Abstract

Measurements of two-photon fluorescence excitation (TPE) spectra are presented for 11 common molecular fluorophores in the excitation wavelength range 690 nm < λ < 1050 nm. Results of excitation by ˜100-fs pulses of a mode-locked Ti:sapphire laser are corroborated by single-mode cw Ti:sapphire excitation data in the range 710 nm < λ < 840 nm. Absolute values of the TPE cross section for Rhodamine B and Fluorescein are obtained by comparison with one-photon-excited fluorescence, assuming equal emission quantum efficiencies. TPE action cross sections for the other nine fluorophores are also determined. No differences between one-photon- and two-photon-excited fluorescence emission spectra are found. TPE emission spectra are independent of excitation wavelength. With both pulsed and cw excitation the fluorescence emission intensities are strictly proportional to the square of the excitation intensity to within ±4% for excitation intensities sufficiently below excited-state saturation.

© 1996 Optical Society of America

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  1. M. Göppert-Mayer, "Über Elementarakte mit zwei Quanten-sprüngen," Ann. Phys. 9, 273–295 (1931).
  2. W. Kaiser and C. G. B. Garrett, "Two-photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229–231 (1961).
  3. A. J. Twarowski and D. S. Kliger, "Multiphoton absorption spectra using thermal blooming," Chem. Phys. 20, 259–264 (1977).
  4. M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760–769 (1990).
  5. J. P. Hermann and J. Ducuing, "Absolute measurement of two-photon cross sections," Phys. Rev. A 5, 2557–2568 (1972).
  6. R. Swofford and W. M. McClain, "The effect of spatial and temporal laser beam characteristics on two-photon absorption," Chem. Phys. Lett. 34, 455–460 (1975).
  7. R. R. Birge, "One-photon and two-photon excitation spectroscopy," in Ultrasensitive Laser Spectroscopy, D. S. Kliger, ed. (Academic, New York, 1983), pp. 109–174.
  8. W. Denk, J. H. Strickler, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73–76 (1990).
  9. W. M. McClain and R. A. Harris, "Two-photon molecular spectroscopy in liquids and gases," in Excited States, E. C. Lim, ed. (Academic, New York, 1977), pp. 1–56.
  10. A. Fischer, C. Cremer, and E. H. K. Stelzer, "Fluorescence of coumarins and xanthenes after two-photon absorption with a pulsed titanium-sapphire laser," Appl. Opt. 34, 1989–2003 (1995).
  11. R. Loudon, The Quantum Theory of Light, 2nd ed. (Clarendon, Oxford, 1983), pp. 82–119.
  12. T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984), pp. 25.
  13. C. J. R. Sheppard and H. J. Matthews, "Imaging in high-aperture optical systems," J. Opt. Soc. Am. A 4, 1354–1360 (1987).
  14. J. Guild, Applied Physics, Cornell University, Ithaca, New York 14853 (personal communications, 1995). The estimated relative accuracy of the volume integration is 3%.
  15. Assuming that the sample thickness is much greater than the Raleigh length of the Gaussian beam, the appropriate form for <F(t)> is <F(t)> = ½gφη2Cδ(nπ/λ)<P(t)>2. We note that the total fluorescence generation is independent of beam waist size.
  16. J. Kafka, M. L. Watts, and J. W. Pieterse, "Picosecond and femtosecond pulses generation in a regeneratively mode-locked Ti:S laser," IEEE J. Quantum Electron. 28, 2151–2161 (1992).
  17. S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in confocal microscopy induced by mismatches in refractive index," J. Microsc. 169, 391–405 (1993).
  18. J. N. Demas and G. A. Crosby, "The measurement of photo-luminescence quantum yields," J. Phys. Chem. 75, 991–1024 (1971).
  19. G. Grynkiewicz, M. Poenie, and R. Y. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Bio. Chem. 260, 3440–3450 (1985).
  20. DAPI not bound to DNA. The fluorescence quantum efficiency of DAPI is expected to go up by 20-fold upon binding to DNA (from Molecular Probes Handbook 1992–1994, R. P. Haugland, ed., p. 222).
  21. B. Dick and G. Hohlneicher, "Importance of initial and final states as intermediate states in two-photon spectroscopy of polar molecules," J. Chem. Phys. 76, 5755–5760 (1982).
