Abstract

We describe theory and experiment for Fourier-transform sum-frequency surface vibrational spectroscopy using femtosecond lasers and discuss some practical issues in comparing it with the multichannel dispersive sum-frequency generation approach to obtain sub-laser-linewidth resolution in vibrational spectra. A signal-to-noise ratio analysis shows that the former is inferior for several inherent reasons if infrared and visible pulses used are derived from a typical 1 kHz femtosecond oscillator–amplifier system.

© 2006 Optical Society of America

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  1. Y. R. Shen, "Surface spectroscopy by nonlinear optics," in Frontiers in Laser Spectroscopy: Proceedings of the International School of Physics "Enrico Fermi" Course CXX, T.W.Hänsch and M.Inguscio, eds. (North-Holland, 1994), pp. 139-165.
    [PubMed]
  2. R. A. Kaindl, M. Wurm, K. Reimann, P. Hamm, A. M. Weiner, and M. Woerner, "Generation, shaping, and characterization of intense femtosecond pulses tunable from 3 to 20 µm," J. Opt. Soc. Am. B 17, 2086-2094 (2000).
    [CrossRef]
  3. A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
    [CrossRef]
  4. M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, "Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes," Proc. Natl. Acad. Sci. U.S.A. 97, 8219-8224 (2000).
    [CrossRef] [PubMed]
  5. M. T. Zanni, N.-H. Ge, Y. S. Kim, and R. M. Hochstrasser, "Two-dimensional IR spectroscopy can be designed to eliminate the diagonal peaks and expose only the crosspeaks needed for structure determination," Proc. Natl. Acad. Sci. U.S.A. 98, 11265-11270 (2001).
    [CrossRef] [PubMed]
  6. O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Coupling and orientation between anharmonic vibrations characterized with two-dimensional infrared vibrational echo spectroscopy," J. Chem. Phys. 115, 10814-10828 (2001).
    [CrossRef]
  7. O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy," Phys. Rev. Lett. 86, 2154-2157 (2001).
    [CrossRef] [PubMed]
  8. S. M. Gallagher Faeder and D. M. Jonas, "Phase-resolved time-domain nonlinear optical signals," Phys. Rev. A 62, 033820 (2000).
    [CrossRef]
  9. A. Albrecht Ferro, J. D. Hybl, and D. M. Jonas, "Complete femtosecond linear free induction decay, Fourier algorithm for dispersion relations, and accuracy of the rotating wave approximation," J. Chem. Phys. 114, 4649-4656 (2001).
    [CrossRef]
  10. J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, "Two-dimensional Fourier transform electronic spectroscopy," J. Chem. Phys. 115, 6606-6622 (2001).
    [CrossRef]
  11. C. Froehly, A. Lacourt, and J. C. Viénot, "Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications," Nouv. Rev. Opt. 4, 183-196 (1973).
    [CrossRef]
  12. L. Lepetit, G. Chériaux, and M. Joffre, "Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy," J. Opt. Soc. Am. B 12, 2467-2474 (1995).
    [CrossRef]
  13. L. Lepetit and M. Joffre, "Two-dimensional nonlinear optics using Fourier-transform spectral interferometry," Opt. Lett. 21, 564-566 (1996).
    [CrossRef] [PubMed]
  14. L. J. Richter, T. P. Petralli-Mallow, and J. C. Stephenson, "Vibrationally resolved sum-frequency generation with broad-bandwidth infrared pulses," Opt. Lett. 23, 1594-1596 (1998).
    [CrossRef]
  15. J. A. McGuire, W. Beck, X. Wei, and Y. R. Shen. "Fourier-transform sum-frequency surface vibrational spectroscopy with femtosecond pulses," Opt. Lett. 24, 1877-1879 (1999).
    [CrossRef]
  16. G. V. Hartland, B. F. Henson, and P. M. Felker, "The dependence of Fourier transform nonlinear Raman spectroscopies on the temporal characteristics of the excitation fields," J. Chem. Phys. 91, 1478-1497 (1989).
    [CrossRef]
  17. G. V. Hartland, P. W. Joireman, L. L. Connell, and P. M. Felker, "High resolution Fourier transform stimulated emission and molecular beam hole-burning spectroscopy with picosecond excitation sources: theoretical and experimental results," J. Chem. Phys. 96, 179-197 (1992).
    [CrossRef]
  18. P. M. Felker, "Fourier-transform nonlinear spectroscopies," in Laser Techniques in Chemistry, A.B.Myers and T.R.Rizzo, eds. (Wiley, 1995), pp. 1-42.
  19. The step size used was much smaller than the lambdaIR/2 step size required by the Nyquist sampling theorem for FT spectroscopy. It was chosen for practical convenience in our experiment.
  20. S. Roke, J. Schins, M. Müller, and M. Bonn, "Vibrational spectroscopic investigation of the phase diagram of a biomimetic lipid monolayer," Phys. Rev. Lett. 90, 128101 (2003).
    [CrossRef] [PubMed]
  21. T. Hirschfeld, "The implications of fluctuation noise in multiplex spectroscopy," Appl. Spectrosc. 30, 234-236 (1976).
    [CrossRef]
  22. T. Hirschfeld, "Ideal FT-IR spectrometers and the efficiency of real instruments," Appl. Spectrosc. 40, 1239-1240 (1986).
    [CrossRef]
  23. E. Voigtman and J. D. Winefordner, "The multiplex disadvantage and excess low-frequency noise," Appl. Spectrosc. 41, 1182-1184 (1987).
    [CrossRef]

