Abstract

We report the application of electric-field-induced optical second-harmonic generation as a new technique for measuring the field of freely propagating terahertz radiation. Using silicon as the nonlinear medium, we demonstrate subpicosecond time resolution and a sampling signal that varies linearly with the terahertz electric field. This approach, which is attractive for centrosymmetric media, permits a significantly broadened class of materials to be exploited for free-space sampling measurements.

© 1998 Optical Society of America

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  1. P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
    [CrossRef]
  2. Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
    [CrossRef]
  3. P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, Phys. Rev. E 53, 3052 (1996).
    [CrossRef]
  4. A. Nahata, D. H. Auston, T. F. Heinz, and C. Wu, Appl. Phys. Lett. 68, 150 (1996).
    [CrossRef]
  5. A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
    [CrossRef]
  6. T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (Elsevier, Amsterdam, 1991), pp. 353–416, and references therein.
    [CrossRef]
  7. Y. R. Shen, Nature (London) 337, 519 (1989); G. L. Richmond, J. M. Robinson, and V. L. Shannon, Prog. Surf. Sci. 28, 1 (1988); R. M. Corn and D. A. Higgins, Chem. Rev. 94, 107 (1994).
    [CrossRef]
  8. R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 8, 404 (1962).
    [CrossRef]
  9. C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967).
    [CrossRef]
  10. See, for example, O. A. Aktsipetrov, A. A. Fedyanin, V. N. Golovkina, and T. V. Murzina, Opt. Lett. 19, 1450 (1994); J. I. Dadap, X. F. Xu, M. H. Anderson, M. C. Downer, J. K. Lowell, and O. A. Aktsipetrov, Phys. Rev. B 53, R7607 (1996); P. Godefroy, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and Th. Rasing, Appl. Phys. Lett. 68, 1981 (1996).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. C. Ohlhoff, C. Meyer, G. Lüpke, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1699 (1996).
    [CrossRef]
  13. A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
    [CrossRef]
  14. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart & Winston, New York, 1976), p. 547.
  15. D. H. Auston and M. C. Nuss, IEEE J. Quantum Electron. 24, 184 (1988).
    [CrossRef]
  16. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), p. 28.

1996

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, Phys. Rev. E 53, 3052 (1996).
[CrossRef]

A. Nahata, D. H. Auston, T. F. Heinz, and C. Wu, Appl. Phys. Lett. 68, 150 (1996).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

C. Ohlhoff, C. Meyer, G. Lüpke, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1699 (1996).
[CrossRef]

A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
[CrossRef]

1995

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
[CrossRef]

1994

1993

See, for example, J. Qi, M. S. Yeganeh, I. Koltover, A. G. Yodh, and W. M. Theis, Phys. Rev. Lett. 71, 633 (1993).
[CrossRef] [PubMed]

1989

Y. R. Shen, Nature (London) 337, 519 (1989); G. L. Richmond, J. M. Robinson, and V. L. Shannon, Prog. Surf. Sci. 28, 1 (1988); R. M. Corn and D. A. Higgins, Chem. Rev. 94, 107 (1994).
[CrossRef]

1988

P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

D. H. Auston and M. C. Nuss, IEEE J. Quantum Electron. 24, 184 (1988).
[CrossRef]

1967

C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967).
[CrossRef]

1962

R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 8, 404 (1962).
[CrossRef]

Aktsipetrov, O. A.

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart & Winston, New York, 1976), p. 547.

Auston, D. H.

A. Nahata, D. H. Auston, T. F. Heinz, and C. Wu, Appl. Phys. Lett. 68, 150 (1996).
[CrossRef]

P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

D. H. Auston and M. C. Nuss, IEEE J. Quantum Electron. 24, 184 (1988).
[CrossRef]

Bloembergen, N.

C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967).
[CrossRef]

Chang, R. K.

C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967).
[CrossRef]

Fedyanin, A. A.

Golovkina, V. N.

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

A. Nahata, D. H. Auston, T. F. Heinz, and C. Wu, Appl. Phys. Lett. 68, 150 (1996).
[CrossRef]

A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
[CrossRef]

T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (Elsevier, Amsterdam, 1991), pp. 353–416, and references therein.
[CrossRef]

Helm, H.

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, Phys. Rev. E 53, 3052 (1996).
[CrossRef]

Jepsen, P. U.

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, Phys. Rev. E 53, 3052 (1996).
[CrossRef]

Keiding, S. R.

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, Phys. Rev. E 53, 3052 (1996).
[CrossRef]

Koltover, I.

See, for example, J. Qi, M. S. Yeganeh, I. Koltover, A. G. Yodh, and W. M. Theis, Phys. Rev. Lett. 71, 633 (1993).
[CrossRef] [PubMed]

Kurz, H.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1699 (1996).
[CrossRef]

Lee, C. H.

C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967).
[CrossRef]

Lüpke, G.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1699 (1996).
[CrossRef]

Maker, P. D.

R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 8, 404 (1962).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart & Winston, New York, 1976), p. 547.