  22. D. J. Bradley, M. H. R. Hutchinson, T. M. H. Koetser, G. H. C. New, and M. S. Petty, "Interaction of picosecond laser pulses with organic molecules I: Two-photon fluorescence quenching and singlet states excitation in rhodamine dyes," Proc. R. Soc. London Ser. A 328, 97–121 (1972).
  23. J. P. Hermann and J. Ducuing, "Dispersion of the two-photon cross-section in rhodamine dyes," Opt. Commun. 6, 101–105 (1972).
  24. L. Goodman and R. P. Pava, "Two-photon spectra of aromatic molecules," Acc. Chem. Res. 17, 250–257 (1984).
  25. D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, "Interaction of picosecond laser pulses with organic molecules II: Two-photon absorption cross-sections," Proc. R. Soc. Lond. A 329, 105–119 (1972).
  26. S. M. Kennedy and F. E. Lytle, "p-Bis(o-methylstyryl) benzene as a power-square sensor for two-photon absorption measurements between 537 and 694 nm," Anal. Chem. 58, 2643–2647 (1986).
  27. I. Gryczynski, J. Kusba, V. Bogdanov, and J. R. Lakowicz, "Quenching of fluorescence by light: a new method to control the excited-state lifetime and orientations of fluorophores," J. Fluoresc. 4, 103–109 (1994).
  28. C. Xu, J. Guild, and W. W. Webb, "Two-photon fluorescence excitation spectra of calcium probe indo-1," Biophys. J. 66, A161 (1994).
  29. C. Xu, J. Guild, and W. W. Webb, "Two-photon excitation cross-sections for commonly used biological fluorophores," Biophys. J. 68, A197 (1995).
  30. J. D. Kafka and T. Baer, "Prism-pair delay lines in optical pulse compression," Opt. Lett. 12, 401–403 (1987).
  31. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).
  32. Z. Bor, "Distortion of femtosecond laser pulses in lenses and lens systems," J. Mod. Opt. 35, 1907–1918 (1988).
  33. J. Guild, C. Xu, and W. W. Webb, "Measurement of group delay dispersion of high numerical aperture objectives using two-photon excited fluorescence," submitted to Appl. Opt.
  34. Two-photon transitions consist of two separate one-photon transitions.
  35. P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, "Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy," Opt. Quantum Electron. 24, 851–859 (1992).
  36. L. Parma and N. Omenetto, "Fluorescence behavior of 7-hydroxycoumarine excited by one-photon and two-photon absorption by means of a tunable dye laser," Chem. Phys. Lett. 54, 544–546 (1978).
  37. R. D. Jones and P. R. Callis, "A power-square sensor for two-photon spectroscopy and dispersion of second-order coherence," J. Appl. Phys. 64, 4301–4305 (1988).
  38. C. Xu, J. Guild, W. W. Webb, and W. Denk, "Determination of absolute two-photon excitation cross-sections by in situ second-order autocorrelation," Opt. Lett. 21, 2372–2374 (1995).
  39. W. L. Smith, "Two-photon absorption in condensed media," in Handbook of Laser Science and Technology, J. Weber, ed. (CRC, Baco Raton, Fla., 1986), pp. 229–258.
  40. C. J. R. Sheppard and M. Gu, "Image formation in two-photon fluorescence microscopy," Optik (Stuttgart) 86, 104–106 (1990).
  41. G. S. He, G. C. Xu, P. N. Prasad, B. A. Reinhardt, J. C. Bhatt, and A. G. Dillard, "Two-photon absorption and optical-limiting properties of novel organic compounds," Opt. Lett. 20, 435–437 (1995).
  42. J. Zyss, I. Ledoux, and J. F. Nicoud, "Advances in molecular engineering for quadratic nonlinear optics," in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 130–200.

1995

A. Fischer, C. Cremer, and E. H. K. Stelzer, "Fluorescence of coumarins and xanthenes after two-photon absorption with a pulsed titanium-sapphire laser," Appl. Opt. 34, 1989–2003 (1995).

J. Guild, Applied Physics, Cornell University, Ithaca, New York 14853 (personal communications, 1995). The estimated relative accuracy of the volume integration is 3%.

C. Xu, J. Guild, and W. W. Webb, "Two-photon excitation cross-sections for commonly used biological fluorophores," Biophys. J. 68, A197 (1995).

C. Xu, J. Guild, W. W. Webb, and W. Denk, "Determination of absolute two-photon excitation cross-sections by in situ second-order autocorrelation," Opt. Lett. 21, 2372–2374 (1995).

