Abstract

Freely propagating terahertz pulses are detected in the time domain by electro-optic sampling in bulk GaAs. We investigate the influence of dispersion of the near-infrared sampling pulse on the transients by varying the thickness of the GaAs crystal. Pronounced propagation effects are identified that originate from the frequency dependence of the phase-matching condition between the terahertz and the sampling pulse.

© 1998 Optical Society of America

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  1. P. R. Smith, D. H. Auston, M. C. Nuss, “Subpicosecond photoconducting dipole antennas,” IEEE J. Quantum Electron. 24, 255–260 (1988).
    [CrossRef]
  2. D. H. Auston, M. C. Nuss, “Electrooptic generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184–197 (1988).
    [CrossRef]
  3. J. E. Pedersen, S. R. Keiding, C. B. Sørensen, P. E. Lindelof, W. W. Rühle, X. Q. Zhou, “5-THz bandwidth from a GaAs-on-silicon photoconductive receiver,” J. Appl. Phys. 74, 7022–7024 (1993).
    [CrossRef]
  4. E. R. Brown, K. A. McIntosh, K. B. Nichols, C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66, 285–287 (1995).
    [CrossRef]
  5. N. Katzenellenbogen, D. Grischkowsky, “Efficient generation of 380 fs pulses of THz radiation by ultrafast laser pulse excitation of a biased metal-semiconductor interface,” Appl. Phys. Lett. 58, 222–224 (1991).
    [CrossRef]
  6. J. T. Darrow, X.-C. Zhang, D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
    [CrossRef]
  7. Q. Wu, T. D. Hewitt, X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
    [CrossRef]
  8. Q. Wu, X.-C. Zhang, “Free-space electro-optic sampling of mid-infrared pulses,” Appl. Phys. Lett. 71, 1285–1286 (1997).
    [CrossRef]
  9. Q. Wu, X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
    [CrossRef]
  10. A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991).
  11. A. Nahata, A. S. Weling, T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
    [CrossRef]
  12. P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
    [CrossRef]
  13. D. Grischkowsky, S. Keiding, M. v. Exter, Ch. Fattinger, “Far-infrared time domain spectroscopy with terahertz beams of dielectrica and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
    [CrossRef]
  14. D. T. F. Marple, “Refractive index of GaAs,” J. Appl. Phys. 35, 1241–1242 (1964).
    [CrossRef]

1997 (1)

Q. Wu, X.-C. Zhang, “Free-space electro-optic sampling of mid-infrared pulses,” Appl. Phys. Lett. 71, 1285–1286 (1997).
[CrossRef]

1996 (3)

Q. Wu, X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

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

Q. Wu, T. D. Hewitt, X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[CrossRef]

1995 (1)

E. R. Brown, K. A. McIntosh, K. B. Nichols, C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66, 285–287 (1995).
[CrossRef]

1993 (1)

J. E. Pedersen, S. R. Keiding, C. B. Sørensen, P. E. Lindelof, W. W. Rühle, X. Q. Zhou, “5-THz bandwidth from a GaAs-on-silicon photoconductive receiver,” J. Appl. Phys. 74, 7022–7024 (1993).
[CrossRef]

1991 (2)

N. Katzenellenbogen, D. Grischkowsky, “Efficient generation of 380 fs pulses of THz radiation by ultrafast laser pulse excitation of a biased metal-semiconductor interface,” Appl. Phys. Lett. 58, 222–224 (1991).
[CrossRef]

J. T. Darrow, X.-C. Zhang, D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
[CrossRef]

1990 (1)

1988 (2)

P. R. Smith, D. H. Auston, M. C. Nuss, “Subpicosecond photoconducting dipole antennas,” IEEE J. Quantum Electron. 24, 255–260 (1988).
[CrossRef]

D. H. Auston, M. C. Nuss, “Electrooptic generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184–197 (1988).
[CrossRef]

1964 (1)

D. T. F. Marple, “Refractive index of GaAs,” J. Appl. Phys. 35, 1241–1242 (1964).
[CrossRef]

1962 (1)

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Auston, D. H.

J. T. Darrow, X.-C. Zhang, D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
[CrossRef]

P. R. Smith, D. H. Auston, M. C. Nuss, “Subpicosecond photoconducting dipole antennas,” IEEE J. Quantum Electron. 24, 255–260 (1988).
[CrossRef]

D. H. Auston, M. C. Nuss, “Electrooptic generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184–197 (1988).
[CrossRef]

Brown, E. R.