2003 (1)

S. Roke, J. Schins, M. Müller, and M. Bonn, "Vibrational spectroscopic investigation of the phase diagram of a biomimetic lipid monolayer," Phys. Rev. Lett. 90, 128101 (2003).
[CrossRef] [PubMed]

2001 (5)

M. T. Zanni, N.-H. Ge, Y. S. Kim, and R. M. Hochstrasser, "Two-dimensional IR spectroscopy can be designed to eliminate the diagonal peaks and expose only the crosspeaks needed for structure determination," Proc. Natl. Acad. Sci. U.S.A. 98, 11265-11270 (2001).
[CrossRef] [PubMed]

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Coupling and orientation between anharmonic vibrations characterized with two-dimensional infrared vibrational echo spectroscopy," J. Chem. Phys. 115, 10814-10828 (2001).
[CrossRef]

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy," Phys. Rev. Lett. 86, 2154-2157 (2001).
[CrossRef] [PubMed]

A. Albrecht Ferro, J. D. Hybl, and D. M. Jonas, "Complete femtosecond linear free induction decay, Fourier algorithm for dispersion relations, and accuracy of the rotating wave approximation," J. Chem. Phys. 114, 4649-4656 (2001).
[CrossRef]

J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, "Two-dimensional Fourier transform electronic spectroscopy," J. Chem. Phys. 115, 6606-6622 (2001).
[CrossRef]

2000 (3)

M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, "Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes," Proc. Natl. Acad. Sci. U.S.A. 97, 8219-8224 (2000).
[CrossRef] [PubMed]

S. M. Gallagher Faeder and D. M. Jonas, "Phase-resolved time-domain nonlinear optical signals," Phys. Rev. A 62, 033820 (2000).
[CrossRef]

R. A. Kaindl, M. Wurm, K. Reimann, P. Hamm, A. M. Weiner, and M. Woerner, "Generation, shaping, and characterization of intense femtosecond pulses tunable from 3 to 20 µm," J. Opt. Soc. Am. B 17, 2086-2094 (2000).
[CrossRef]

1999 (1)

1998 (1)

1996 (2)

L. Lepetit and M. Joffre, "Two-dimensional nonlinear optics using Fourier-transform spectral interferometry," Opt. Lett. 21, 564-566 (1996).
[CrossRef] [PubMed]

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

1995 (1)

1992 (1)

G. V. Hartland, P. W. Joireman, L. L. Connell, and P. M. Felker, "High resolution Fourier transform stimulated emission and molecular beam hole-burning spectroscopy with picosecond excitation sources: theoretical and experimental results," J. Chem. Phys. 96, 179-197 (1992).
[CrossRef]

1989 (1)

G. V. Hartland, B. F. Henson, and P. M. Felker, "The dependence of Fourier transform nonlinear Raman spectroscopies on the temporal characteristics of the excitation fields," J. Chem. Phys. 91, 1478-1497 (1989).
[CrossRef]

1987 (1)

1986 (1)

1976 (1)

1973 (1)

C. Froehly, A. Lacourt, and J. C. Viénot, "Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications," Nouv. Rev. Opt. 4, 183-196 (1973).
[CrossRef]

Asplund, M. C.

