Abstract

We present measurements of fourth-harmonic generation in reflection from the interface between two centrosymmetric media Si001SiO2, using femtosecond pulses well below damage threshold. Analyses of signal amplitudes, rotational anisotropy, and sensitivity to surface roughening reveal that the surface dipole fourth-harmonic contribution dominates the bulk quadrupole contribution much more strongly than for second-harmonic generation.

© 1998 Optical Society of America

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  1. Y.-S. Lee, M. H. Anderson, and M. C. Downer, Opt. Lett. 22, 973 (1997).
    [CrossRef] [PubMed]
  2. C. Yamada and T. Kimura, Phys. Rev. B 49, 14,372 (1994).
    [CrossRef]
  3. O. A. Aktsipetrov, I. M. Baranova, and Yu. A Il’inski?, Sov. Phys. JETP 64, 167 (1986).
  4. W. H. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
    [CrossRef]
  5. The FH, TH, and SH count rates reported here have been corrected for losses totaling a factor of 30±5 in the filters and optics between sample and detector and for the quantum efficiency of the detector. In addition, fundamental intensity I? was higher by a factor of 3.4±0.5 than for the GaAs data in Ref.??1. Thus the uncorrected raw count rates in Ref.??1 should be multiplied by ?4000 (factor-of-2 uncertainty) for direct comparison with the present results.
  6. Y.-S. Lee, M. H. Anderson, and M. C. Downer, “Symmetry analysis of optical fourth-harmonic generation at crystalline surfaces,” submitted to Phys. Rev. B; Y.-S. Lee, “Optical fourth-harmonic generation at crystalline surfaces,” Ph.D. dissertation (University of Texas at Austin, Austin, Texas, 1997).
  7. J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
    [CrossRef]
  8. P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
    [CrossRef]
  9. M. Miyashita, T. Tusga, K. Makihara, and T. Ohmi, J. Electrochem. Soc. 139, 2133 (1992).
    [CrossRef]
  10. K. Sawara, T. Yasaka, S. Miyazaki, and M. Hirose, Jpn. J. Appl. Phys. 31, L931 (1992).
    [CrossRef]
  11. D. Gräf, M. Grundner, and R. Schulz, J. Appl. Phys. 68, 5155 (1990); M. Niwano, J. Kageyama, K. Kinashi, J. Sawahata, and N. Miyamoto, Surf. Sci. 301, L245 (1994); J. Westermann, H. Nienhaus, and W. Mönch, Surf. Sci. 311, 101 (1994).
    [CrossRef]
  12. S. T. Cundiff, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997).
    [CrossRef]

1997 (2)

S. T. Cundiff, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997).
[CrossRef]

Y.-S. Lee, M. H. Anderson, and M. C. Downer, Opt. Lett. 22, 973 (1997).
[CrossRef] [PubMed]

1994 (1)

C. Yamada and T. Kimura, Phys. Rev. B 49, 14,372 (1994).
[CrossRef]

1992 (2)

M. Miyashita, T. Tusga, K. Makihara, and T. Ohmi, J. Electrochem. Soc. 139, 2133 (1992).
[CrossRef]

K. Sawara, T. Yasaka, S. Miyazaki, and M. Hirose, Jpn. J. Appl. Phys. 31, L931 (1992).
[CrossRef]

1990 (1)

D. Gräf, M. Grundner, and R. Schulz, J. Appl. Phys. 68, 5155 (1990); M. Niwano, J. Kageyama, K. Kinashi, J. Sawahata, and N. Miyamoto, Surf. Sci. 301, L245 (1994); J. Westermann, H. Nienhaus, and W. Mönch, Surf. Sci. 311, 101 (1994).
[CrossRef]

1987 (1)

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

1986 (2)

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
[CrossRef]

O. A. Aktsipetrov, I. M. Baranova, and Yu. A Il’inski?, Sov. Phys. JETP 64, 167 (1986).

1983 (1)

W. H. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
[CrossRef]

Aktsipetrov, O. A.

O. A. Aktsipetrov, I. M. Baranova, and Yu. A Il’inski?, Sov. Phys. JETP 64, 167 (1986).

Anderson, M. H.

Y.-S. Lee, M. H. Anderson, and M. C. Downer, Opt. Lett. 22, 973 (1997).
[CrossRef] [PubMed]

Y.-S. Lee, M. H. Anderson, and M. C. Downer, “Symmetry analysis of optical fourth-harmonic generation at crystalline surfaces,” submitted to Phys. Rev. B; Y.-S. Lee, “Optical fourth-harmonic generation at crystalline surfaces,” Ph.D. dissertation (University of Texas at Austin, Austin, Texas, 1997).

