Download Fluorescence of coumarins and xanthenes after two

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
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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.
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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.
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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
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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. The analyses of the experimental data
were performed with Mathematica.30
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