G. S. He, G. C. Xu, P. N. Prasad, B. A. Reinhardt, J. C. Bhatt, and A. G. Dillard, "Two-photon absorption and optical-limiting properties of novel organic compounds," Opt. Lett. 20, 435–437 (1995).

1994

J. Zyss, I. Ledoux, and J. F. Nicoud, "Advances in molecular engineering for quadratic nonlinear optics," in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 130–200.

I. Gryczynski, J. Kusba, V. Bogdanov, and J. R. Lakowicz, "Quenching of fluorescence by light: a new method to control the excited-state lifetime and orientations of fluorophores," J. Fluoresc. 4, 103–109 (1994).

C. Xu, J. Guild, and W. W. Webb, "Two-photon fluorescence excitation spectra of calcium probe indo-1," Biophys. J. 66, A161 (1994).

1993

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in confocal microscopy induced by mismatches in refractive index," J. Microsc. 169, 391–405 (1993).

1992

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, "Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy," Opt. Quantum Electron. 24, 851–859 (1992).

J. Kafka, M. L. Watts, and J. W. Pieterse, "Picosecond and femtosecond pulses generation in a regeneratively mode-locked Ti:S laser," IEEE J. Quantum Electron. 28, 2151–2161 (1992).

1990

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760–769 (1990).

W. Denk, J. H. Strickler, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73–76 (1990).

C. J. R. Sheppard and M. Gu, "Image formation in two-photon fluorescence microscopy," Optik (Stuttgart) 86, 104–106 (1990).

1988

Z. Bor, "Distortion of femtosecond laser pulses in lenses and lens systems," J. Mod. Opt. 35, 1907–1918 (1988).

R. D. Jones and P. R. Callis, "A power-square sensor for two-photon spectroscopy and dispersion of second-order coherence," J. Appl. Phys. 64, 4301–4305 (1988).

1987

1986

W. L. Smith, "Two-photon absorption in condensed media," in Handbook of Laser Science and Technology, J. Weber, ed. (CRC, Baco Raton, Fla., 1986), pp. 229–258.

S. M. Kennedy and F. E. Lytle, "p-Bis(o-methylstyryl) benzene as a power-square sensor for two-photon absorption measurements between 537 and 694 nm," Anal. Chem. 58, 2643–2647 (1986).

1985

G. Grynkiewicz, M. Poenie, and R. Y. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Bio. Chem. 260, 3440–3450 (1985).

1984

L. Goodman and R. P. Pava, "Two-photon spectra of aromatic molecules," Acc. Chem. Res. 17, 250–257 (1984).

1983

R. R. Birge, "One-photon and two-photon excitation spectroscopy," in Ultrasensitive Laser Spectroscopy, D. S. Kliger, ed. (Academic, New York, 1983), pp. 109–174.

1982

B. Dick and G. Hohlneicher, "Importance of initial and final states as intermediate states in two-photon spectroscopy of polar molecules," J. Chem. Phys. 76, 5755–5760 (1982).

1980

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).

1978

L. Parma and N. Omenetto, "Fluorescence behavior of 7-hydroxycoumarine excited by one-photon and two-photon absorption by means of a tunable dye laser," Chem. Phys. Lett. 54, 544–546 (1978).

1977

W. M. McClain and R. A. Harris, "Two-photon molecular spectroscopy in liquids and gases," in Excited States, E. C. Lim, ed. (Academic, New York, 1977), pp. 1–56.

A. J. Twarowski and D. S. Kliger, "Multiphoton absorption spectra using thermal blooming," Chem. Phys. 20, 259–264 (1977).

1975

R. Swofford and W. M. McClain, "The effect of spatial and temporal laser beam characteristics on two-photon absorption," Chem. Phys. Lett. 34, 455–460 (1975).

1972

J. P. Hermann and J. Ducuing, "Absolute measurement of two-photon cross sections," Phys. Rev. A 5, 2557–2568 (1972).

D. J. Bradley, M. H. R. Hutchinson, T. M. H. Koetser, G. H. C. New, and M. S. Petty, "Interaction of picosecond laser pulses with organic molecules I: Two-photon fluorescence quenching and singlet states excitation in rhodamine dyes," Proc. R. Soc. London Ser. A 328, 97–121 (1972).

J. P. Hermann and J. Ducuing, "Dispersion of the two-photon cross-section in rhodamine dyes," Opt. Commun. 6, 101–105 (1972).