Baranova, I. M.

O. A. Aktsipetrov, I. M. Baranova, and Yu. A Il’inski?, Sov. Phys. JETP 64, 167 (1986).

Baumann, F. H.

S. T. Cundiff, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997).
[CrossRef]

Chen, W.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
[CrossRef]

Cundiff, S. T.

S. T. Cundiff, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997).
[CrossRef]

Downer, M. C.

Y.-S. Lee, M. H. Anderson, and M. C. Downer, Opt. Lett. 22, 973 (1997).
[CrossRef] [PubMed]

Y.-S. Lee, M. H. Anderson, and M. C. Downer, “Symmetry analysis of optical fourth-harmonic generation at crystalline surfaces,” submitted to Phys. Rev. B; Y.-S. Lee, “Optical fourth-harmonic generation at crystalline surfaces,” Ph.D. dissertation (University of Texas at Austin, Austin, Texas, 1997).

Evans-Lutterodt, K. W.

S. T. Cundiff, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997).
[CrossRef]

Gräf, D.

D. Gräf, M. Grundner, and R. Schulz, J. Appl. Phys. 68, 5155 (1990); M. Niwano, J. Kageyama, K. Kinashi, J. Sawahata, and N. Miyamoto, Surf. Sci. 301, L245 (1994); J. Westermann, H. Nienhaus, and W. Mönch, Surf. Sci. 311, 101 (1994).
[CrossRef]

Green, M. L.

S. T. Cundiff, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997).
[CrossRef]

Grundner, M.

D. Gräf, M. Grundner, and R. Schulz, J. Appl. Phys. 68, 5155 (1990); M. Niwano, J. Kageyama, K. Kinashi, J. Sawahata, and N. Miyamoto, Surf. Sci. 301, L245 (1994); J. Westermann, H. Nienhaus, and W. Mönch, Surf. Sci. 311, 101 (1994).
[CrossRef]

Guyot-Sionnest, P.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
[CrossRef]

Heinz, T. F.

W. H. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
[CrossRef]

Hirose, M.

K. Sawara, T. Yasaka, S. Miyazaki, and M. Hirose, Jpn. J. Appl. Phys. 31, L931 (1992).
[CrossRef]

Il’inskii, Yu. A

O. A. Aktsipetrov, I. M. Baranova, and Yu. A Il’inski?, Sov. Phys. JETP 64, 167 (1986).

Kimura, T.

C. Yamada and T. Kimura, Phys. Rev. B 49, 14,372 (1994).
[CrossRef]

Knox, W. H.

S. T. Cundiff, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997).
[CrossRef]

Lee, Y.-S.

Y.-S. Lee, M. H. Anderson, and M. C. Downer, Opt. Lett. 22, 973 (1997).
[CrossRef] [PubMed]

Y.-S. Lee, M. H. Anderson, and M. C. Downer, “Symmetry analysis of optical fourth-harmonic generation at crystalline surfaces,” submitted to Phys. Rev. B; Y.-S. Lee, “Optical fourth-harmonic generation at crystalline surfaces,” Ph.D. dissertation (University of Texas at Austin, Austin, Texas, 1997).

Makihara, K.

M. Miyashita, T. Tusga, K. Makihara, and T. Ohmi, J. Electrochem. Soc. 139, 2133 (1992).
[CrossRef]

Miyashita, M.

M. Miyashita, T. Tusga, K. Makihara, and T. Ohmi, J. Electrochem. Soc. 139, 2133 (1992).
[CrossRef]

Miyazaki, S.

K. Sawara, T. Yasaka, S. Miyazaki, and M. Hirose, Jpn. J. Appl. Phys. 31, L931 (1992).
[CrossRef]

Moss, D. J.

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Ohmi, T.

M. Miyashita, T. Tusga, K. Makihara, and T. Ohmi, J. Electrochem. Soc. 139, 2133 (1992).
[CrossRef]

Sawara, K.

K. Sawara, T. Yasaka, S. Miyazaki, and M. Hirose, Jpn. J. Appl. Phys. 31, L931 (1992).
[CrossRef]

Schulz, R.

D. Gräf, M. Grundner, and R. Schulz, J. Appl. Phys. 68, 5155 (1990); M. Niwano, J. Kageyama, K. Kinashi, J. Sawahata, and N. Miyamoto, Surf. Sci. 301, L245 (1994); J. Westermann, H. Nienhaus, and W. Mönch, Surf. Sci. 311, 101 (1994).
[CrossRef]

Shen, Y. R.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
[CrossRef]

W. H. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
[CrossRef]

Sipe, J. E.

