Abstract

We have developed and applied a maximum-entropy phase-retrieval procedure to analyze sum-frequency vibrational spectra from a CCl4/octadecyl tricholosilane/silica interface and a hydrogen-terminated diamond C(111) surface. Some a priori knowledge of a nonlinear optical spectrum was employed for determining the phase of nonlinear optical susceptibility, and therefore the requirement for experimental phase measurement can be avoided. The results agree well with those from the Lorentzian line-shape model and justify the applicability of the a priori constraints employed in our phase-retrieval procedure.

© 2000 Optical Society of America

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  1. E. M. Vartiainen, “Phase retrieval approach for coherent anti-Stokes Raman scattering spectrum analysis,” J. Opt. Soc. Am. B 9, 1209–1214 (1992).
  2. E. M. Vartiainen and K.-E. Peiponen, “Meromorphic degenerate nonlinear susceptibility: phase retrieval from the amplitude spectrum,” Phys. Rev. B 50, 1941–1944 (1994).
  3. E. M. Vartiainen, K.-E. Peiponen, and H. Kishida, “Phase retrieval in nonlinear optical spectroscopy by the maximum-entropy method: an application to the |χ(3)| spectra of polysilane, T. Koda,” J. Opt. Soc. Am. B 13, 2106–2114 (1996).
  4. E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: resolving optical constants from power spectra,” Appl. Spectrosc. 50, 1283–1289 (1996).
  5. K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory and phase retrieval of meromorphic total susceptibility,” J. Phys.: Condens. Matter 9, 8937–8943 (1997).
  6. K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory of effective meromorphic nonlinear susceptibility of nanocomposites,” J. Phys.: Condens. Matter 10, 2483–2488 (1998).
  7. F. L. Ridener and R. H. Good, “Dispersion relations for nonlinear systems of arbitrary degree,” Phys. Rev. B 11, 2768–2770 (1975).
  8. H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, “Dispersion relation in the third-order electric susceptibility for polysilane films,” Phys. Rev. Lett. 70, 3724–3727 (1993).
  9. P.-K. Yang and J. Y. Huang, “Phase-retrieval problems in infrared-visible sum-frequency generation spectroscopy by the maximum-entropy method,” J. Opt. Soc. Am. B 14, 2443–2448 (1997).
  10. R. Superfine, J. Y. Huang, and Y. R. Shen, “Phase measurement for surface infrared-visible sum-frequency generation,” Opt. Lett. 15, 1276–1278 (1990).
  11. R. Superfine, J. Y. Huang, and Y. R. Shen, “Experimental determination of the sign of molecular dipole derivatives: an infrared-visible sum frequency generation absolute measurement study,” Chem. Phys. Lett. 172, 303–306 (1990).
  12. J. Y. Huang and Y. R. Shen, “Sum-frequency as a surface probe,” in Laser Spectroscopy and Photochemistry on Metal Surfaces, H. L. Dai and W. Ho, eds. (World Scientific, Singapore, 1995), Vol. 1, pp. 5–53.
  13. S. H. Lin and A. A. Villaeys, “Theoretical description of steady-state sum-frequency generation in molecular adsorbates,” Phys. Rev. A 50, 5134–5144 (1994).
  14. P. Guyot-Sionnest, R. Superfine, J. H. Hunt, and Y. R. Shen, “Vibrational spectroscopy of a silane monolayer at air/solid and liquid/solid interfaces using sum-frequency generation,” Chem. Phys. Lett. 144, 1–5 (1998).
  15. R. P. Chin, J. Y. Huang, Y. R. Shen, T. J. Chuang, H. Seki, and M. Buck, “Vibrational spectra of hydrogen on diamond C(111)-(1×1),” Phys. Rev. B 45, 1522–1524 (1992); R. P. Chin, J. Y. Huang, Y. R. Shen, T. J. Chuang, and H. Seki, “Interaction of atomic hydrogen with the diamond C(111) surface studied by infrared-visible sum-frequency generation spectroscopy,” Phys. Rev. B 52, 5985–5995 (1995).
  16. T. H. Ong, P. B. Davies, and A. M. Creeth, “Polymer-surfactant aggregates at a hydrophobic surface studied using sum-frequency vibrational spectroscopy,” Langmuir 11, 2931–2937 (1995).
  17. P.-K. Yang and J. Y. Huang, “Linewidth-deduction method for nonlinear optical spectroscopy with transform-limited light pulses,” J. Opt. Soc. Am. B 15, 1130–1134 (1998).
  18. Van den Bos, “Alternative interpretation of maximum entropy spectral analysis,” IEEE Trans. Inf. Theory IT-17, 493–494 (1971).
  19. T. J. Ulrych and M. Ooe, “Autoregressive and mixed autoregressive-moving average models and spectra,” in Nonlinear Methods of Spectral Analysis, S. Haykin, ed. (Springer-Verlag, Berlin, 1983), Chap. 3, pp. 73–125.
  20. J. Ihm, S. G. Louie, and M. L. Cohen, “Self-consistent pseudopotential calculations for Ge and diamond (111) surfaces,” Phys. Rev. B 17, 769–775 (1978).

