of the fluorescence after two-photon absorption 1Fig. 52 with the one-photon absorption spectra between 375 and 425 nm 1Fig. 82 shows that fluorescence after two-photon absorption is different from fluorescence after one-photon absorption. Note that the fluorescence spectra after onephoton absorption and the fluorescence spectra after two-photon absorption cannot be compared quantitatively because two different experimental setups have been used. Only the fluorescence spectra after onephoton absorption of Rhodamine 6G that were recorded with the same optical setup as the fluorescence spectra after two-photon absorption 1Figs. 5 and 62 can be compared directly. Nevertheless the qualitative changes in the fluorescence after one- and two-photon absorption can be found directly. The fluorescence signal after onephoton absorption of fluorescein is increasing with the excitation wavelength, while in the case of twophoton absorption the fluorescence signal is smaller at higher excitation wavelengths. For Rhodamine B the situation is reversed. The fluorescence of Rhodamine B is increasing with the excitation wavelength Fig. 10. Estimated values of the two-photon absorption coefficient d with Eq. 1162 and the fluorescence spectra presented in Figs. 5 and 6 measured in cm4 s 1see also Table 42. Note that different scales are used for coumarins and xanthenes. The errors in determining d for the xanthenes are higher because the fluorescence signals of the xanthenes after two-photon absorption were quenched. d was calculated with Eq. 1162. For all xanthenes we assumed a quenching factor of 1.8 1see also Table 62. s, experimental values; 3, probably not correct. 20 April 1995 @ Vol. 34, No. 12 @ APPLIED OPTICS 1999 in the case of two-photon absorption and decreasing in the case of one-photon absorption. In addition the fluorescence signals after two-photon absorption of the xanthenes are approximately 5 times bigger than the fluorescence signals after two-photon absorption of the coumarins. From the fluorescence spectra after one-photon absorption between 375 and 425 nm 1Fig. 72 and the absorption spectra in the same range of wavelengths 1Fig. 82 we calculated the quantum efficiency relative to Rhodamine 6G with Eq. 1112. The results are summarized in Table 2. We also calculated the ratio of the fluorescence quantum efficiency for the excitation wavelength of 514.5 nm and the mean value of the relative fluorescence quantum efficiencies of 375–425 nm. This could only be done for the xanthenes. The results are shown in Table 3. For Rhodamine B the results are in agreement with the value from Ref. 22. The quenching of the fluorescence signal after two-photon absorption can be estimated by the use of the fitting absorption coefficients for the linear loss term in Eqs. 1122 to the experimental data. The relaxation time t21 is of the order of 1 ps.25 The pulse duration is approximately 100 fs. The measured slope is <1.8 at 770 nm and <1.5 at 825 nm for the xanthenes. Fitting the sum N11t2 1 N21t2, from Eq. 1132, where t is the pulse duration, to the experimental data 1Fig. 42, with s2n as a parameter, we calculated 5.5 3 10216 cm2 as an average result 1Table 32. This is in good agreement with values for s2n known to us from the literature on xanthenes23 but derived under different conditions. Using Eq. 1152, one can calculate the expected quenching factor for the fluorescence after two-photon absorption. The quenching factor is plotted as a function of the incident flux for three excited-state absorption coefficients in Fig. 9 The experiments for the measurement of the twophoton absorption coefficients were carried out with fluxes of the order of 12.6 6 12 3 1028 photons@cm2 s. Therefore quenching factors of approximately 1.8 are to be expected 1Fig. 92. Taking this into account, we estimated the twophoton cross sections that are shown in Fig. 10 with Eq. 1162. A relative error of one order of magnitude in the determination of the two-photon cross section should be reasonable for the xanthenes. For the coumarins we estimated the relative error to be a factor of 2 smaller. We performed the same measurements for the two-photon absorption cross section with the 1023-M solutions in ethanol. For calibration purposes we again used the fluorescence signal of a 1025-M solution of Rhodamine 6G in ethanol excited with the 514.5-nm line of an argon–ion laser with a cw power of the order of 1026 W. Because the fluorescence spectra of 1023-M solutions cannot be corrected for self-absorption, the values for d are lower than the