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, "Interaction of picosecond laser pulses with organic molecules II: Two-photon absorption cross-sections," Proc. R. Soc. Lond. A 329, 105–119 (1972).

1971

J. N. Demas and G. A. Crosby, "The measurement of photo-luminescence quantum yields," J. Phys. Chem. 75, 991–1024 (1971).

1961

W. Kaiser and C. G. B. Garrett, "Two-photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229–231 (1961).

1931

M. Göppert-Mayer, "Über Elementarakte mit zwei Quanten-sprüngen," Ann. Phys. 9, 273–295 (1931).

Amos, W. B.

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, "Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy," Opt. Quantum Electron. 24, 851–859 (1992).

Baer, T.

Bhatt, J. C.

Birge, R. R.

R. R. Birge, "One-photon and two-photon excitation spectroscopy," in Ultrasensitive Laser Spectroscopy, D. S. Kliger, ed. (Academic, New York, 1983), pp. 109–174.

Bogdanov, V.

I. Gryczynski, J. Kusba, V. Bogdanov, and J. R. Lakowicz, "Quenching of fluorescence by light: a new method to control the excited-state lifetime and orientations of fluorophores," J. Fluoresc. 4, 103–109 (1994).

Bor, Z.

Z. Bor, "Distortion of femtosecond laser pulses in lenses and lens systems," J. Mod. Opt. 35, 1907–1918 (1988).

Bradley, D. J.

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, "Interaction of picosecond laser pulses with organic molecules II: Two-photon absorption cross-sections," Proc. R. Soc. Lond. A 329, 105–119 (1972).

D. J. Bradley, M. H. R. Hutchinson, T. M. H. Koetser, G. H. C. New, and M. S. Petty, "Interaction of picosecond laser pulses with organic molecules I: Two-photon fluorescence quenching and singlet states excitation in rhodamine dyes," Proc. R. Soc. London Ser. A 328, 97–121 (1972).

Callis, P. R.

R. D. Jones and P. R. Callis, "A power-square sensor for two-photon spectroscopy and dispersion of second-order coherence," J. Appl. Phys. 64, 4301–4305 (1988).

Cremer, C.

A. Fischer, C. Cremer, and E. H. K. Stelzer, "Fluorescence of coumarins and xanthenes after two-photon absorption with a pulsed titanium-sapphire laser," Appl. Opt. 34, 1989–2003 (1995).

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in confocal microscopy induced by mismatches in refractive index," J. Microsc. 169, 391–405 (1993).

Crosby, G. A.

J. N. Demas and G. A. Crosby, "The measurement of photo-luminescence quantum yields," J. Phys. Chem. 75, 991–1024 (1971).

Curley, P. F.

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, "Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy," Opt. Quantum Electron. 24, 851–859 (1992).

Demas, J. N.

J. N. Demas and G. A. Crosby, "The measurement of photo-luminescence quantum yields," J. Phys. Chem. 75, 991–1024 (1971).

Denk, W.

C. Xu, J. Guild, W. W. Webb, and W. Denk, "Determination of absolute two-photon excitation cross-sections by in situ second-order autocorrelation," Opt. Lett. 21, 2372–2374 (1995).

W. Denk, J. H. Strickler, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73–76 (1990).

Dick, B.

B. Dick and G. Hohlneicher, "Importance of initial and final states as intermediate states in two-photon spectroscopy of polar molecules," J. Chem. Phys. 76, 5755–5760 (1982).

Dillard, A. G.

Ducuing, J.

J. P. Hermann and J. Ducuing, "Dispersion of the two-photon cross-section in rhodamine dyes," Opt. Commun. 6, 101–105 (1972).

J. P. Hermann and J. Ducuing, "Absolute measurement of two-photon cross sections," Phys. Rev. A 5, 2557–2568 (1972).

Ferguson, A. I.

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, "Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy," Opt. Quantum Electron. 24, 851–859 (1992).

Fischer, A.

Garrett, C. G. B.

W. Kaiser and C. G. B. Garrett, "Two-photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229–231 (1961).

Goodman, L.

L. Goodman and R. P. Pava, "Two-photon spectra of aromatic molecules," Acc. Chem. Res. 17, 250–257 (1984).

Göppert-Mayer, M.

M. Göppert-Mayer, "Über Elementarakte mit zwei Quanten-sprüngen," Ann. Phys. 9, 273–295 (1931).

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).