M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, "Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes," Proc. Natl. Acad. Sci. U.S.A. 97, 8219-8224 (2000).
[CrossRef] [PubMed]

Beck, W.

Bonn, M.

S. Roke, J. Schins, M. Müller, and M. Bonn, "Vibrational spectroscopic investigation of the phase diagram of a biomimetic lipid monolayer," Phys. Rev. Lett. 90, 128101 (2003).
[CrossRef] [PubMed]

Chériaux, G.

Connell, L. L.

G. V. Hartland, P. W. Joireman, L. L. Connell, and P. M. Felker, "High resolution Fourier transform stimulated emission and molecular beam hole-burning spectroscopy with picosecond excitation sources: theoretical and experimental results," J. Chem. Phys. 96, 179-197 (1992).
[CrossRef]

Demirdöven, N.

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Coupling and orientation between anharmonic vibrations characterized with two-dimensional infrared vibrational echo spectroscopy," J. Chem. Phys. 115, 10814-10828 (2001).
[CrossRef]

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy," Phys. Rev. Lett. 86, 2154-2157 (2001).
[CrossRef] [PubMed]

Faeder, S. M.

S. M. Gallagher Faeder and D. M. Jonas, "Phase-resolved time-domain nonlinear optical signals," Phys. Rev. A 62, 033820 (2000).
[CrossRef]

Felker, P. M.

G. V. Hartland, P. W. Joireman, L. L. Connell, and P. M. Felker, "High resolution Fourier transform stimulated emission and molecular beam hole-burning spectroscopy with picosecond excitation sources: theoretical and experimental results," J. Chem. Phys. 96, 179-197 (1992).
[CrossRef]

G. V. Hartland, B. F. Henson, and P. M. Felker, "The dependence of Fourier transform nonlinear Raman spectroscopies on the temporal characteristics of the excitation fields," J. Chem. Phys. 91, 1478-1497 (1989).
[CrossRef]

P. M. Felker, "Fourier-transform nonlinear spectroscopies," in Laser Techniques in Chemistry, A.B.Myers and T.R.Rizzo, eds. (Wiley, 1995), pp. 1-42.

Ferro, A. Albrecht

J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, "Two-dimensional Fourier transform electronic spectroscopy," J. Chem. Phys. 115, 6606-6622 (2001).
[CrossRef]

A. Albrecht Ferro, J. D. Hybl, and D. M. Jonas, "Complete femtosecond linear free induction decay, Fourier algorithm for dispersion relations, and accuracy of the rotating wave approximation," J. Chem. Phys. 114, 4649-4656 (2001).
[CrossRef]

Froehly, C.

C. Froehly, A. Lacourt, and J. C. Viénot, "Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications," Nouv. Rev. Opt. 4, 183-196 (1973).
[CrossRef]

Ge, N.-H.

M. T. Zanni, N.-H. Ge, Y. S. Kim, and R. M. Hochstrasser, "Two-dimensional IR spectroscopy can be designed to eliminate the diagonal peaks and expose only the crosspeaks needed for structure determination," Proc. Natl. Acad. Sci. U.S.A. 98, 11265-11270 (2001).
[CrossRef] [PubMed]

Golonzka, O.

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy," Phys. Rev. Lett. 86, 2154-2157 (2001).
[CrossRef] [PubMed]

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Coupling and orientation between anharmonic vibrations characterized with two-dimensional infrared vibrational echo spectroscopy," J. Chem. Phys. 115, 10814-10828 (2001).
[CrossRef]

Hamm, P.

Hartland, G. V.

