Abstract

We have experimentally studied the propagation in free space and through focusing optics of subpicosecond half- and single-cycle terahertz pulses emitted by large-aperture emitters. The spatial transformations of the beams are connected to phase changes and effective frequency filtering and lead to spectacular changes in the pulse time profile. The experimental results are in excellent agreement with the predictions of a simple analytical model based on a Gaussian-beam approximation.

© 1999 Optical Society of America

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    [CrossRef]
  2. D. H. Auston and M. C. Nuss, “Electro-optical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24, 184–197 (1988).
    [CrossRef]
  3. X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, D. P. Phelps, K. R. Stewart, and C. P. Yakymyshyn, “Terahertz optical rectification from a nonlinear organic crystal,” Appl. Phys. Lett. 61, 3080–3082 (1992).
    [CrossRef]
  4. P. R. Smith, D. H. Auston, and M. C. Nuss, “Subpicosecond photoconducting dipole antennas,” IEEE J. Quantum Electron. 24, 255–260 (1988).
    [CrossRef]
  5. C. H. Fattinger and D. Grischkowsky, “Terahertz beams,” Appl. Phys. Lett. 54, 490–492 (1989).
    [CrossRef]
  6. B. B. Hu, J. T. Darrow, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Optically steerable photoconducting antennas,” Appl. Phys. Lett. 56, 886–888 (1990).
    [CrossRef]
  7. J. T. Darrow, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Subpicosecond electromagnetic pulses from large-aperture photoconducting antennas,” Opt. Lett. 15, 323–325 (1990).
    [CrossRef] [PubMed]
  8. X.-C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, “Generation of femtosecond electromagnetic pulses from semiconductor surfaces,” Appl. Phys. Lett. 56, 1011–1013 (1990).
    [CrossRef]
  9. X.-C. Zhang, B. B. Hu, S. H. Xin, and D. H. Auston, “Optically induced femtosecond electromagnetic pulses from GaSb/AlSb strained-layer superlattices,” Appl. Phys. Lett. 57, 753–755 (1990).
    [CrossRef]
  10. Ch. Fattinger and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53, 1480–1482 (1988).
    [CrossRef]
  11. D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett. 45, 284–286 (1984).
    [CrossRef]
  12. D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
    [CrossRef]
  13. Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
    [CrossRef]
  14. Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
    [CrossRef]
  15. P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
    [CrossRef]
  16. A. Nahata, D. H. Auston, T. F. Heinz, and C. J. Wu, “Coherent detection of freely propagating terahertz radiation by electro-optic sampling,” Appl. Phys. Lett. 68, 150–152 (1996).
    [CrossRef]
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    [CrossRef]
  23. D. You and P. H. Bucksbaum, “Propagation of half-cycle far infrared pulses,” J. Opt. Soc. Am. B 14, 1651–1655 (1997).
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    [CrossRef]
  29. G. W. Chantry, “Spectroscopy at optical and longer wavelengths,” in Long-Wave Optics (Academic, London, 1984), Vol. 2, p. 456.

1998 (3)

1997 (1)

1996 (5)

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

P. U. Jepsen, R. H. Jacobsen, and S. R. Keiding, “Generation and detection of terahertz pulses from biased semiconductor antennas,” J. Opt. Soc. Am. B 13, 2424–2436 (1996).
[CrossRef]

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

A. Nahata, D. H. Auston, T. F. Heinz, and C. J. Wu, “Coherent detection of freely propagating terahertz radiation by electro-optic sampling,” Appl. Phys. Lett. 68, 150–152 (1996).
[CrossRef]

1995 (1)

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

1992 (2)

R. W. Ziolkowski and J. B. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021–2030 (1992).
[CrossRef]

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, D. P. Phelps, K. R. Stewart, and C. P. Yakymyshyn, “Terahertz optical rectification from a nonlinear organic crystal,” Appl. Phys. Lett. 61, 3080–3082 (1992).
[CrossRef]

1990 (6)

M. van Exter and D. R. Grischkowsky, “Characterization of an optoelectronic terahertz beam system,” IEEE Trans. Microwave Theory Tech. 38, 1684–1691 (1990).
[CrossRef]

B. B. Hu, J. T. Darrow, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Optically steerable photoconducting antennas,” Appl. Phys. Lett. 56, 886–888 (1990).
[CrossRef]

J. T. Darrow, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Subpicosecond electromagnetic pulses from large-aperture photoconducting antennas,” Opt. Lett. 15, 323–325 (1990).
[CrossRef] [PubMed]

X.-C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, “Generation of femtosecond electromagnetic pulses from semiconductor surfaces,” Appl. Phys. Lett. 56, 1011–1013 (1990).
[CrossRef]

X.-C. Zhang, B. B. Hu, S. H. Xin, and D. H. Auston, “Optically induced femtosecond electromagnetic pulses from GaSb/AlSb strained-layer superlattices,” Appl. Phys. Lett. 57, 753–755 (1990).
[CrossRef]

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

1989 (2)

1988 (3)

Ch. Fattinger and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53, 1480–1482 (1988).
[CrossRef]

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

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

1985 (1)

1984 (2)

D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett. 45, 284–286 (1984).
[CrossRef]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[CrossRef]

1965 (1)

Auston, D. H.