Gryczynski, I.

I. Gryczynski, J. Kusba, V. Bogdanov, and J. R. Lakowicz, "Quenching of fluorescence by light: a new method to control the excited-state lifetime and orientations of fluorophores," J. Fluoresc. 4, 103–109 (1994).

Grynkiewicz, G.

G. Grynkiewicz, M. Poenie, and R. Y. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Bio. Chem. 260, 3440–3450 (1985).

Gu, M.

C. J. R. Sheppard and M. Gu, "Image formation in two-photon fluorescence microscopy," Optik (Stuttgart) 86, 104–106 (1990).

Guild, J.

C. Xu, J. Guild, W. W. Webb, and W. Denk, "Determination of absolute two-photon excitation cross-sections by in situ second-order autocorrelation," Opt. Lett. 21, 2372–2374 (1995).

C. Xu, J. Guild, and W. W. Webb, "Two-photon excitation cross-sections for commonly used biological fluorophores," Biophys. J. 68, A197 (1995).

J. Guild, Applied Physics, Cornell University, Ithaca, New York 14853 (personal communications, 1995). The estimated relative accuracy of the volume integration is 3%.

C. Xu, J. Guild, and W. W. Webb, "Two-photon fluorescence excitation spectra of calcium probe indo-1," Biophys. J. 66, A161 (1994).

J. Guild, C. Xu, and W. W. Webb, "Measurement of group delay dispersion of high numerical aperture objectives using two-photon excited fluorescence," submitted to Appl. Opt.

Hagan, D.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760–769 (1990).

Harris, R. A.

W. M. McClain and R. A. Harris, "Two-photon molecular spectroscopy in liquids and gases," in Excited States, E. C. Lim, ed. (Academic, New York, 1977), pp. 1–56.

He, G. S.

Hell, S.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in confocal microscopy induced by mismatches in refractive index," J. Microsc. 169, 391–405 (1993).

Hermann, J. P.

J. P. Hermann and J. Ducuing, "Absolute measurement of two-photon cross sections," Phys. Rev. A 5, 2557–2568 (1972).

J. P. Hermann and J. Ducuing, "Dispersion of the two-photon cross-section in rhodamine dyes," Opt. Commun. 6, 101–105 (1972).

Hohlneicher, G.

B. Dick and G. Hohlneicher, "Importance of initial and final states as intermediate states in two-photon spectroscopy of polar molecules," J. Chem. Phys. 76, 5755–5760 (1982).

Hutchinson, M. H. R.

D. J. Bradley, M. H. R. Hutchinson, T. M. H. Koetser, G. H. C. New, and M. S. Petty, "Interaction of picosecond laser pulses with organic molecules I: Two-photon fluorescence quenching and singlet states excitation in rhodamine dyes," Proc. R. Soc. London Ser. A 328, 97–121 (1972).

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, "Interaction of picosecond laser pulses with organic molecules II: Two-photon absorption cross-sections," Proc. R. Soc. Lond. A 329, 105–119 (1972).

Jones, R. D.

R. D. Jones and P. R. Callis, "A power-square sensor for two-photon spectroscopy and dispersion of second-order coherence," J. Appl. Phys. 64, 4301–4305 (1988).

Kafka, J.

J. Kafka, M. L. Watts, and J. W. Pieterse, "Picosecond and femtosecond pulses generation in a regeneratively mode-locked Ti:S laser," IEEE J. Quantum Electron. 28, 2151–2161 (1992).

Kafka, J. D.

Kaiser, W.

W. Kaiser and C. G. B. Garrett, "Two-photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229–231 (1961).

Kennedy, S. M.

S. M. Kennedy and F. E. Lytle, "p-Bis(o-methylstyryl) benzene as a power-square sensor for two-photon absorption measurements between 537 and 694 nm," Anal. Chem. 58, 2643–2647 (1986).

Kliger, D. S.

A. J. Twarowski and D. S. Kliger, "Multiphoton absorption spectra using thermal blooming," Chem. Phys. 20, 259–264 (1977).

Koetser, H.

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, "Interaction of picosecond laser pulses with organic molecules II: Two-photon absorption cross-sections," Proc. R. Soc. Lond. A 329, 105–119 (1972).

Koetser, T. M. H.