E. R. Brown, K. A. McIntosh, K. B. Nichols, C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66, 285–287 (1995).
[CrossRef]

Darrow, J. T.

J. T. Darrow, X.-C. Zhang, D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
[CrossRef]

Dennis, C. L.

E. R. Brown, K. A. McIntosh, K. B. Nichols, C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66, 285–287 (1995).
[CrossRef]

Exter, M. v.

Fattinger, Ch.

Grischkowsky, D.

N. Katzenellenbogen, D. Grischkowsky, “Efficient generation of 380 fs pulses of THz radiation by ultrafast laser pulse excitation of a biased metal-semiconductor interface,” Appl. Phys. Lett. 58, 222–224 (1991).
[CrossRef]

D. Grischkowsky, S. Keiding, M. v. Exter, Ch. Fattinger, “Far-infrared time domain spectroscopy with terahertz beams of dielectrica and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
[CrossRef]

Heinz, T. F.

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

Hewitt, T. D.

Q. Wu, T. D. Hewitt, X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[CrossRef]

Katzenellenbogen, N.

N. Katzenellenbogen, D. Grischkowsky, “Efficient generation of 380 fs pulses of THz radiation by ultrafast laser pulse excitation of a biased metal-semiconductor interface,” Appl. Phys. Lett. 58, 222–224 (1991).
[CrossRef]

Keiding, S.

Keiding, S. R.

J. E. Pedersen, S. R. Keiding, C. B. Sørensen, P. E. Lindelof, W. W. Rühle, X. Q. Zhou, “5-THz bandwidth from a GaAs-on-silicon photoconductive receiver,” J. Appl. Phys. 74, 7022–7024 (1993).
[CrossRef]

Lindelof, P. E.

J. E. Pedersen, S. R. Keiding, C. B. Sørensen, P. E. Lindelof, W. W. Rühle, X. Q. Zhou, “5-THz bandwidth from a GaAs-on-silicon photoconductive receiver,” J. Appl. Phys. 74, 7022–7024 (1993).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Marple, D. T. F.

D. T. F. Marple, “Refractive index of GaAs,” J. Appl. Phys. 35, 1241–1242 (1964).
[CrossRef]

McIntosh, K. A.

E. R. Brown, K. A. McIntosh, K. B. Nichols, C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66, 285–287 (1995).
[CrossRef]

Nahata, A.

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

Nichols, K. B.

E. R. Brown, K. A. McIntosh, K. B. Nichols, C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66, 285–287 (1995).
[CrossRef]

Nisenoff, M.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Nuss, M. C.

D. H. Auston, M. C. Nuss, “Electrooptic generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184–197 (1988).
[CrossRef]

P. R. Smith, D. H. Auston, M. C. Nuss, “Subpicosecond photoconducting dipole antennas,” IEEE J. Quantum Electron. 24, 255–260 (1988).
[CrossRef]

Pedersen, J. E.

J. E. Pedersen, S. R. Keiding, C. B. Sørensen, P. E. Lindelof, W. W. Rühle, X. Q. Zhou, “5-THz bandwidth from a GaAs-on-silicon photoconductive receiver,” J. Appl. Phys. 74, 7022–7024 (1993).
[CrossRef]

Rühle, W. W.

J. E. Pedersen, S. R. Keiding, C. B. Sørensen, P. E. Lindelof, W. W. Rühle, X. Q. Zhou, “5-THz bandwidth from a GaAs-on-silicon photoconductive receiver,” J. Appl. Phys. 74, 7022–7024 (1993).
[CrossRef]

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Smith, P. R.

P. R. Smith, D. H. Auston, M. C. Nuss, “Subpicosecond photoconducting dipole antennas,” IEEE J. Quantum Electron. 24, 255–260 (1988).
[CrossRef]

Sørensen, C. B.

J. E. Pedersen, S. R. Keiding, C. B. Sørensen, P. E. Lindelof, W. W. Rühle, X. Q. Zhou, “5-THz bandwidth from a GaAs-on-silicon photoconductive receiver,” J. Appl. Phys. 74, 7022–7024 (1993).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Weling, A. S.