Meyer, C.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1699 (1996).
[CrossRef]

Misewich, J. A.

A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
[CrossRef]

Murzina, T. V.

Nahata, A.

A. Nahata, D. H. Auston, T. F. Heinz, and C. Wu, Appl. Phys. Lett. 68, 150 (1996).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
[CrossRef]

Nuss, M. C.

D. H. Auston and M. C. Nuss, IEEE J. Quantum Electron. 24, 184 (1988).
[CrossRef]

P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

Ohlhoff, C.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1699 (1996).
[CrossRef]

Pfeifer, T.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1699 (1996).
[CrossRef]

Qi, J.

See, for example, J. Qi, M. S. Yeganeh, I. Koltover, A. G. Yodh, and W. M. Theis, Phys. Rev. Lett. 71, 633 (1993).
[CrossRef] [PubMed]

Roskos, H. G.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1699 (1996).
[CrossRef]

Savage, C. M.

R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 8, 404 (1962).
[CrossRef]

Schall, M.

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, Phys. Rev. E 53, 3052 (1996).
[CrossRef]

Schyja, V.

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, Phys. Rev. E 53, 3052 (1996).
[CrossRef]

Shen, Y. R.

Y. R. Shen, Nature (London) 337, 519 (1989); G. L. Richmond, J. M. Robinson, and V. L. Shannon, Prog. Surf. Sci. 28, 1 (1988); R. M. Corn and D. A. Higgins, Chem. Rev. 94, 107 (1994).
[CrossRef]

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), p. 28.

Smith, P. R.

P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

Terhune, R. W.

R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 8, 404 (1962).
[CrossRef]

Theis, W. M.

See, for example, J. Qi, M. S. Yeganeh, I. Koltover, A. G. Yodh, and W. M. Theis, Phys. Rev. Lett. 71, 633 (1993).
[CrossRef] [PubMed]

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Winnewisser, C.

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, Phys. Rev. E 53, 3052 (1996).
[CrossRef]

Wu, C.

A. Nahata, D. H. Auston, T. F. Heinz, and C. Wu, Appl. Phys. Lett. 68, 150 (1996).
[CrossRef]

Wu, Q.

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
[CrossRef]

Yeganeh, M. S.

See, for example, J. Qi, M. S. Yeganeh, I. Koltover, A. G. Yodh, and W. M. Theis, Phys. Rev. Lett. 71, 633 (1993).
[CrossRef] [PubMed]

Yodh, A. G.

See, for example, J. Qi, M. S. Yeganeh, I. Koltover, A. G. Yodh, and W. M. Theis, Phys. Rev. Lett. 71, 633 (1993).
[CrossRef] [PubMed]

Zhang, X.-C.

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
[CrossRef]

Appl. Phys. Lett.

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
[CrossRef]

A. Nahata, D. H. Auston, T. F. Heinz, and C. Wu, Appl. Phys. Lett. 68, 150 (1996).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

C. Ohlhoff, C. Meyer, G. Lüpke, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1699 (1996).
[CrossRef]

A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
[CrossRef]

IEEE J. Quantum Electron.

D. H. Auston and M. C. Nuss, IEEE J. Quantum Electron. 24, 184 (1988).
[CrossRef]

P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

Nature (London)

Y. R. Shen, Nature (London) 337, 519 (1989); G. L. Richmond, J. M. Robinson, and V. L. Shannon, Prog. Surf. Sci. 28, 1 (1988); R. M. Corn and D. A. Higgins, Chem. Rev. 94, 107 (1994).
[CrossRef]

Opt. Lett.

Phys. Rev. E

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, Phys. Rev. E 53, 3052 (1996).
[CrossRef]

Phys. Rev. Lett.

See, for example, J. Qi, M. S. Yeganeh, I. Koltover, A. G. Yodh, and W. M. Theis, Phys. Rev. Lett. 71, 633 (1993).
[CrossRef] [PubMed]

R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 8, 404 (1962).
[CrossRef]

C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967).
[CrossRef]

Other

T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (Elsevier, Amsterdam, 1991), pp. 353–416, and references therein.
[CrossRef]

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), p. 28.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart & Winston, New York, 1976), p. 547.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the experimental setup. PMT, photomultiplier tube. Inset: Detail of the electric-field-induced SHG configuration.

Fig. 2
Fig. 2

Variation in the SH intensity from the silicon sample as a function of the polarization of the probe laser (φ=0° corresponds to s polarization) in the absence of a THz electric field. The filled circles are experimental data, and the solid curve represents a fit to theory.

Fig. 3
Fig. 3

Waveform of the THz electric field measured by the field-induced SHG sampling technique. Curves are shown for probe polarizations of φ=14° and φ=8°. In both cases the quiescent contribution to the SH intensity, Io2ω, was subtracted and the waveforms were offset from the origin for clarity.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

ΔEx2ωχxxxx3 cos2 φ+χxyyx3 sin2 φEωEωExTHz·l,
Eo2ωsin θ sin 2φχs,xzx2EωEω,
I2ωIo2ω+aETHzIω2Io2ω+ΔI2ω,

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