Abstract

We present a powerful experimental tool and analysis for characterization of two-photon absorption (2PA) spectra. We demonstrate this method with ZnS and then apply it to organic dyes in solution. We also compare the results with those from other methods such as two-photon fluorescence spectroscopy. This femtosecond pump–probe method uses a white-light continuum (WLC) as the probe to produce a nondegenerate 2PA spectrum. The extreme chirp of the WLC requires that transmittance data be collected over a range of temporal delays between pump and probe pulses. These data then need to be corrected for the effects of this chirp as well as for the temporal walk-off of the pulses in the sample that result from the frequency nondegenerate nature of the experiment. We present a simple analytic solution for the transmitted fluence through the sample, which is applicable for most practical cases.

© 2002 Optical Society of America

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References

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  1. S. R. Marder, J. W. Perry, J. L. Bredas, D. McCord-Maughon, M. E. Dickinson, S. E. Fraser, D. Beljonne, and T. Kogej, in Conjugated Oligomers, Polymers, and Dendrimers: From Polyacetylene to DNA, J. L. Bredas, ed., Proceedings of the Fourth Francqui Colloquium (DeBoeck University, France, 1998), pp. 395–424.
  2. R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989).
    [CrossRef]
  3. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
    [CrossRef] [PubMed]
  4. D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
    [CrossRef]
  5. P. S. Spencer and K. A. Shore, J. Opt. Soc. Am B 12, 67 (1995).
    [CrossRef]
  6. M. Ziólek, M. Lorenc, and R. Naskrecki, Appl. Phys. B 72, 843 (2001).
    [CrossRef]
  7. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chap. 7.
  8. S. Yamaguchi and H. Hamaguchi, Appl. Spectrosc. 49, 1513 (1995).
    [CrossRef]
  9. K. D. Belfield, K. J. Schafer, W. Mourad, and B. A. Reinhardt, J. Org. Chem. 65, 4475 (2000).
    [CrossRef] [PubMed]
  10. R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
    [CrossRef]
  11. C. Xu and W. W. Webb, J. Opt. Soc. Am. B 13, 481 (1996).
    [CrossRef]
  12. A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics III, R. Hann and O. Bloor, eds. (Royal Society of Chemistry, London, 1989), p. 16.

2001 (1)

M. Ziólek, M. Lorenc, and R. Naskrecki, Appl. Phys. B 72, 843 (2001).
[CrossRef]

2000 (1)

K. D. Belfield, K. J. Schafer, W. Mourad, and B. A. Reinhardt, J. Org. Chem. 65, 4475 (2000).
[CrossRef] [PubMed]

1996 (2)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

C. Xu and W. W. Webb, J. Opt. Soc. Am. B 13, 481 (1996).
[CrossRef]

1995 (2)

P. S. Spencer and K. A. Shore, J. Opt. Soc. Am B 12, 67 (1995).
[CrossRef]

S. Yamaguchi and H. Hamaguchi, Appl. Spectrosc. 49, 1513 (1995).
[CrossRef]

1992 (1)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

1989 (1)

Belfield, K. D.

K. D. Belfield, K. J. Schafer, W. Mourad, and B. A. Reinhardt, J. Org. Chem. 65, 4475 (2000).
[CrossRef] [PubMed]

Beljonne, D.

S. R. Marder, J. W. Perry, J. L. Bredas, D. McCord-Maughon, M. E. Dickinson, S. E. Fraser, D. Beljonne, and T. Kogej, in Conjugated Oligomers, Polymers, and Dendrimers: From Polyacetylene to DNA, J. L. Bredas, ed., Proceedings of the Fourth Francqui Colloquium (DeBoeck University, France, 1998), pp. 395–424.

Bredas, J. L.

S. R. Marder, J. W. Perry, J. L. Bredas, D. McCord-Maughon, M. E. Dickinson, S. E. Fraser, D. Beljonne, and T. Kogej, in Conjugated Oligomers, Polymers, and Dendrimers: From Polyacetylene to DNA, J. L. Bredas, ed., Proceedings of the Fourth Francqui Colloquium (DeBoeck University, France, 1998), pp. 395–424.

Butcher, P. N.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chap. 7.

Cotter, D.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chap. 7.

DeSalvo, R.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

Dickinson, M. E.

S. R. Marder, J. W. Perry, J. L. Bredas, D. McCord-Maughon, M. E. Dickinson, S. E. Fraser, D. Beljonne, and T. Kogej, in Conjugated Oligomers, Polymers, and Dendrimers: From Polyacetylene to DNA, J. L. Bredas, ed., Proceedings of the Fourth Francqui Colloquium (DeBoeck University, France, 1998), pp. 395–424.

Fraser, S. E.

S. R. Marder, J. W. Perry, J. L. Bredas, D. McCord-Maughon, M. E. Dickinson, S. E. Fraser, D. Beljonne, and T. Kogej, in Conjugated Oligomers, Polymers, and Dendrimers: From Polyacetylene to DNA, J. L. Bredas, ed., Proceedings of the Fourth Francqui Colloquium (DeBoeck University, France, 1998), pp. 395–424.

Garito, A. F.

A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics III, R. Hann and O. Bloor, eds. (Royal Society of Chemistry, London, 1989), p. 16.

Hagan, D. J.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

Hamaguchi, H.

Heflin, J. R.

A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics III, R. Hann and O. Bloor, eds. (Royal Society of Chemistry, London, 1989), p. 16.

Hutchings, D. C.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

Kogej, T.

S. R. Marder, J. W. Perry, J. L. Bredas, D. McCord-Maughon, M. E. Dickinson, S. E. Fraser, D. Beljonne, and T. Kogej, in Conjugated Oligomers, Polymers, and Dendrimers: From Polyacetylene to DNA, J. L. Bredas, ed., Proceedings of the Fourth Francqui Colloquium (DeBoeck University, France, 1998), pp. 395–424.