G. V. Hartland, P. W. Joireman, L. L. Connell, and P. M. Felker, "High resolution Fourier transform stimulated emission and molecular beam hole-burning spectroscopy with picosecond excitation sources: theoretical and experimental results," J. Chem. Phys. 96, 179-197 (1992).
[CrossRef]

G. V. Hartland, B. F. Henson, and P. M. Felker, "The dependence of Fourier transform nonlinear Raman spectroscopies on the temporal characteristics of the excitation fields," J. Chem. Phys. 91, 1478-1497 (1989).
[CrossRef]

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Henson, B. F.

G. V. Hartland, B. F. Henson, and P. M. Felker, "The dependence of Fourier transform nonlinear Raman spectroscopies on the temporal characteristics of the excitation fields," J. Chem. Phys. 91, 1478-1497 (1989).
[CrossRef]

Hirschfeld, T.

Hochstrasser, R. M.

M. T. Zanni, N.-H. Ge, Y. S. Kim, and R. M. Hochstrasser, "Two-dimensional IR spectroscopy can be designed to eliminate the diagonal peaks and expose only the crosspeaks needed for structure determination," Proc. Natl. Acad. Sci. U.S.A. 98, 11265-11270 (2001).
[CrossRef] [PubMed]

M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, "Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes," Proc. Natl. Acad. Sci. U.S.A. 97, 8219-8224 (2000).
[CrossRef] [PubMed]

Hybl, J. D.

A. Albrecht Ferro, J. D. Hybl, and D. M. Jonas, "Complete femtosecond linear free induction decay, Fourier algorithm for dispersion relations, and accuracy of the rotating wave approximation," J. Chem. Phys. 114, 4649-4656 (2001).
[CrossRef]

J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, "Two-dimensional Fourier transform electronic spectroscopy," J. Chem. Phys. 115, 6606-6622 (2001).
[CrossRef]

Joffre, M.

Joireman, P. W.

G. V. Hartland, P. W. Joireman, L. L. Connell, and P. M. Felker, "High resolution Fourier transform stimulated emission and molecular beam hole-burning spectroscopy with picosecond excitation sources: theoretical and experimental results," J. Chem. Phys. 96, 179-197 (1992).
[CrossRef]

Jonas, D. M.

J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, "Two-dimensional Fourier transform electronic spectroscopy," J. Chem. Phys. 115, 6606-6622 (2001).
[CrossRef]

A. Albrecht Ferro, J. D. Hybl, and D. M. Jonas, "Complete femtosecond linear free induction decay, Fourier algorithm for dispersion relations, and accuracy of the rotating wave approximation," J. Chem. Phys. 114, 4649-4656 (2001).
[CrossRef]

S. M. Gallagher Faeder and D. M. Jonas, "Phase-resolved time-domain nonlinear optical signals," Phys. Rev. A 62, 033820 (2000).
[CrossRef]

Kaindl, R. A.

Khalil, M.

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Coupling and orientation between anharmonic vibrations characterized with two-dimensional infrared vibrational echo spectroscopy," J. Chem. Phys. 115, 10814-10828 (2001).
[CrossRef]

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy," Phys. Rev. Lett. 86, 2154-2157 (2001).
[CrossRef] [PubMed]

Kim, Y. S.

M. T. Zanni, N.-H. Ge, Y. S. Kim, and R. M. Hochstrasser, "Two-dimensional IR spectroscopy can be designed to eliminate the diagonal peaks and expose only the crosspeaks needed for structure determination," Proc. Natl. Acad. Sci. U.S.A. 98, 11265-11270 (2001).
[CrossRef] [PubMed]

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Viénot, "Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications," Nouv. Rev. Opt. 4, 183-196 (1973).
[CrossRef]

Lepetit, L.

McGuire, J. A.

Müller, M.

S. Roke, J. Schins, M. Müller, and M. Bonn, "Vibrational spectroscopic investigation of the phase diagram of a biomimetic lipid monolayer," Phys. Rev. Lett. 90, 128101 (2003).
[CrossRef] [PubMed]

Nahata, A.

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Petralli-Mallow, T. P.

Reimann, K.

Richter, L. J.

Roke, S.