D. J. Bradley, M. H. R. Hutchinson, T. M. H. Koetser, G. H. C. New, and M. S. Petty, "Interaction of picosecond laser pulses with organic molecules I: Two-photon fluorescence quenching and singlet states excitation in rhodamine dyes," Proc. R. Soc. London Ser. A 328, 97–121 (1972).

Kusba, J.

I. Gryczynski, J. Kusba, V. Bogdanov, and J. R. Lakowicz, "Quenching of fluorescence by light: a new method to control the excited-state lifetime and orientations of fluorophores," J. Fluoresc. 4, 103–109 (1994).

Lakowicz, J. R.

I. Gryczynski, J. Kusba, V. Bogdanov, and J. R. Lakowicz, "Quenching of fluorescence by light: a new method to control the excited-state lifetime and orientations of fluorophores," J. Fluoresc. 4, 103–109 (1994).

Ledoux, I.

J. Zyss, I. Ledoux, and J. F. Nicoud, "Advances in molecular engineering for quadratic nonlinear optics," in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 130–200.

Loudon, R.

R. Loudon, The Quantum Theory of Light, 2nd ed. (Clarendon, Oxford, 1983), pp. 82–119.

Lytle, F. E.

S. M. Kennedy and F. E. Lytle, "p-Bis(o-methylstyryl) benzene as a power-square sensor for two-photon absorption measurements between 537 and 694 nm," Anal. Chem. 58, 2643–2647 (1986).

Matthews, H. J.

McClain, W. M.

W. M. McClain and R. A. Harris, "Two-photon molecular spectroscopy in liquids and gases," in Excited States, E. C. Lim, ed. (Academic, New York, 1977), pp. 1–56.

R. Swofford and W. M. McClain, "The effect of spatial and temporal laser beam characteristics on two-photon absorption," Chem. Phys. Lett. 34, 455–460 (1975).

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).

New, G. H. C.

D. J. Bradley, M. H. R. Hutchinson, T. M. H. Koetser, G. H. C. New, and M. S. Petty, "Interaction of picosecond laser pulses with organic molecules I: Two-photon fluorescence quenching and singlet states excitation in rhodamine dyes," Proc. R. Soc. London Ser. A 328, 97–121 (1972).

Nicoud, J. F.

J. Zyss, I. Ledoux, and J. F. Nicoud, "Advances in molecular engineering for quadratic nonlinear optics," in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 130–200.

Omenetto, N.

L. Parma and N. Omenetto, "Fluorescence behavior of 7-hydroxycoumarine excited by one-photon and two-photon absorption by means of a tunable dye laser," Chem. Phys. Lett. 54, 544–546 (1978).

Parma, L.

L. Parma and N. Omenetto, "Fluorescence behavior of 7-hydroxycoumarine excited by one-photon and two-photon absorption by means of a tunable dye laser," Chem. Phys. Lett. 54, 544–546 (1978).

Pava, R. P.

L. Goodman and R. P. Pava, "Two-photon spectra of aromatic molecules," Acc. Chem. Res. 17, 250–257 (1984).

Petty, M. S.

D. J. Bradley, M. H. R. Hutchinson, T. M. H. Koetser, G. H. C. New, and M. S. Petty, "Interaction of picosecond laser pulses with organic molecules I: Two-photon fluorescence quenching and singlet states excitation in rhodamine dyes," Proc. R. Soc. London Ser. A 328, 97–121 (1972).

Pieterse, J. W.

J. Kafka, M. L. Watts, and J. W. Pieterse, "Picosecond and femtosecond pulses generation in a regeneratively mode-locked Ti:S laser," IEEE J. Quantum Electron. 28, 2151–2161 (1992).

Poenie, M.

G. Grynkiewicz, M. Poenie, and R. Y. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Bio. Chem. 260, 3440–3450 (1985).

Prasad, P. N.

Reiner, G.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in confocal microscopy induced by mismatches in refractive index," J. Microsc. 169, 391–405 (1993).

Reinhardt, B. A.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760–769 (1990).

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760–769 (1990).

Sheppard, C. J. R.

C. J. R. Sheppard and M. Gu, "Image formation in two-photon fluorescence microscopy," Optik (Stuttgart) 86, 104–106 (1990).

C. J. R. Sheppard and H. J. Matthews, "Imaging in high-aperture optical systems," J. Opt. Soc. Am. A 4, 1354–1360 (1987).

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984), pp. 25.

Smith, W. L.

W. L. Smith, "Two-photon absorption in condensed media," in Handbook of Laser Science and Technology, J. Weber, ed. (CRC, Baco Raton, Fla., 1986), pp. 229–258.