Lorenc, M.

M. Ziólek, M. Lorenc, and R. Naskrecki, Appl. Phys. B 72, 843 (2001).
[CrossRef]

Marder, S. R.

S. R. Marder, J. W. Perry, J. L. Bredas, D. McCord-Maughon, M. E. Dickinson, S. E. Fraser, D. Beljonne, and T. Kogej, in Conjugated Oligomers, Polymers, and Dendrimers: From Polyacetylene to DNA, J. L. Bredas, ed., Proceedings of the Fourth Francqui Colloquium (DeBoeck University, France, 1998), pp. 395–424.

McCord-Maughon, D.

S. R. Marder, J. W. Perry, J. L. Bredas, D. McCord-Maughon, M. E. Dickinson, S. E. Fraser, D. Beljonne, and T. Kogej, in Conjugated Oligomers, Polymers, and Dendrimers: From Polyacetylene to DNA, J. L. Bredas, ed., Proceedings of the Fourth Francqui Colloquium (DeBoeck University, France, 1998), pp. 395–424.

Mourad, W.

K. D. Belfield, K. J. Schafer, W. Mourad, and B. A. Reinhardt, J. Org. Chem. 65, 4475 (2000).
[CrossRef] [PubMed]

Naskrecki, R.

M. Ziólek, M. Lorenc, and R. Naskrecki, Appl. Phys. B 72, 843 (2001).
[CrossRef]

Perry, J. W.

S. R. Marder, J. W. Perry, J. L. Bredas, D. McCord-Maughon, M. E. Dickinson, S. E. Fraser, D. Beljonne, and T. Kogej, in Conjugated Oligomers, Polymers, and Dendrimers: From Polyacetylene to DNA, J. L. Bredas, ed., Proceedings of the Fourth Francqui Colloquium (DeBoeck University, France, 1998), pp. 395–424.

Reinhardt, B. A.

K. D. Belfield, K. J. Schafer, W. Mourad, and B. A. Reinhardt, J. Org. Chem. 65, 4475 (2000).
[CrossRef] [PubMed]

Said, A. A.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Schafer, K. J.

K. D. Belfield, K. J. Schafer, W. Mourad, and B. A. Reinhardt, J. Org. Chem. 65, 4475 (2000).
[CrossRef] [PubMed]

Sheik-Bahae, M.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Shore, K. A.

P. S. Spencer and K. A. Shore, J. Opt. Soc. Am B 12, 67 (1995).
[CrossRef]

Spencer, P. S.

P. S. Spencer and K. A. Shore, J. Opt. Soc. Am B 12, 67 (1995).
[CrossRef]

Van Stryland, E. W.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Webb, W. W.

Wong, K. Y.

A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics III, R. Hann and O. Bloor, eds. (Royal Society of Chemistry, London, 1989), p. 16.

Xu, C.

Yamaguchi, S.

Zamani-Khamiri, O.

A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics III, R. Hann and O. Bloor, eds. (Royal Society of Chemistry, London, 1989), p. 16.

Ziólek, M.

M. Ziólek, M. Lorenc, and R. Naskrecki, Appl. Phys. B 72, 843 (2001).
[CrossRef]

Appl. Phys. B (1)

M. Ziólek, M. Lorenc, and R. Naskrecki, Appl. Phys. B 72, 843 (2001).
[CrossRef]

Appl. Spectrosc. (1)

IEEE J. Quantum Electron. (1)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

J. Opt. Soc. Am B (1)

P. S. Spencer and K. A. Shore, J. Opt. Soc. Am B 12, 67 (1995).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Org. Chem. (1)

K. D. Belfield, K. J. Schafer, W. Mourad, and B. A. Reinhardt, J. Org. Chem. 65, 4475 (2000).
[CrossRef] [PubMed]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

Other (4)

S. R. Marder, J. W. Perry, J. L. Bredas, D. McCord-Maughon, M. E. Dickinson, S. E. Fraser, D. Beljonne, and T. Kogej, in Conjugated Oligomers, Polymers, and Dendrimers: From Polyacetylene to DNA, J. L. Bredas, ed., Proceedings of the Fourth Francqui Colloquium (DeBoeck University, France, 1998), pp. 395–424.

R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989).
[CrossRef]

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chap. 7.

A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics III, R. Hann and O. Bloor, eds. (Royal Society of Chemistry, London, 1989), p. 16.

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Figures (3)

Fig. 1
Fig. 1

Normalized probe fluence transmittance T at λ=480,532,580 nm in ZnS. Solid curves, fits of experimental data (dashed curves) with Eq. (1); the corresponding material and nonlinearity parameters are given in the text. Curves are vertically offset for ease of viewing.

Fig. 2
Fig. 2

Nondegenerate 2PA coefficient, β, of ZnS versus probe wavelength: (a) WLC spectral measurement, pump–probe walk-off not included; (b) WLC spectral measurement with walk-off correction; (c) theoretical model for ZnS, Eg=3.54 eV. Experimental parameters are L=0.84 mm, wp=72 fs HW1/eM, W=0.85, λp=0.75 µm.

Fig. 3
Fig. 3

Nondegenerate cross section δ (open squares) and degenerate 2PA cross sections from 2PF (filled circles) versus photon energy (pump+pump, solid curve) vertically scaled linear absorption spectrum.

Equations (2)

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Tσ,τd,W,ρ,Γ= exp-2σWπ-exp-τ+τd-ρW2-Γπρerfτ-erfτ-ρdτ,
ρ=Lwpcn-np+λpdndλ λp-λdndλλ

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