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Tang, M.-T.

S. T. Cundiff, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997).
[CrossRef]

Tom, W. H. K.

W. H. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
[CrossRef]

Tusga, T.

M. Miyashita, T. Tusga, K. Makihara, and T. Ohmi, J. Electrochem. Soc. 139, 2133 (1992).
[CrossRef]

van Driel, H. M.

S. T. Cundiff, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997).
[CrossRef]

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Yamada, C.

C. Yamada and T. Kimura, Phys. Rev. B 49, 14,372 (1994).
[CrossRef]

Yasaka, T.

K. Sawara, T. Yasaka, S. Miyazaki, and M. Hirose, Jpn. J. Appl. Phys. 31, L931 (1992).
[CrossRef]

Appl. Phys. Lett. (1)

S. T. Cundiff, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997).
[CrossRef]

J. Appl. Phys. (1)

D. Gräf, M. Grundner, and R. Schulz, J. Appl. Phys. 68, 5155 (1990); M. Niwano, J. Kageyama, K. Kinashi, J. Sawahata, and N. Miyamoto, Surf. Sci. 301, L245 (1994); J. Westermann, H. Nienhaus, and W. Mönch, Surf. Sci. 311, 101 (1994).
[CrossRef]

J. Electrochem. Soc. (1)

M. Miyashita, T. Tusga, K. Makihara, and T. Ohmi, J. Electrochem. Soc. 139, 2133 (1992).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Sawara, T. Yasaka, S. Miyazaki, and M. Hirose, Jpn. J. Appl. Phys. 31, L931 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (3)

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
[CrossRef]

C. Yamada and T. Kimura, Phys. Rev. B 49, 14,372 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

W. H. K. Tom, T. F. Heinz, and Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983).
[CrossRef]

Sov. Phys. JETP (1)

O. A. Aktsipetrov, I. M. Baranova, and Yu. A Il’inski?, Sov. Phys. JETP 64, 167 (1986).

Other (2)

The FH, TH, and SH count rates reported here have been corrected for losses totaling a factor of 30±5 in the filters and optics between sample and detector and for the quantum efficiency of the detector. In addition, fundamental intensity I? was higher by a factor of 3.4±0.5 than for the GaAs data in Ref.??1. Thus the uncorrected raw count rates in Ref.??1 should be multiplied by ?4000 (factor-of-2 uncertainty) for direct comparison with the present results.

Y.-S. Lee, M. H. Anderson, and M. C. Downer, “Symmetry analysis of optical fourth-harmonic generation at crystalline surfaces,” submitted to Phys. Rev. B; Y.-S. Lee, “Optical fourth-harmonic generation at crystalline surfaces,” Ph.D. dissertation (University of Texas at Austin, Austin, Texas, 1997).

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Figures (2)

Fig. 1
Fig. 1

Azimuthal-angle-dependent (a) FHG and (b) SHG from Si(001) for four polarization combinations. Solid curves, fits to the data based on Eqs.  (1)–(4) with fit parameters listed in Table  1. Inset, simulated FH data in (S-in, S-out) configuration, assuming a ratio of bulk-to-surface contributions similar to that for SHG.

Fig. 2
Fig. 2

Azimuthal-angle-dependent FHG from Si(001) in an (S-in, P-out) configuration (a) immediately following exposure of the sample to a buffered oxide etch for times ranging from 0 to 60  min and (b) at times of 0, 3, and 76  h following a 10-min exposure of sample to etch.

Tables (1)

Tables Icon

Table 1 Fitted Azimuthal Fourier Coefficients of FHG and SHG Fields

Equations (4)

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IPP4ω=aPP4ω, B+aPP4ω, S+cPP4ω, B+cPP4ω, Scos 4ϕ2,  IPP2ω=aPP2ω, B+a2ω, S+cPP2ω, B cos 4ϕ2,
IPS4ω=cPS4ω, B+cPS4ω, S sin 4ϕ2,  IPS2ω=cPS2ω, B sin 4ϕ2,
ISP4ω=aSP4ω, B+aPP4ω, S+cSP4ω, B+cSP4ω, S cos 4ϕ2,  ISP2ω=aSP2ω, B+aSP2ω, S+cSP2ω, B cos 4ϕ2,
ISS4ω=cSS4ω, B sin 4ϕ2,  ISS2ω=cSS2ω, B sin 4ϕ2,

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