values one gets with 1025-M solutions. Nevertheless the results were qualitatively the same. The values 2000 APPLIED OPTICS @ Vol. 34, No. 12 @ 20 April 1995 for the two-photon absorption coefficients are presented in Table 4 and plotted in Fig. 10. A comparison with the experimental results of other authors 1Table 52 in a straightforward manner is not possible. In these experiments lasers with different wavelengths and pulse widths in the picosecond and nanosecond time scales were used, which are therefore 3 to 6 orders of magnitude longer than those available from our laser. The values of the two-photon absorption coefficients estimated by us 1Table 42 are one order of magnitude higher than the experimental results reported by other authors 1Table 52. The calculations were performed under the assumption of different experimental conditions to rule out simple calculation errors. Nevertheless the relative values of the fluorescence after two-photon absorption are much more precise. An explanation for the shape of the two-photon absorption spectra is possible for the coumarins. The shapes of the absorption spectra are very similar Table 4. Estimation of the Two-Photon Absorption Cross Section for the Solutions in Ethanol Excited with the Titanium–Sapphire Lasera Substance lexc 1nm2 d 3 10250 1cm4 s2 Coumarin 120 754.5 774.5 797.0 814.5 840.5 19.3 6.8 2.0 0.01 — Coumarin 1 754.5 774.5 797.0 814.5 840.5 103.5 75.6 28.4 9.0 1.4 Coumarin 151 754.0 774.5 797.0 813.5 840.0 47.1 40.0 24.1 16.5 11.6 Fluorescein 754.5 774.5 796.5 813.5 840.5 188.6 210.5 170.2 75.4 27.3 Rhodamine 6G 754.0 774.5 795.5 814.0 840.0 197.0 221.5 243.5 169.1 155.1 Rhodamine B 754.5 774.5 797.0 814.0 840.5 421.1 532.9 719.9 474.7 796.7 aValues were calculated with Eq. 1162. The fluorescence signal after two-photon absorption of the xanthenes was believed to be quenched 1Fig. 42. The quenching factors used are shown in Table 6. Comparison with the values found by other authors shows that the values measured by us are systematically one order of magnitude higher. Table 5. Substance Values for the Two-Photon Absorption Cross Section Taken from the Literaturea lexc 1nm2 d 3 10250 1cm4 s2 Laser Ruby Pulse Width Ref. 40 ns 26 Coumarin 1 694 14.5 6 6 Fluorescein 1064 1064 0.18 0.075 Neodymium Neodymium ns ps 5 5 Rhodamine 6G 1064 1064 1064 976 870 765 694 12.9 6 6 3.6 5.5 18.2 3.37 20.1 355 6 170 Neodymium Neodymium Neodymium Neodymium Neodymium Neodymium Ruby 60 ns ps ns 60 ns 60 ns 60 ns ns 6 7 7 6 6 6 6 Rhodamine B 1064 1064 1064 694 14.3 14 7 148 6 70 Neodymium Neodymium Neodymium Ruby 60 ns ns ps ns 6 7 7 6 aMeasurements were all made with ruby or neodymium lasers with nanosecond or picosecond pulses. The fluxes used were of the same order of magnitude or higher because giant pulse lasers were used. When only ns 1nanoseconds2 or ps 1picoseconds2 are indicated for a particular case, it means that specific pulse-width values were not available. for coumarins in one- and two-photon absorption. Because the coumarins are excited from the ground state into the first excited singlet state by one- and two-photon absorption, they need a minimal energy to reach the first excited singlet state. This corresponds to a maximal wavelength beyond which a transition is not possible. For the xanthenes the behavior is more complicated since they are excited into higher excited singlet states. The xanthene chromophore in the ground state has got the C2v symmetry.6 The ground state of the p electrons belongs therefore to the totally symmetric representation A1, whereas the excited states are represented by A1 or B2.6 The first excited singlet state is represented by B2. It has been shown by two different methods that the singlet state with its one-photon absorption maximum around 350 nm is of symmetry A1.6,22 The dispersion of the twophoton absorption cross section of Rhodamine 6G between the first excited singlet state S1 and the fourth excited singlet state S4 1commonly termed the S2 state if two lower lying singlet states are neglected222 can be explained: The two-photon transition between two states of equal symmetry is preferred. The situation is reversed in the case of one-photon absorption.6 When these considerations are applied to fluorescein, the behavior in two-photon absorption can be also explained. Between 375 and 425 nm the onephoton absorption cross section increases 1Fig. 82 with the wavelength. This is due to the absorption band of the first singlet state S1. This state should have the symmetry B2, whereas the ground state has the symmetry A1. According to Ref. 6 a two-photon transition between two states of different symmetry is of low probability. Therefore the two-photon absorption coefficient of fluorescein decreases with the excitation wavelength. 