S. Roke, J. Schins, M. Müller, and M. Bonn, "Vibrational spectroscopic investigation of the phase diagram of a biomimetic lipid monolayer," Phys. Rev. Lett. 90, 128101 (2003).
[CrossRef] [PubMed]

Schins, J.

S. Roke, J. Schins, M. Müller, and M. Bonn, "Vibrational spectroscopic investigation of the phase diagram of a biomimetic lipid monolayer," Phys. Rev. Lett. 90, 128101 (2003).
[CrossRef] [PubMed]

Shen, Y. R.

J. A. McGuire, W. Beck, X. Wei, and Y. R. Shen. "Fourier-transform sum-frequency surface vibrational spectroscopy with femtosecond pulses," Opt. Lett. 24, 1877-1879 (1999).
[CrossRef]

Y. R. Shen, "Surface spectroscopy by nonlinear optics," in Frontiers in Laser Spectroscopy: Proceedings of the International School of Physics "Enrico Fermi" Course CXX, T.W.Hänsch and M.Inguscio, eds. (North-Holland, 1994), pp. 139-165.
[PubMed]

Stephenson, J. C.

Tokmakoff, A.

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy," Phys. Rev. Lett. 86, 2154-2157 (2001).
[CrossRef] [PubMed]

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Coupling and orientation between anharmonic vibrations characterized with two-dimensional infrared vibrational echo spectroscopy," J. Chem. Phys. 115, 10814-10828 (2001).
[CrossRef]

Viénot, J. C.

C. Froehly, A. Lacourt, and J. C. Viénot, "Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications," Nouv. Rev. Opt. 4, 183-196 (1973).
[CrossRef]

Voigtman, E.

Wei, X.

Weiner, A. M.

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Winefordner, J. D.

Woerner, M.

Wurm, M.

Zanni, M. T.

M. T. Zanni, N.-H. Ge, Y. S. Kim, and R. M. Hochstrasser, "Two-dimensional IR spectroscopy can be designed to eliminate the diagonal peaks and expose only the crosspeaks needed for structure determination," Proc. Natl. Acad. Sci. U.S.A. 98, 11265-11270 (2001).
[CrossRef] [PubMed]

M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, "Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes," Proc. Natl. Acad. Sci. U.S.A. 97, 8219-8224 (2000).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Appl. Spectrosc. (3)

J. Chem. Phys. (5)

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Coupling and orientation between anharmonic vibrations characterized with two-dimensional infrared vibrational echo spectroscopy," J. Chem. Phys. 115, 10814-10828 (2001).
[CrossRef]

G. V. Hartland, B. F. Henson, and P. M. Felker, "The dependence of Fourier transform nonlinear Raman spectroscopies on the temporal characteristics of the excitation fields," J. Chem. Phys. 91, 1478-1497 (1989).
[CrossRef]

G. V. Hartland, P. W. Joireman, L. L. Connell, and P. M. Felker, "High resolution Fourier transform stimulated emission and molecular beam hole-burning spectroscopy with picosecond excitation sources: theoretical and experimental results," J. Chem. Phys. 96, 179-197 (1992).
[CrossRef]

A. Albrecht Ferro, J. D. Hybl, and D. M. Jonas, "Complete femtosecond linear free induction decay, Fourier algorithm for dispersion relations, and accuracy of the rotating wave approximation," J. Chem. Phys. 114, 4649-4656 (2001).
[CrossRef]

J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, "Two-dimensional Fourier transform electronic spectroscopy," J. Chem. Phys. 115, 6606-6622 (2001).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nouv. Rev. Opt. (1)

C. Froehly, A. Lacourt, and J. C. Viénot, "Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications," Nouv. Rev. Opt. 4, 183-196 (1973).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

S. M. Gallagher Faeder and D. M. Jonas, "Phase-resolved time-domain nonlinear optical signals," Phys. Rev. A 62, 033820 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

S. Roke, J. Schins, M. Müller, and M. Bonn, "Vibrational spectroscopic investigation of the phase diagram of a biomimetic lipid monolayer," Phys. Rev. Lett. 90, 128101 (2003).
[CrossRef] [PubMed]