Stelzer, E. H. K.

A. Fischer, C. Cremer, and E. H. K. Stelzer, "Fluorescence of coumarins and xanthenes after two-photon absorption with a pulsed titanium-sapphire laser," Appl. Opt. 34, 1989–2003 (1995).

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in confocal microscopy induced by mismatches in refractive index," J. Microsc. 169, 391–405 (1993).

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73–76 (1990).

Stryland, E. W. Van

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760–769 (1990).

Swofford, R.

R. Swofford and W. M. McClain, "The effect of spatial and temporal laser beam characteristics on two-photon absorption," Chem. Phys. Lett. 34, 455–460 (1975).

Tsien, R. Y.

G. Grynkiewicz, M. Poenie, and R. Y. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Bio. Chem. 260, 3440–3450 (1985).

Twarowski, A. J.

A. J. Twarowski and D. S. Kliger, "Multiphoton absorption spectra using thermal blooming," Chem. Phys. 20, 259–264 (1977).

Watts, M. L.

J. Kafka, M. L. Watts, and J. W. Pieterse, "Picosecond and femtosecond pulses generation in a regeneratively mode-locked Ti:S laser," IEEE J. Quantum Electron. 28, 2151–2161 (1992).

Webb, W. W.

C. Xu, J. Guild, and W. W. Webb, "Two-photon excitation cross-sections for commonly used biological fluorophores," Biophys. J. 68, A197 (1995).

C. Xu, J. Guild, W. W. Webb, and W. Denk, "Determination of absolute two-photon excitation cross-sections by in situ second-order autocorrelation," Opt. Lett. 21, 2372–2374 (1995).

C. Xu, J. Guild, and W. W. Webb, "Two-photon fluorescence excitation spectra of calcium probe indo-1," Biophys. J. 66, A161 (1994).

W. Denk, J. H. Strickler, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73–76 (1990).

J. Guild, C. Xu, and W. W. Webb, "Measurement of group delay dispersion of high numerical aperture objectives using two-photon excited fluorescence," submitted to Appl. Opt.

Wei, T.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760–769 (1990).

White, J. G.

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, "Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy," Opt. Quantum Electron. 24, 851–859 (1992).

Wilson, T.

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984), pp. 25.

Xu, C.

C. Xu, J. Guild, and W. W. Webb, "Two-photon excitation cross-sections for commonly used biological fluorophores," Biophys. J. 68, A197 (1995).

C. Xu, J. Guild, W. W. Webb, and W. Denk, "Determination of absolute two-photon excitation cross-sections by in situ second-order autocorrelation," Opt. Lett. 21, 2372–2374 (1995).

C. Xu, J. Guild, and W. W. Webb, "Two-photon fluorescence excitation spectra of calcium probe indo-1," Biophys. J. 66, A161 (1994).

J. Guild, C. Xu, and W. W. Webb, "Measurement of group delay dispersion of high numerical aperture objectives using two-photon excited fluorescence," submitted to Appl. Opt.

Xu, G. C.

Zyss, J.

J. Zyss, I. Ledoux, and J. F. Nicoud, "Advances in molecular engineering for quadratic nonlinear optics," in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 130–200.

Acc. Chem. Res.

L. Goodman and R. P. Pava, "Two-photon spectra of aromatic molecules," Acc. Chem. Res. 17, 250–257 (1984).

Anal. Chem.

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Ann. Phys.

M. Göppert-Mayer, "Über Elementarakte mit zwei Quanten-sprüngen," Ann. Phys. 9, 273–295 (1931).

Appl. Opt.

Biophys. J.

C. Xu, J. Guild, and W. W. Webb, "Two-photon fluorescence excitation spectra of calcium probe indo-1," Biophys. J. 66, A161 (1994).

C. Xu, J. Guild, and W. W. Webb, "Two-photon excitation cross-sections for commonly used biological fluorophores," Biophys. J. 68, A197 (1995).

Chem. Phys.

A. J. Twarowski and D. S. Kliger, "Multiphoton absorption spectra using thermal blooming," Chem. Phys. 20, 259–264 (1977).

Chem. Phys. Lett.

R. Swofford and W. M. McClain, "The effect of spatial and temporal laser beam characteristics on two-photon absorption," Chem. Phys. Lett. 34, 455–460 (1975).