8. Conclusion We quantitated two-photon absorption in the range of the titanium–sapphire laser for coumarins and xanthenes. This has not been reported before, to our knowledge. Xanthene dyes, which are well known, turned out to be very efficient for two-photon absorption. This is of great interest for biological applications, in which one can profit from the enormous knowledge about coupling of these dyes to antibodies or DNA-specific labels. Simultaneous excitation of several dyes is also possible with two-photon excitation since fluorescence signals can easily be separated by the use of commonly used fluorescence filter sets. It is therefore possible to record multicolor pictures in confocal two-photon fluorescence microscopy with simple filter sets with the enhanced resolution described in Ref. 10. Because only one excitation wavelength has to be used, one has the advantage of a nonshifting focus, in contrast with applications in which several excitation wavelengths have to be used. Another interesting consequence is that the technique of squaring the normalized single-photon point-spread function to account for the intensity-squared dependence of the excitation light on the emission light is not in general correct. Instead of a power of 2 the powers indicated in Table 6 have to be used. The net effect is that the resolution is lower when dyes such as Rhodamine 6G are observed. An important point to be considered in the near future is fluorescent dyes that have spectra at longer emission wavelengths. Because all xanthenes showed high two-photon absorption coefficients across the whole tuning range of the titanium–sapphire laser, it is interesting to investigate the recently developed Rhodamine derivatives known as multiplex dyes,27 which exhibit absorption and emission bands beyond 600 nm. Time-resolved fluorescence measurements 20 April 1995 @ Vol. 34, No. 12 @ APPLIED OPTICS 2001 Table 6. Estimated Excited-State Absorption Coefficients s2n of the Xanthenes for Excitation Wavelengths 770 and 825 nma s2n 3 10216 1cm22 Substance lexc 5 770 nm lexc 5 825 nm D Quenching Factor Fluorescein Rhodamine 6G Rhodamine B 3.0 1.7 5.2 — 8.0 6.3 1.4 1.8 1.8 aValues are the results of the fits of the sum N 1t 2 1 N 1t 2 according 1 2 to Eq. 1132 to the experimental data 1Fig. 42. We assumed the constant values t21 5 1 ps for the relaxation time and t 5 100 fs for the pulse duration. The resulting quenching factors are calculated for a flux of 12.7 6 12 3 1028 photons@1cm2 s2, which was used in the experimental determination of the two-photon absorption cross sections 1Fig. 102. The slopes of the experimental data were nearly equal for the same excitation wavelength. Since this result is not fulfilled for the results of the simple fit, we averaged the results of the fits. We therefore assumed a quenching factor of 1.8 for all xanthenes and all excitation wavelengths. after one-photon absorption with this dyes have been reported. Because the shape of the fluorescence spectra is independent of the fluorescence wavelength,25 this should also be true for the excitation lifetime. With time-resolved measurements one would get a second parameter for measurements of fluorescence after two-photon absorption since dyes with similar absorption and emission characteristics can be distinguished by their fluorescence lifetime. By the use of pattern-recognition techniques it has been shown28 that one needs only 300 photons to test a sample with a monoexponential decay for a known lifetime and an accuracy of 8%. This is ideal for the relative weak fluorescence signals after two-photon absorption. Another possibility is measurements of the polarization dependence of the two-photon absorption coefficient. It has been shown theoretically and experimentally6,8,29 that the two-photon aborption coefficient is also polarization dependent in randomly oriented samples. Because the samples in microscopy are liquids, it should be possible to use the polarization dependence of the two-photon absorption coefficient in two-photon confocal fluorescence microscopy. A. Fischer acknowledges financial support by the Deutsche Forschungsgemeinschaft and continuous encouragement from J. Wolfrum and S. Seeger of the Physikalisch-Chemisches Institut der Universität Heidelberg. 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