Abstract

It is shown that one can obtain absolute two-photon fluorescence excitation (TPE) cross sections without prior knowledge of the temporal profile of the excitation pulse. It is sufficient to record the fluorescence generated by two spatially superimposed but temporally shifted halves of the excitation beam as a function of their relative delay. Measurements employed a Michelson interferometer with a mode-locked Ti:sapphire laser as the excitation source. The TPE cross section for fluorescein [(46 ± 10) × 10−58 m4 s/photon] obtained at 782 nm with this technique agrees with single-mode cw excitation data. We find no indication of a deviation from the power-squared dependence of TPE.

© 1995 Optical Society of America

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  1. W. Denk, J. H. Strickler, W. W. Webb, Science 248, 73 (1990).
    [CrossRef] [PubMed]
  2. W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, J. Neurosci. Methods 54, 151 (1994).
    [CrossRef] [PubMed]
  3. W. Denk, D. W. Piston, W. W. Webb, in The Handbook of Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), p. 445.
  4. R. Yuste, W. Denk, Nature (London) 375, 682 (1995).
    [CrossRef] [PubMed]
  5. D. W. Piston, B. R. Masters, W. W. Webb, J. Microsc. 178, 20 (1995).
    [CrossRef] [PubMed]
  6. R. M. Williams, D. W. Piston, W. W. Webb, FASEB J. 8, 804 (1994).
    [PubMed]
  7. A. J. Twarowski, D. S. Kliger, Chem. Phys. 20, 259 (1977)M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  8. J. P. Hermann, J. Ducuing, Phys. Rev. A 5, 2557 (1972).
    [CrossRef]
  9. R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1983), p. 82.
  10. S. M. Kennedy, F. E. Lytle, Anal. Chem. 58, 2643 (1986)R. D. Jones, P. R. Callis, J. Appl. Phys. 64, 4301 (1988).
    [CrossRef]
  11. M. Muller, J. Squier, G. J. Brakenhoff, Opt. Lett. 20, 1038 (1995).
    [CrossRef] [PubMed]
  12. J. Diels, in Dye Laser Principles, F. J. Duarte, L. W. Hillman, eds. (Academic, San Diego, Calif., 1990), p. 104.
  13. W. W. Webb, C. Xu, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 nm to 990 nm,” J. Opt. Soc. Am. B (to be published)C. Xu, J. Guild, W. W. Webb, Biophys. J. 68, A197 (1995).

1995 (3)

R. Yuste, W. Denk, Nature (London) 375, 682 (1995).
[CrossRef] [PubMed]

D. W. Piston, B. R. Masters, W. W. Webb, J. Microsc. 178, 20 (1995).
[CrossRef] [PubMed]

M. Muller, J. Squier, G. J. Brakenhoff, Opt. Lett. 20, 1038 (1995).
[CrossRef] [PubMed]

1994 (2)

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, J. Neurosci. Methods 54, 151 (1994).
[CrossRef] [PubMed]

R. M. Williams, D. W. Piston, W. W. Webb, FASEB J. 8, 804 (1994).
[PubMed]

1990 (1)

W. Denk, J. H. Strickler, W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

1986 (1)

S. M. Kennedy, F. E. Lytle, Anal. Chem. 58, 2643 (1986)R. D. Jones, P. R. Callis, J. Appl. Phys. 64, 4301 (1988).
[CrossRef]

1977 (1)

A. J. Twarowski, D. S. Kliger, Chem. Phys. 20, 259 (1977)M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1972 (1)

J. P. Hermann, J. Ducuing, Phys. Rev. A 5, 2557 (1972).
[CrossRef]

Brakenhoff, G. J.

Delaney, K. R.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, J. Neurosci. Methods 54, 151 (1994).
[CrossRef] [PubMed]

Denk, W.

R. Yuste, W. Denk, Nature (London) 375, 682 (1995).
[CrossRef] [PubMed]

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, J. Neurosci. Methods 54, 151 (1994).
[CrossRef] [PubMed]

W. Denk, J. H. Strickler, W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

W. Denk, D. W. Piston, W. W. Webb, in The Handbook of Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), p. 445.

Diels, J.