A. Nahata, D. H. Auston, T. F. Heinz, and C. J. Wu, “Coherent detection of freely propagating terahertz radiation by electro-optic sampling,” Appl. Phys. Lett. 68, 150–152 (1996).
[CrossRef]

B. B. Hu, J. T. Darrow, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Optically steerable photoconducting antennas,” Appl. Phys. Lett. 56, 886–888 (1990).
[CrossRef]

J. T. Darrow, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Subpicosecond electromagnetic pulses from large-aperture photoconducting antennas,” Opt. Lett. 15, 323–325 (1990).
[CrossRef] [PubMed]

X.-C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, “Generation of femtosecond electromagnetic pulses from semiconductor surfaces,” Appl. Phys. Lett. 56, 1011–1013 (1990).
[CrossRef]

X.-C. Zhang, B. B. Hu, S. H. Xin, and D. H. Auston, “Optically induced femtosecond electromagnetic pulses from GaSb/AlSb strained-layer superlattices,” Appl. Phys. Lett. 57, 753–755 (1990).
[CrossRef]

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

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

D. H. Auston and K. P. Cheung, “Coherent time-domain far-infrared spectroscopy,” J. Opt. Soc. Am. B 2, 606–612 (1985).
[CrossRef]

D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett. 45, 284–286 (1984).
[CrossRef]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[CrossRef]

Boden, E. P.

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, D. P. Phelps, K. R. Stewart, and C. P. Yakymyshyn, “Terahertz optical rectification from a nonlinear organic crystal,” Appl. Phys. Lett. 61, 3080–3082 (1992).
[CrossRef]

Bokor, J.

Bucksbaum, P. H.

Budiarto, E.

Cheung, K. P.

D. H. Auston and K. P. Cheung, “Coherent time-domain far-infrared spectroscopy,” J. Opt. Soc. Am. B 2, 606–612 (1985).
[CrossRef]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[CrossRef]

D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett. 45, 284–286 (1984).
[CrossRef]

Darrow, J. T.

X.-C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, “Generation of femtosecond electromagnetic pulses from semiconductor surfaces,” Appl. Phys. Lett. 56, 1011–1013 (1990).
[CrossRef]

J. T. Darrow, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Subpicosecond electromagnetic pulses from large-aperture photoconducting antennas,” Opt. Lett. 15, 323–325 (1990).
[CrossRef] [PubMed]

B. B. Hu, J. T. Darrow, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Optically steerable photoconducting antennas,” Appl. Phys. Lett. 56, 886–888 (1990).
[CrossRef]

Fattinger, C. H.

C. H. Fattinger and D. Grischkowsky, “Terahertz beams,” Appl. Phys. Lett. 54, 490–492 (1989).
[CrossRef]

Fattinger, Ch.

Feng, S.

Grischkowsky, D.

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

C. H. Fattinger and D. Grischkowsky, “Terahertz beams,” Appl. Phys. Lett. 54, 490–492 (1989).
[CrossRef]

Ch. Fattinger and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53, 1480–1482 (1988).
[CrossRef]

Grischkowsky, D. R.

M. van Exter and D. R. Grischkowsky, “Characterization of an optoelectronic terahertz beam system,” IEEE Trans. Microwave Theory Tech. 38, 1684–1691 (1990).
[CrossRef]

Grishkowsky, D.

Heinz, T. F.

A. Nahata, D. H. Auston, T. F. Heinz, and C. J. Wu, “Coherent detection of freely propagating terahertz radiation by electro-optic sampling,” Appl. Phys. Lett. 68, 150–152 (1996).
[CrossRef]

Hellwarth, R. W.

Helm, H.

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Hu, B. B.

B. B. Hu, J. T. Darrow, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Optically steerable photoconducting antennas,” Appl. Phys. Lett. 56, 886–888 (1990).
[CrossRef]

X.-C. Zhang, B. B. Hu, S. H. Xin, and D. H. Auston, “Optically induced femtosecond electromagnetic pulses from GaSb/AlSb strained-layer superlattices,” Appl. Phys. Lett. 57, 753–755 (1990).
[CrossRef]

X.-C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, “Generation of femtosecond electromagnetic pulses from semiconductor surfaces,” Appl. Phys. Lett. 56, 1011–1013 (1990).
[CrossRef]

J. T. Darrow, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Subpicosecond electromagnetic pulses from large-aperture photoconducting antennas,” Opt. Lett. 15, 323–325 (1990).
[CrossRef] [PubMed]

Jacobsen, R. H.