1998 (3)

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory of effective meromorphic nonlinear susceptibility of nanocomposites,” J. Phys.: Condens. Matter 10, 2483–2488 (1998).

P. Guyot-Sionnest, R. Superfine, J. H. Hunt, and Y. R. Shen, “Vibrational spectroscopy of a silane monolayer at air/solid and liquid/solid interfaces using sum-frequency generation,” Chem. Phys. Lett. 144, 1–5 (1998).

P.-K. Yang and J. Y. Huang, “Linewidth-deduction method for nonlinear optical spectroscopy with transform-limited light pulses,” J. Opt. Soc. Am. B 15, 1130–1134 (1998).

1997 (2)

P.-K. Yang and J. Y. Huang, “Phase-retrieval problems in infrared-visible sum-frequency generation spectroscopy by the maximum-entropy method,” J. Opt. Soc. Am. B 14, 2443–2448 (1997).

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory and phase retrieval of meromorphic total susceptibility,” J. Phys.: Condens. Matter 9, 8937–8943 (1997).

1996 (2)

1995 (1)

T. H. Ong, P. B. Davies, and A. M. Creeth, “Polymer-surfactant aggregates at a hydrophobic surface studied using sum-frequency vibrational spectroscopy,” Langmuir 11, 2931–2937 (1995).

1994 (2)

E. M. Vartiainen and K.-E. Peiponen, “Meromorphic degenerate nonlinear susceptibility: phase retrieval from the amplitude spectrum,” Phys. Rev. B 50, 1941–1944 (1994).

S. H. Lin and A. A. Villaeys, “Theoretical description of steady-state sum-frequency generation in molecular adsorbates,” Phys. Rev. A 50, 5134–5144 (1994).

1993 (1)

H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, “Dispersion relation in the third-order electric susceptibility for polysilane films,” Phys. Rev. Lett. 70, 3724–3727 (1993).

1992 (1)

1990 (2)

R. Superfine, J. Y. Huang, and Y. R. Shen, “Phase measurement for surface infrared-visible sum-frequency generation,” Opt. Lett. 15, 1276–1278 (1990).

R. Superfine, J. Y. Huang, and Y. R. Shen, “Experimental determination of the sign of molecular dipole derivatives: an infrared-visible sum frequency generation absolute measurement study,” Chem. Phys. Lett. 172, 303–306 (1990).

1978 (1)

J. Ihm, S. G. Louie, and M. L. Cohen, “Self-consistent pseudopotential calculations for Ge and diamond (111) surfaces,” Phys. Rev. B 17, 769–775 (1978).

1975 (1)

F. L. Ridener and R. H. Good, “Dispersion relations for nonlinear systems of arbitrary degree,” Phys. Rev. B 11, 2768–2770 (1975).