J. Diels, in Dye Laser Principles, F. J. Duarte, L. W. Hillman, eds. (Academic, San Diego, Calif., 1990), p. 104.

Ducuing, J.

J. P. Hermann, J. Ducuing, Phys. Rev. A 5, 2557 (1972).
[CrossRef]

Gelperin, A.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, J. Neurosci. Methods 54, 151 (1994).
[CrossRef] [PubMed]

Hermann, J. P.

J. P. Hermann, J. Ducuing, Phys. Rev. A 5, 2557 (1972).
[CrossRef]

Kennedy, S. M.

S. M. Kennedy, F. E. Lytle, Anal. Chem. 58, 2643 (1986)R. D. Jones, P. R. Callis, J. Appl. Phys. 64, 4301 (1988).
[CrossRef]

Kleinfeld, D.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, J. Neurosci. Methods 54, 151 (1994).
[CrossRef] [PubMed]

Kliger, D. S.

A. J. Twarowski, D. S. Kliger, Chem. Phys. 20, 259 (1977)M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1983), p. 82.

Lytle, F. E.

S. M. Kennedy, F. E. Lytle, Anal. Chem. 58, 2643 (1986)R. D. Jones, P. R. Callis, J. Appl. Phys. 64, 4301 (1988).
[CrossRef]

Masters, B. R.

D. W. Piston, B. R. Masters, W. W. Webb, J. Microsc. 178, 20 (1995).
[CrossRef] [PubMed]

Muller, M.

Piston, D. W.

D. W. Piston, B. R. Masters, W. W. Webb, J. Microsc. 178, 20 (1995).
[CrossRef] [PubMed]

R. M. Williams, D. W. Piston, W. W. Webb, FASEB J. 8, 804 (1994).
[PubMed]

W. Denk, D. W. Piston, W. W. Webb, in The Handbook of Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), p. 445.

Squier, J.

Strickler, J. H.

W. Denk, J. H. Strickler, W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Strowbridge, B. W.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, J. Neurosci. Methods 54, 151 (1994).
[CrossRef] [PubMed]

Tank, D. W.

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, J. Neurosci. Methods 54, 151 (1994).
[CrossRef] [PubMed]

Twarowski, A. J.

A. J. Twarowski, D. S. Kliger, Chem. Phys. 20, 259 (1977)M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Webb, W. W.

D. W. Piston, B. R. Masters, W. W. Webb, J. Microsc. 178, 20 (1995).
[CrossRef] [PubMed]

R. M. Williams, D. W. Piston, W. W. Webb, FASEB J. 8, 804 (1994).
[PubMed]

W. Denk, J. H. Strickler, W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

W. Denk, D. W. Piston, W. W. Webb, in The Handbook of Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), p. 445.

W. W. Webb, C. Xu, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 nm to 990 nm,” J. Opt. Soc. Am. B (to be published)C. Xu, J. Guild, W. W. Webb, Biophys. J. 68, A197 (1995).

Williams, R. M.

R. M. Williams, D. W. Piston, W. W. Webb, FASEB J. 8, 804 (1994).
[PubMed]

Xu, C.

W. W. Webb, C. Xu, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 nm to 990 nm,” J. Opt. Soc. Am. B (to be published)C. Xu, J. Guild, W. W. Webb, Biophys. J. 68, A197 (1995).

Yuste, R.

R. Yuste, W. Denk, Nature (London) 375, 682 (1995).
[CrossRef] [PubMed]

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, J. Neurosci. Methods 54, 151 (1994).
[CrossRef] [PubMed]

Anal. Chem. (1)

S. M. Kennedy, F. E. Lytle, Anal. Chem. 58, 2643 (1986)R. D. Jones, P. R. Callis, J. Appl. Phys. 64, 4301 (1988).
[CrossRef]

Chem. Phys. (1)

A. J. Twarowski, D. S. Kliger, Chem. Phys. 20, 259 (1977)M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

FASEB J. (1)