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

Wu, Q.

Q. Wu, X.-C. Zhang, “Free-space electro-optic sampling of mid-infrared pulses,” Appl. Phys. Lett. 71, 1285–1286 (1997).
[CrossRef]

Q. Wu, X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

Q. Wu, T. D. Hewitt, X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991).

Zhang, X.-C.

Q. Wu, X.-C. Zhang, “Free-space electro-optic sampling of mid-infrared pulses,” Appl. Phys. Lett. 71, 1285–1286 (1997).
[CrossRef]

Q. Wu, X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

Q. Wu, T. D. Hewitt, X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[CrossRef]

J. T. Darrow, X.-C. Zhang, D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
[CrossRef]

Zhou, X. Q.

J. E. Pedersen, S. R. Keiding, C. B. Sørensen, P. E. Lindelof, W. W. Rühle, X. Q. Zhou, “5-THz bandwidth from a GaAs-on-silicon photoconductive receiver,” J. Appl. Phys. 74, 7022–7024 (1993).
[CrossRef]

Appl. Phys. Lett. (7)

E. R. Brown, K. A. McIntosh, K. B. Nichols, C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66, 285–287 (1995).
[CrossRef]

N. Katzenellenbogen, D. Grischkowsky, “Efficient generation of 380 fs pulses of THz radiation by ultrafast laser pulse excitation of a biased metal-semiconductor interface,” Appl. Phys. Lett. 58, 222–224 (1991).
[CrossRef]

J. T. Darrow, X.-C. Zhang, D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
[CrossRef]

Q. Wu, T. D. Hewitt, X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[CrossRef]

Q. Wu, X.-C. Zhang, “Free-space electro-optic sampling of mid-infrared pulses,” Appl. Phys. Lett. 71, 1285–1286 (1997).
[CrossRef]

Q. Wu, X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

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

IEEE J. Quantum Electron. (2)

P. R. Smith, D. H. Auston, M. C. Nuss, “Subpicosecond photoconducting dipole antennas,” IEEE J. Quantum Electron. 24, 255–260 (1988).
[CrossRef]

D. H. Auston, M. C. Nuss, “Electrooptic generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184–197 (1988).
[CrossRef]

J. Appl. Phys. (2)

J. E. Pedersen, S. R. Keiding, C. B. Sørensen, P. E. Lindelof, W. W. Rühle, X. Q. Zhou, “5-THz bandwidth from a GaAs-on-silicon photoconductive receiver,” J. Appl. Phys. 74, 7022–7024 (1993).
[CrossRef]

D. T. F. Marple, “Refractive index of GaAs,” J. Appl. Phys. 35, 1241–1242 (1964).
[CrossRef]

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

Phys. Rev. Lett. (1)

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Other (1)

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991).

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Figures (4)

Fig. 1
Fig. 1

Difference of the refractive indices Δn in GaAs between the near-infrared sampling pulse and the terahertz pulse a, without and b, with dispersion around 900 nm as a function of terahertz frequency. The calculated coherence length from Eq. (3) is also plotted.

Fig. 2
Fig. 2

Experimental setup for the EO detection of free-space terahertz pulses. Terahertz radiation is generated in an InGaAs surface-field emitter.

Fig. 3
Fig. 3

Terahertz-pulse traces sampled with 〈110〉-oriented ZnTe and GaAs crystals. The signal recorded with GaAs is multiplied by a factor of 20. (b) Terahertz pulses measured with a PC antenna with and without a 0.5-mm-thick GaAs crystal in the beam path.

Fig. 4
Fig. 4

Upper part: calculated and experimental Fourier amplitude spectra of terahertz signals for three GaAs crystals of different thicknesses. The calculated spectra were obtained by multiplying the amplitude factor with the spectrum of the free-space terahertz transient. Lower part: amplitude factor γ for EO sampling in GaAs according to Eq. (4) and the Fourier spectrum of the free-space terahertz pulse.

Equations (4)

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

Δ k = k ν opt - ν THz - k ν opt + k ν THz = 0
Δ k = 2 π ν THz 1 v ph ν THz - 1 v gr ν opt = 0 .
l c ν THz = 2 π Δ k = c ν THz | n eff ν opt - n ν THz | .
γ ν THz = sin π l / l c ν THz π l / l c ν THz ,

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