1971 (1)

Van den Bos, “Alternative interpretation of maximum entropy spectral analysis,” IEEE Trans. Inf. Theory IT-17, 493–494 (1971).

Asakura, T.

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory of effective meromorphic nonlinear susceptibility of nanocomposites,” J. Phys.: Condens. Matter 10, 2483–2488 (1998).

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory and phase retrieval of meromorphic total susceptibility,” J. Phys.: Condens. Matter 9, 8937–8943 (1997).

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: resolving optical constants from power spectra,” Appl. Spectrosc. 50, 1283–1289 (1996).

Cohen, M. L.

J. Ihm, S. G. Louie, and M. L. Cohen, “Self-consistent pseudopotential calculations for Ge and diamond (111) surfaces,” Phys. Rev. B 17, 769–775 (1978).

Creeth, A. M.

T. H. Ong, P. B. Davies, and A. M. Creeth, “Polymer-surfactant aggregates at a hydrophobic surface studied using sum-frequency vibrational spectroscopy,” Langmuir 11, 2931–2937 (1995).

Davies, P. B.

T. H. Ong, P. B. Davies, and A. M. Creeth, “Polymer-surfactant aggregates at a hydrophobic surface studied using sum-frequency vibrational spectroscopy,” Langmuir 11, 2931–2937 (1995).

Good, R. H.

F. L. Ridener and R. H. Good, “Dispersion relations for nonlinear systems of arbitrary degree,” Phys. Rev. B 11, 2768–2770 (1975).

Guyot-Sionnest, P.

P. Guyot-Sionnest, R. Superfine, J. H. Hunt, and Y. R. Shen, “Vibrational spectroscopy of a silane monolayer at air/solid and liquid/solid interfaces using sum-frequency generation,” Chem. Phys. Lett. 144, 1–5 (1998).

Hasegawa, T.

H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, “Dispersion relation in the third-order electric susceptibility for polysilane films,” Phys. Rev. Lett. 70, 3724–3727 (1993).

Huang, J. Y.

Hunt, J. H.

P. Guyot-Sionnest, R. Superfine, J. H. Hunt, and Y. R. Shen, “Vibrational spectroscopy of a silane monolayer at air/solid and liquid/solid interfaces using sum-frequency generation,” Chem. Phys. Lett. 144, 1–5 (1998).

Ihm, J.

J. Ihm, S. G. Louie, and M. L. Cohen, “Self-consistent pseudopotential calculations for Ge and diamond (111) surfaces,” Phys. Rev. B 17, 769–775 (1978).

Iwasa, Y.

H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, “Dispersion relation in the third-order electric susceptibility for polysilane films,” Phys. Rev. Lett. 70, 3724–3727 (1993).

Kishida, H.

E. M. Vartiainen, K.-E. Peiponen, and H. Kishida, “Phase retrieval in nonlinear optical spectroscopy by the maximum-entropy method: an application to the |χ(3)| spectra of polysilane, T. Koda,” J. Opt. Soc. Am. B 13, 2106–2114 (1996).

H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, “Dispersion relation in the third-order electric susceptibility for polysilane films,” Phys. Rev. Lett. 70, 3724–3727 (1993).

Koda, T.

H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, “Dispersion relation in the third-order electric susceptibility for polysilane films,” Phys. Rev. Lett. 70, 3724–3727 (1993).

Lin, S. H.

S. H. Lin and A. A. Villaeys, “Theoretical description of steady-state sum-frequency generation in molecular adsorbates,” Phys. Rev. A 50, 5134–5144 (1994).

Louie, S. G.

J. Ihm, S. G. Louie, and M. L. Cohen, “Self-consistent pseudopotential calculations for Ge and diamond (111) surfaces,” Phys. Rev. B 17, 769–775 (1978).

Ong, T. H.

T. H. Ong, P. B. Davies, and A. M. Creeth, “Polymer-surfactant aggregates at a hydrophobic surface studied using sum-frequency vibrational spectroscopy,” Langmuir 11, 2931–2937 (1995).

Peiponen, K.-E.