Jeong, S.

Jepsen, P. U.

P. U. Jepsen, R. H. Jacobsen, and S. R. Keiding, “Generation and detection of terahertz pulses from biased semiconductor antennas,” J. Opt. Soc. Am. B 13, 2424–2436 (1996).
[CrossRef]

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Jin, Y.

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, D. P. Phelps, K. R. Stewart, and C. P. Yakymyshyn, “Terahertz optical rectification from a nonlinear organic crystal,” Appl. Phys. Lett. 61, 3080–3082 (1992).
[CrossRef]

Judkins, J. B.

Kaplan, A. E.

Keiding, S.

Keiding, S. R.

P. U. Jepsen, R. H. Jacobsen, and S. R. Keiding, “Generation and detection of terahertz pulses from biased semiconductor antennas,” J. Opt. Soc. Am. B 13, 2424–2436 (1996).
[CrossRef]

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Kleinman, D. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[CrossRef]

Kogelnik, H.

Litz, M.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

Lu, T.-M.

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, D. P. Phelps, K. R. Stewart, and C. P. Yakymyshyn, “Terahertz optical rectification from a nonlinear organic crystal,” Appl. Phys. Lett. 61, 3080–3082 (1992).
[CrossRef]

Ma, X. F.

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, D. P. Phelps, K. R. Stewart, and C. P. Yakymyshyn, “Terahertz optical rectification from a nonlinear organic crystal,” Appl. Phys. Lett. 61, 3080–3082 (1992).
[CrossRef]

Nahata, A.

A. Nahata, D. H. Auston, T. F. Heinz, and C. J. Wu, “Coherent detection of freely propagating terahertz radiation by electro-optic sampling,” Appl. Phys. Lett. 68, 150–152 (1996).
[CrossRef]

Nuss, M. C.

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

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

Phelps, D. P.

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, D. P. Phelps, K. R. Stewart, and C. P. Yakymyshyn, “Terahertz optical rectification from a nonlinear organic crystal,” Appl. Phys. Lett. 61, 3080–3082 (1992).
[CrossRef]

Pu, N.-W.

Schall, M.

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Schyja, V.

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Smith, P. R.

B. B. Hu, J. T. Darrow, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Optically steerable photoconducting antennas,” Appl. Phys. Lett. 56, 886–888 (1990).
[CrossRef]

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

D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett. 45, 284–286 (1984).
[CrossRef]

Stewart, K. R.

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, D. P. Phelps, K. R. Stewart, and C. P. Yakymyshyn, “Terahertz optical rectification from a nonlinear organic crystal,” Appl. Phys. Lett. 61, 3080–3082 (1992).
[CrossRef]

Valdmanis, J. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[CrossRef]

van Exter, M.

Winful, H. G.

Winnewisser, C.

P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, “Detection of THz pulses by phase retardation in lithium tantalate,” Phys. Rev. E 53, R3052–R3054 (1996).
[CrossRef]

Wu, C. J.

A. Nahata, D. H. Auston, T. F. Heinz, and C. J. Wu, “Coherent detection of freely propagating terahertz radiation by electro-optic sampling,” Appl. Phys. Lett. 68, 150–152 (1996).
[CrossRef]

Wu, Q.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

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

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

Xin, S. H.

X.-C. Zhang, B. B. Hu, S. H. Xin, and D. H. Auston, “Optically induced femtosecond electromagnetic pulses from GaSb/AlSb strained-layer superlattices,” Appl. Phys. Lett. 57, 753–755 (1990).
[CrossRef]

Yakymyshyn, C. P.

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, D. P. Phelps, K. R. Stewart, and C. P. Yakymyshyn, “Terahertz optical rectification from a nonlinear organic crystal,” Appl. Phys. Lett. 61, 3080–3082 (1992).
[CrossRef]

You, D.

Zhang, X.-C.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

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

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, D. P. Phelps, K. R. Stewart, and C. P. Yakymyshyn, “Terahertz optical rectification from a nonlinear organic crystal,” Appl. Phys. Lett. 61, 3080–3082 (1992).
[CrossRef]

X.-C. Zhang, B. B. Hu, S. H. Xin, and D. H. Auston, “Optically induced femtosecond electromagnetic pulses from GaSb/AlSb strained-layer superlattices,” Appl. Phys. Lett. 57, 753–755 (1990).
[CrossRef]

B. B. Hu, J. T. Darrow, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Optically steerable photoconducting antennas,” Appl. Phys. Lett. 56, 886–888 (1990).
[CrossRef]

J. T. Darrow, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Subpicosecond electromagnetic pulses from large-aperture photoconducting antennas,” Opt. Lett. 15, 323–325 (1990).
[CrossRef] [PubMed]

X.-C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, “Generation of femtosecond electromagnetic pulses from semiconductor surfaces,” Appl. Phys. Lett. 56, 1011–1013 (1990).
[CrossRef]

Ziolkowski, R. W.