O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, "Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy," Phys. Rev. Lett. 86, 2154-2157 (2001).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (2)

M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, "Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes," Proc. Natl. Acad. Sci. U.S.A. 97, 8219-8224 (2000).
[CrossRef] [PubMed]

M. T. Zanni, N.-H. Ge, Y. S. Kim, and R. M. Hochstrasser, "Two-dimensional IR spectroscopy can be designed to eliminate the diagonal peaks and expose only the crosspeaks needed for structure determination," Proc. Natl. Acad. Sci. U.S.A. 98, 11265-11270 (2001).
[CrossRef] [PubMed]

Other (3)

P. M. Felker, "Fourier-transform nonlinear spectroscopies," in Laser Techniques in Chemistry, A.B.Myers and T.R.Rizzo, eds. (Wiley, 1995), pp. 1-42.

The step size used was much smaller than the lambdaIR/2 step size required by the Nyquist sampling theorem for FT spectroscopy. It was chosen for practical convenience in our experiment.

Y. R. Shen, "Surface spectroscopy by nonlinear optics," in Frontiers in Laser Spectroscopy: Proceedings of the International School of Physics "Enrico Fermi" Course CXX, T.W.Hänsch and M.Inguscio, eds. (North-Holland, 1994), pp. 139-165.
[PubMed]

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Figures (2)

Fig. 1
Fig. 1

Experimental setup for performing FT-SFG measurements. BS = beam splitter , CP = compensation plate , PD = photodiode , and PMT = photomultiplier .

Fig. 2
Fig. 2

(a) Interferogram from OTS on fused silica for SF, visible, and IR polarizations s, s, and p, respectively, and (c) spectrum generated by Fourier transformation of the interferogram in (a). (b) The interferogram over a short portion of the scan to clearly illustrate the oscillations of the interferogram. (c) Also shown is the input IR spectrum obtained by detection of the IR through a monochromator. (d) The spectrum at frequencies far from the vibrational resonance, which illustrates the noise level of the experiment.

Equations (38)