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory of effective meromorphic nonlinear susceptibility of nanocomposites,” J. Phys.: Condens. Matter 10, 2483–2488 (1998).

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory and phase retrieval of meromorphic total susceptibility,” J. Phys.: Condens. Matter 9, 8937–8943 (1997).

E. M. Vartiainen, K.-E. Peiponen, and H. Kishida, “Phase retrieval in nonlinear optical spectroscopy by the maximum-entropy method: an application to the |χ(3)| spectra of polysilane, T. Koda,” J. Opt. Soc. Am. B 13, 2106–2114 (1996).

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: resolving optical constants from power spectra,” Appl. Spectrosc. 50, 1283–1289 (1996).

E. M. Vartiainen and K.-E. Peiponen, “Meromorphic degenerate nonlinear susceptibility: phase retrieval from the amplitude spectrum,” Phys. Rev. B 50, 1941–1944 (1994).

Ridener, F. L.

F. L. Ridener and R. H. Good, “Dispersion relations for nonlinear systems of arbitrary degree,” Phys. Rev. B 11, 2768–2770 (1975).

Shen, Y. R.

P. Guyot-Sionnest, R. Superfine, J. H. Hunt, and Y. R. Shen, “Vibrational spectroscopy of a silane monolayer at air/solid and liquid/solid interfaces using sum-frequency generation,” Chem. Phys. Lett. 144, 1–5 (1998).

R. Superfine, J. Y. Huang, and Y. R. Shen, “Phase measurement for surface infrared-visible sum-frequency generation,” Opt. Lett. 15, 1276–1278 (1990).

R. Superfine, J. Y. Huang, and Y. R. Shen, “Experimental determination of the sign of molecular dipole derivatives: an infrared-visible sum frequency generation absolute measurement study,” Chem. Phys. Lett. 172, 303–306 (1990).

Superfine, R.

P. Guyot-Sionnest, R. Superfine, J. H. Hunt, and Y. R. Shen, “Vibrational spectroscopy of a silane monolayer at air/solid and liquid/solid interfaces using sum-frequency generation,” Chem. Phys. Lett. 144, 1–5 (1998).

R. Superfine, J. Y. Huang, and Y. R. Shen, “Phase measurement for surface infrared-visible sum-frequency generation,” Opt. Lett. 15, 1276–1278 (1990).

R. Superfine, J. Y. Huang, and Y. R. Shen, “Experimental determination of the sign of molecular dipole derivatives: an infrared-visible sum frequency generation absolute measurement study,” Chem. Phys. Lett. 172, 303–306 (1990).

Tokura, Y.

H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, “Dispersion relation in the third-order electric susceptibility for polysilane films,” Phys. Rev. Lett. 70, 3724–3727 (1993).

Van den Bos,

Van den Bos, “Alternative interpretation of maximum entropy spectral analysis,” IEEE Trans. Inf. Theory IT-17, 493–494 (1971).

Vartiainen, E. M.

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory of effective meromorphic nonlinear susceptibility of nanocomposites,” J. Phys.: Condens. Matter 10, 2483–2488 (1998).

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory and phase retrieval of meromorphic total susceptibility,” J. Phys.: Condens. Matter 9, 8937–8943 (1997).

E. M. Vartiainen, K.-E. Peiponen, and H. Kishida, “Phase retrieval in nonlinear optical spectroscopy by the maximum-entropy method: an application to the |χ(3)| spectra of polysilane, T. Koda,” J. Opt. Soc. Am. B 13, 2106–2114 (1996).

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: resolving optical constants from power spectra,” Appl. Spectrosc. 50, 1283–1289 (1996).

E. M. Vartiainen and K.-E. Peiponen, “Meromorphic degenerate nonlinear susceptibility: phase retrieval from the amplitude spectrum,” Phys. Rev. B 50, 1941–1944 (1994).

E. M. Vartiainen, “Phase retrieval approach for coherent anti-Stokes Raman scattering spectrum analysis,” J. Opt. Soc. Am. B 9, 1209–1214 (1992).