L. Parma and N. Omenetto, "Fluorescence behavior of 7-hydroxycoumarine excited by one-photon and two-photon absorption by means of a tunable dye laser," Chem. Phys. Lett. 54, 544–546 (1978).

IEEE J. Quantum Electron.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760–769 (1990).

J. Kafka, M. L. Watts, and J. W. Pieterse, "Picosecond and femtosecond pulses generation in a regeneratively mode-locked Ti:S laser," IEEE J. Quantum Electron. 28, 2151–2161 (1992).

J. Appl. Phys.

R. D. Jones and P. R. Callis, "A power-square sensor for two-photon spectroscopy and dispersion of second-order coherence," J. Appl. Phys. 64, 4301–4305 (1988).

J. Bio. Chem.

G. Grynkiewicz, M. Poenie, and R. Y. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Bio. Chem. 260, 3440–3450 (1985).

J. Chem. Phys.

B. Dick and G. Hohlneicher, "Importance of initial and final states as intermediate states in two-photon spectroscopy of polar molecules," J. Chem. Phys. 76, 5755–5760 (1982).

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J. Microsc.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in confocal microscopy induced by mismatches in refractive index," J. Microsc. 169, 391–405 (1993).

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Z. Bor, "Distortion of femtosecond laser pulses in lenses and lens systems," J. Mod. Opt. 35, 1907–1918 (1988).

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Opt. Commun.

J. P. Hermann and J. Ducuing, "Dispersion of the two-photon cross-section in rhodamine dyes," Opt. Commun. 6, 101–105 (1972).

Opt. Lett.

Opt. Quantum Electron.

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, "Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy," Opt. Quantum Electron. 24, 851–859 (1992).

Optik

C. J. R. Sheppard and M. Gu, "Image formation in two-photon fluorescence microscopy," Optik (Stuttgart) 86, 104–106 (1990).

Phys. Rev. A

J. P. Hermann and J. Ducuing, "Absolute measurement of two-photon cross sections," Phys. Rev. A 5, 2557–2568 (1972).

Phys. Rev. Lett.

W. Kaiser and C. G. B. Garrett, "Two-photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229–231 (1961).

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).

Proc. R. Soc. Lond. A

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Proc. R. Soc. London Ser. A

D. J. Bradley, M. H. R. Hutchinson, T. M. H. Koetser, G. H. C. New, and M. S. Petty, "Interaction of picosecond laser pulses with organic molecules I: Two-photon fluorescence quenching and singlet states excitation in rhodamine dyes," Proc. R. Soc. London Ser. A 328, 97–121 (1972).

Science

W. Denk, J. H. Strickler, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73–76 (1990).

Other

W. M. McClain and R. A. Harris, "Two-photon molecular spectroscopy in liquids and gases," in Excited States, E. C. Lim, ed. (Academic, New York, 1977), pp. 1–56.

R. R. Birge, "One-photon and two-photon excitation spectroscopy," in Ultrasensitive Laser Spectroscopy, D. S. Kliger, ed. (Academic, New York, 1983), pp. 109–174.

DAPI not bound to DNA. The fluorescence quantum efficiency of DAPI is expected to go up by 20-fold upon binding to DNA (from Molecular Probes Handbook 1992–1994, R. P. Haugland, ed., p. 222).

J. Guild, Applied Physics, Cornell University, Ithaca, New York 14853 (personal communications, 1995). The estimated relative accuracy of the volume integration is 3%.

Assuming that the sample thickness is much greater than the Raleigh length of the Gaussian beam, the appropriate form for <F(t)> is <F(t)> = ½gφη2Cδ(nπ/λ)<P(t)>2. We note that the total fluorescence generation is independent of beam waist size.

R. Loudon, The Quantum Theory of Light, 2nd ed. (Clarendon, Oxford, 1983), pp. 82–119.

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984), pp. 25.

W. L. Smith, "Two-photon absorption in condensed media," in Handbook of Laser Science and Technology, J. Weber, ed. (CRC, Baco Raton, Fla., 1986), pp. 229–258.

J. Guild, C. Xu, and W. W. Webb, "Measurement of group delay dispersion of high numerical aperture objectives using two-photon excited fluorescence," submitted to Appl. Opt.

Two-photon transitions consist of two separate one-photon transitions.

J. Zyss, I. Ledoux, and J. F. Nicoud, "Advances in molecular engineering for quadratic nonlinear optics," in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), pp. 130–200.

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