Appl. Opt. (1)

Appl. Phys. Lett. (11)

X.-C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, “Generation of femtosecond electromagnetic pulses from semiconductor surfaces,” Appl. Phys. Lett. 56, 1011–1013 (1990).
[CrossRef]

X.-C. Zhang, B. B. Hu, S. H. Xin, and D. H. Auston, “Optically induced femtosecond electromagnetic pulses from GaSb/AlSb strained-layer superlattices,” Appl. Phys. Lett. 57, 753–755 (1990).
[CrossRef]

Ch. Fattinger and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53, 1480–1482 (1988).
[CrossRef]

D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett. 45, 284–286 (1984).
[CrossRef]

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Scheme of phase shifts and effective amplitude filters that result from propagation of the THz pulse through a set of lenses. Both filters and phase shifts refer to the far-field spectrum.

Fig. 2
Fig. 2

Schematic of the experimental setups. (a) Free-space propagation measurement (emitter–sensor distance variable); (b) focusing with a sooted polyethylene lens (lens position variable); (c) focusing with a pair of ellipsoidal mirrors with one common focus (second mirror—sensor distance variable). E, emitter; S, sensor; PBS, pellicle beam splitter.

Fig. 3
Fig. 3

Peak values of the waveforms (solid symbols) and integrated amplitude spectrum values (open symbols) as a function of the emitter–sensor distance in the setup of Fig. 2(a). Solid curves, fits with 1/les function.

Fig. 4
Fig. 4

Solid curves, waveforms taken by use of the setup in Fig. 2(b) (the emitter–lens distance is indicated in the figures). Dotted lines, simulations based on the numerical Fourier transform of formula (9); a reference waveform taken during the free-space propagation measurement alignment was introduced into the calculation to simulate e0(ν). See the text for details.

Fig. 5
Fig. 5

THz waveforms and corresponding spectra obtained with a 3-mm GaAs:Cr emitter in the setup with two ellipsoidal mirrors for four different lms. Dotted lines, simulations obtained from the reference waveform (same as in Fig. 4) based on Eq. (9) for two mirrors. lms in centimeters: (a) experimental 11.5, model 13.5; (b) experimental 15, model 15; (c) experimental 19, model 16.5; and (d) experimental 26, model 20.

Fig. 6
Fig. 6

THz waveforms and corresponding spectra obtained with 3-mm LT GaAs emitter. (a) Free-space propagation geometry [Fig. 2(a)], les=7 cm; (b) setup with two ellipsoidal mirrors, lms=15 cm [Fig. 2(c)]. Dotted curves, simulations obtained from the reference waveform (a).

Equations (24)

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e(ν)=- E(t)exp(-2πiνt)d t.
e(ν; z)=e0(ν) w0w(z)exp-ikz-arctanzz0,
w2(z)=w021+zz02,z0=πw02cν;
L=f(L2+z02)(L2+z02-fL)(L2+z02-fL)2+f2z02X2,
w0=w0LfL2+z02-fL1/2X,
z0=πw02cν,w2(z)=w021+zz02
ν>νm : X=1,
ν<νm : X=2w0A2L2z02+1,
νm=α(L)[(2w0/A)2-1]1/2,
α(z)=cπw02z=zz0ν.
fLL-fπ(A/2)2λ
νm=α(L) 2w0A,L=fLL-f
ν>νm : w0=w0 LL,
ν<νm : w0=w0 LLνmν.
e(ν; z)=e0(ν) w0w(z)w(-L)w(L)×expiarctanLz0-arctan-Lz0+arctanzz0,
e(ν; z)=e0(ν)1-i α(L)ν-1×1+i α(L)ν1-i α(z)ν-1,
E(t)=12παE0(t)t;
e(n-1)(ν; Ln)=e(n-1)(ν; 0) iναn-1(Ln),
e(n)(ν; 0)=e(n-1)(ν; Ln) iFn(ν)ναn-1(Ln),
e(n)(ν; 0)=-e(n-1)(ν; 0)Fn(ν).
ν>νm : Fn(ν)=LnLn,
ν<νm : Fn(ν)=LnLnννm2.
E(n)(t)=-LnLnE(n-1)(t)*δ(t)+4νmcos(ωmt)(ωmt)2-sin(ωmt)(ωmt)3,
1R2(r)=1R1-1f(r).

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