Villaeys, A. A.

S. H. Lin and A. A. Villaeys, “Theoretical description of steady-state sum-frequency generation in molecular adsorbates,” Phys. Rev. A 50, 5134–5144 (1994).

Yang, P.-K.

Appl. Spectrosc. (1)

Chem. Phys. Lett. (2)

R. Superfine, J. Y. Huang, and Y. R. Shen, “Experimental determination of the sign of molecular dipole derivatives: an infrared-visible sum frequency generation absolute measurement study,” Chem. Phys. Lett. 172, 303–306 (1990).

P. Guyot-Sionnest, R. Superfine, J. H. Hunt, and Y. R. Shen, “Vibrational spectroscopy of a silane monolayer at air/solid and liquid/solid interfaces using sum-frequency generation,” Chem. Phys. Lett. 144, 1–5 (1998).

IEEE Trans. Inf. Theory (1)

Van den Bos, “Alternative interpretation of maximum entropy spectral analysis,” IEEE Trans. Inf. Theory IT-17, 493–494 (1971).

J. Opt. Soc. Am. B (4)

J. Phys.: Condens. Matter (2)

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory and phase retrieval of meromorphic total susceptibility,” J. Phys.: Condens. Matter 9, 8937–8943 (1997).

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, “Dispersion theory of effective meromorphic nonlinear susceptibility of nanocomposites,” J. Phys.: Condens. Matter 10, 2483–2488 (1998).

Langmuir (1)

T. H. Ong, P. B. Davies, and A. M. Creeth, “Polymer-surfactant aggregates at a hydrophobic surface studied using sum-frequency vibrational spectroscopy,” Langmuir 11, 2931–2937 (1995).

Opt. Lett. (1)

Phys. Rev. A (1)

S. H. Lin and A. A. Villaeys, “Theoretical description of steady-state sum-frequency generation in molecular adsorbates,” Phys. Rev. A 50, 5134–5144 (1994).

Phys. Rev. B (3)

E. M. Vartiainen and K.-E. Peiponen, “Meromorphic degenerate nonlinear susceptibility: phase retrieval from the amplitude spectrum,” Phys. Rev. B 50, 1941–1944 (1994).

F. L. Ridener and R. H. Good, “Dispersion relations for nonlinear systems of arbitrary degree,” Phys. Rev. B 11, 2768–2770 (1975).

J. Ihm, S. G. Louie, and M. L. Cohen, “Self-consistent pseudopotential calculations for Ge and diamond (111) surfaces,” Phys. Rev. B 17, 769–775 (1978).

Phys. Rev. Lett. (1)

H. Kishida, T. Hasegawa, Y. Iwasa, T. Koda, and Y. Tokura, “Dispersion relation in the third-order electric susceptibility for polysilane films,” Phys. Rev. Lett. 70, 3724–3727 (1993).

Other (3)

J. Y. Huang and Y. R. Shen, “Sum-frequency as a surface probe,” in Laser Spectroscopy and Photochemistry on Metal Surfaces, H. L. Dai and W. Ho, eds. (World Scientific, Singapore, 1995), Vol. 1, pp. 5–53.

T. J. Ulrych and M. Ooe, “Autoregressive and mixed autoregressive-moving average models and spectra,” in Nonlinear Methods of Spectral Analysis, S. Haykin, ed. (Springer-Verlag, Berlin, 1983), Chap. 3, pp. 73–125.

R. P. Chin, J. Y. Huang, Y. R. Shen, T. J. Chuang, H. Seki, and M. Buck, “Vibrational spectra of hydrogen on diamond C(111)-(1×1),” Phys. Rev. B 45, 1522–1524 (1992); R. P. Chin, J. Y. Huang, Y. R. Shen, T. J. Chuang, and H. Seki, “Interaction of atomic hydrogen with the diamond C(111) surface studied by infrared-visible sum-frequency generation spectroscopy,” Phys. Rev. B 52, 5985–5995 (1995).

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