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S SF ( τ ) d t P SF ( 2 ) ( t , τ ) 2 ,
P SF ( 2 ) ( t , τ ) = d t v d t IR R ( 2 ) ( t t v , t t IR ) E v ( t v ) E IR IF ( t IR , τ ) ,
E IR IF ( t IR , τ ) = 1 2 [ E IR ( t IR ) + E IR ( t IR + τ ) ] ,
P SF ( t , τ ) = E v ( t ) d t IR R ( 2 ) ( 0 , t t IR ) E IR IF ( t IR , τ ) = E v ( t ) d ν IR χ ( 2 ) ( ν IR ) E ̃ IR IF ( ν IR , τ ) exp ( i 2 π ν IR t ) ,
E ̃ IR IF ( ν IR , τ ) = E ̃ IR ( ν IR ) [ 1 + exp ( i 2 π ν IR τ ) ] ,
S SF ( τ ) d t E v ( t ) 2 d ν IR χ ( 2 ) ( ν IR ) E ̃ IR IF ( ν IR , τ ) exp ( i 2 π ν IR t ) 2 .
S SF ( τ ) d ν IR χ ( 2 ) ( ν IR ) E ̃ IR ( ν IR ) 2 [ 1 + cos ( 2 π ν IR τ ) ] ,
S SF ( ν ) χ ( 2 ) ( ν ) E ̃ IR ( ν ) 2 + δ ( ν ) d ν χ ( 2 ) ( ν ) E ̃ IR ( ν ) 2 .
S SF ( τ , τ v ) d ν IR d ν IR χ ( 2 ) ( ν IR ) E ̃ IR ( ν IR ) × χ ( 2 ) * ( ν IR ) E ̃ IR * ( ν IR ) [ 1 + exp ( i 2 π ν IR τ ) ] [ 1 + exp ( i 2 π ν IR τ ) ] d t E v ( t τ v ) 2 exp [ i 2 π ( ν IR ν IR ) t ] .
S ̃ SF ( ν , τ v ) 2 χ ( 2 ) ( ν ) E ̃ IR ( ν ) d ν IR χ ( 2 ) * ( ν IR ) E ̃ IR * ( ν IR ) F ̃ ( ν ν IR , τ v ) + F ̃ ( ν , τ v ) d ν IR χ ( 2 ) ( ν IR ) E ̃ IR ( ν IR ) χ ( 2 ) ( ν ν IR ) E ̃ IR ( ν ν IR ) + δ ( ν ) d ν IR d ν IR χ ( 2 ) ( ν IR ) E ̃ IR ( ν IR ) χ ( 2 ) * ( ν IR ) E ̃ IR * ( ν IR ) F ̃ ( ν IR ν IR , τ v ) ,
F ̃ ( ν , τ v ) = d t E v ( t τ v ) 2 exp ( i 2 π ν t ) = d ν E ̃ v ( ν ) E ̃ v * ( ν + ν ) exp ( i 2 π ν τ v ) = F ̃ ( ν , 0 ) exp ( i 2 π ν τ v ) .
S ̃ SF ( ν , τ v ) 2 χ ( 2 ) ( ν ) E ̃ IR ( ν ) { [ χ ( 2 ) * ( ν ) E ̃ IR * ( ν ) ] F ̃ ( ν , τ v ) } + F ̃ ( ν , τ v ) { [ χ ( 2 ) ( ν ) E ̃ IR ( ν ) ] [ χ ( 2 ) ( ν ) E ̃ IR ( ν ) ] } + δ ( ν ) d ν IR χ ( 2 ) ( ν IR ) E ̃ IR ( ν IR ) { [ χ ( 2 ) * ( ν IR ) E ̃ IR * ( ν IR ) ] F ̃ ( ν IR , τ v ) } ,
S ̃ SF ( ν ) = n = N 2 N 2 S ̃ SF ( ν , n δ τ v ) ,
n exp ( i 2 π ν n δ τ v ) = d t Щ ( t δ τ v ) Π ( t T v ) exp ( i 2 π ν t ) ,
Π ( x ) { 1 : 1 2 < x < 1 2 0 : otherwise } ,
Щ ( x ) n = δ ( x n ) .
n exp ( i 2 π ν δ τ v ) = T v δ τ v Π ̃ ( ν T v ) Щ ̃ ( ν δ τ v ) ,
Π ̃ ( ν T v ) = sinc ( ν T v ) ,
Щ ̃ ( ν δ τ v ) = Щ ( ν δ τ v ) .
S ̃ SF ( ν ) 2 χ ( 2 ) ( ν ) E ̃ IR ( ν ) ( { χ ( 2 ) * ( ν ) E ̃ IR * ( ν ) } { F ̃ ( ν , 0 ) [ sinc ( ν T v ) Щ ( ν δ τ v ) ] } ) .
F m = F m + N s = 1 N n = N 2 N 2 1 f n exp ( i 2 π m n N ) ,
f n = 1 N m = N 2 N 2 1 F m exp ( i 2 π m n N ) ,
m = N 2 N 2 1 exp [ i 2 π m ( n n ) N ] = N δ n , n ,
m = N 2 N 2 1 F m 2 = n = N 2 N 2 1 f n 2 .
f n = f n 0 + δ n ,
F m = F m 0 + Δ m ,
Δ m = 1 N n δ n exp ( i 2 π m n N ) .
σ f 2 = δ n δ n * ,
σ F 2 = Δ m Δ m * ,
σ F 2 = σ f 2 .
F m = 0 0 2 + M F m 0 0 2 = N f n 0 2 ,
F m 0 0 2 N M ( M + 1 ) f n 0 2 .
( SNR ) FT = F m 0 σ F [ N M ( M + 1 ) ] 1 2 f n 0 σ f .
( SNR ) MC = N f n 0 M σ M .
( SNR ) MC ( SNR ) FT [ M ( M + 1 ) M 2 ] 1 2 1 .
( SNR ) FT [ N M ( M + 1 ) f n 0 ] 1 2 N f n 0 M ,
( SNR ) MC = ( N f n 0 M ) 1 2 ,
( SNR ) MC ( SNR ) FT M .

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