R. M. Williams, D. W. Piston, W. W. Webb, FASEB J. 8, 804 (1994).
[PubMed]

J. Microsc. (1)

D. W. Piston, B. R. Masters, W. W. Webb, J. Microsc. 178, 20 (1995).
[CrossRef] [PubMed]

J. Neurosci. Methods (1)

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strowbridge, D. W. Tank, R. Yuste, J. Neurosci. Methods 54, 151 (1994).
[CrossRef] [PubMed]

Nature (1)

R. Yuste, W. Denk, Nature (London) 375, 682 (1995).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (1)

J. P. Hermann, J. Ducuing, Phys. Rev. A 5, 2557 (1972).
[CrossRef]

Science (1)

W. Denk, J. H. Strickler, W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Other (4)

W. Denk, D. W. Piston, W. W. Webb, in The Handbook of Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), p. 445.

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1983), p. 82.

J. Diels, in Dye Laser Principles, F. J. Duarte, L. W. Hillman, eds. (Academic, San Diego, Calif., 1990), p. 104.

W. W. Webb, C. Xu, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 nm to 990 nm,” J. Opt. Soc. Am. B (to be published)C. Xu, J. Guild, W. W. Webb, Biophys. J. 68, A197 (1995).

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Figures (2)

Fig. 1
Fig. 1

Experiments were performed with a mode-locked femtosecond Ti:sapphire laser. A prism pair (PC) was used to compensate for the GDD of the microscope objective. A long-pass filter (>630 nm) eliminates residual argon pump light and Ti:sapphire fluorescence. After two sequential 5× beam expanders (BE) the beam was approximately 25 mm in diameter (1/e2), which was sufficient to overfill the back aperture (10-mm diameter) of the objective (Zeiss Neofluoar, 0.3 N.A., 10×). A long-pass dichroic mirror (DC) with reflectivity > 95% for λ < 610 nm separated the fluorescence from the excitation light. The incident power at the sample was measured by recollimating the transmitted beam onto a calibrated power meter. To ensure that the total generated fluorescence did not depend on the N.A. [as assumed in Eq. (6)], we used a sample that was significantly thicker (100 μm) than the focal depth (~40 μm). Fluorescence was detected by a photomultiplier tube (PMT; Hamamatsu R1924) and recorded as a function of the interferometer delay.

Fig. 2
Fig. 2

Autocorrelation traces of the excitation pulses in fluorescein solution (water, pH ~ 13). Fluorescence intensity is normalized to the average background (F). (a), (b) Are both measured with wavelength spectrum FWHM Δλ = 14.5 nm but with different amounts of prechirp; (c) Δλ = 7.8 nm; (d) expanded version of (c): note the 8:1 peak-to-background ratio. FWHM pulse widths tp were calculated from the measured autocorrelation FWHM assuming a sech2 pulse profile. Note the time–bandwidth products (Δtp * Δν) and TPE cross sections (δ) for each trace. Each trace was taken during a single scan.

Equations (7)

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F = 1 2 δ C η ϕ sample - I 2 ( t , x ) d t d V ,
F = 1 2 δ C η ϕ sample S 2 ( x ) d V - P 2 ( t ) d t ,
F ( τ ) = 1 2 A δ C η ϕ - d t { P 2 ( t ) + P 2 ( t + τ ) + 4 P ( t ) P ( t + τ ) + 2 P ( t ) P ( t + τ ) × cos  2 [ ω τ + φ ( t + τ ) - φ ( t ) ] + 4 P ( t ) P ( t + τ ) [ P ( t ) + P ( t + τ ) ] × cos [ ω τ + φ ( t + τ ) - φ ( t ) ] } .
- T T F ( τ ) d τ = 1 2 A δ C η ϕ × { 4 [ - P ( t ) d t ] 2 + 4 T - P 2 ( t ) d t } .
F = A δ C η ϕ - P 2 ( t ) d t .
δ = - T T F ( τ ) d τ - 2 T F 2 A C η ϕ [ - P ( t ) d t ] 2 .
g ( 2 ) ( 0 ) = 2 F [ f - T T F ( τ ) d τ - 2 f T F ] - 1 ,

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