Abstract

We demonstrate that some signal-processing techniques, such as the fractional Fourier transform and the spectrogram, which are known to be effective for optical signals, can be implemented at terahertz frequencies and with available terahertz devices. These techniques, contrary to the frequency-resolved optical-gating method for pulse characterization, do not require nonlinear media, which do not exist at terahertz frequencies. Thus the fractional Fourier transform or the spectrogram offers the only possibility of characterizing terahertz pulses simultaneously in time and frequency.

© 2004 Optical Society of America

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  1. D. Dragoman, M. Dragoman, “Terahertz fields and applications,” Prog. Quantum Electron. 28, 1–66 (2004).
    [Crossref]
  2. D. Mittleman, ed., Sensing with Terahertz Radiation, Vol. 85 of the Springer Series in Optical Sciences (Springer, Berlin, New York, 2003).
    [Crossref]
  3. R. Köhler, H. E. Beere, D. A. Richie, “Terahertz semiconductor-heterostructure laser,” Nature (London) 417, 156–159 (2002).
    [Crossref]
  4. H. Roskos, “Overview on time-domain terahertz spectroscopy and its applications in atomic and semiconductor physics,” Phys. Scr. T86, 51–54 (2000).
    [Crossref]
  5. S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, A. J. Taylor, “High-power narrow-band terahertz generation using large-aperture photoconductors,” IEEE J. Quantum Electron. 35, 1257–1266 (1999).
    [Crossref]
  6. S. Michan, D. Abbott, J. Munch, X.-C. Zhang, T. van Doorn, “Analysis trade-off for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
    [Crossref]
  7. D. Dragoman, “The Wigner distribution function in optics and optoelectronics” in Progress in Optics, Vol. XXXVII,E. Wolf, ed. (Elsevier, North-Holland, Amsterdam, 1997), pp. 1–56.
    [Crossref]
  8. A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
    [Crossref]
  9. Z. Jiang, X.-C. Zhang, “THz imaging via electro-optic effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
    [Crossref]
  10. R. Kersting, G. Strasser, K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36, 1156–1158 (2002).
    [Crossref]
  11. T. Kleine-Ostmann, M. Koch, P. Dawson, “Modulation of THz radiation by semiconductor nanostructures,” Microwave Opt. Technol. Lett. 35, 343–345 (2002).
    [Crossref]
  12. C.-Y. Chen, T.-R. Tsai, C.-L. Pan, R.-P. Pan, “Room temperature terahertz phase shifter based on magnetically controlled birefringence in liquid crystals,” Appl. Phys. Lett. 83, 4497–4499 (2003).
    [Crossref]
  13. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
    [Crossref]
  14. A. A. Godil, B. A. Auld, D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827–837 (1994).
    [Crossref]
  15. A. Nahata, A. S. Weling, T. F. Heinz, “A wideband coherent THz detection spectroscopy system using rectification and electro-optical sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996).
    [Crossref]
  16. G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, D. Grischkowsky, “Measurement of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of the THz radiation,” Appl. Phys. Lett. 74, 3450–3452 (1999).
    [Crossref]
  17. A. W. Lohmann, D. Mendlovic, Z. Zalevsky, “Fractional transformations in optics,” in Progress in Optics, Vol. XXXVIII, E. Wolf, ed. (Elsevier, North-Holland, Amsterdam, 1998), pp. 263–342.
    [Crossref]
  18. D. Dragoman, M. Dragoman, “Temporal implementation of Fourier-related transforms,” Opt. Commun. 145, 33–37 (1998).
    [Crossref]
  19. A. W. Lohmann, B. Soffer, “Relationship between the Radon-Wigner and the fractional Fourier transform,” J. Opt. Soc. Am. A 11, 1798–1801 (1994).
    [Crossref]
  20. A. W. Lohmann, D. Mendlovic, “Fractional Fourier transform: Photonic implementation,” Appl. Opt. 33, 7661–7664 (1994).
    [Crossref] [PubMed]
  21. M. F. Erden, H. M. Ozaktas, A. Sahin, D. Mendlovic, “Design of dynamically adjustable anamorphic fractional Fourier transformer,” Opt. Commun. 136, 52–60 (1997).
    [Crossref]
  22. D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, C. Ferreira, “Optical illustration of a varied fractional Fourier-transform order and the Radon-Wigner display,” Appl. Opt. 35, 3925–3929 (1996).
    [Crossref] [PubMed]
  23. L. Cohen, “Time-frequency distributions—A review,” Proc. IEEE 77, 941–981 (1989).
    [Crossref]
  24. D. J. Kane, A. J. Taylor, R. Trebino, R. W. DeLong, “Single-shot measurement of the intensity and phase of a femtosecond UV laser pulse with frequency-resolved optical gating,” Opt. Lett. 19, 1061–1063 (1994).
    [Crossref] [PubMed]
  25. D. Dragoman, M. Dragoman, “Implementation of the spatial and the temporal cross-ambiguity functions for waveguide fields and optical pulses,” Appl. Opt. 38, 822–827 (1999).
    [Crossref]
  26. M. Drabbels, G. M. Lankhuijinzen, L. D. Noordam, “Demonstration of a far-infrared streak camera,” IEEE J. Quantum Electron. 34, 2138–2145 (1998).
    [Crossref]
  27. D. Dragoman, M. Dragoman, “Wigner-transform implementation in the time-frequency domain,” Appl. Opt. 35, 7025–7030 (1996).
    [Crossref] [PubMed]

2004 (1)

D. Dragoman, M. Dragoman, “Terahertz fields and applications,” Prog. Quantum Electron. 28, 1–66 (2004).
[Crossref]

2003 (1)

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, R.-P. Pan, “Room temperature terahertz phase shifter based on magnetically controlled birefringence in liquid crystals,” Appl. Phys. Lett. 83, 4497–4499 (2003).
[Crossref]

2002 (3)

R. Köhler, H. E. Beere, D. A. Richie, “Terahertz semiconductor-heterostructure laser,” Nature (London) 417, 156–159 (2002).
[Crossref]

R. Kersting, G. Strasser, K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36, 1156–1158 (2002).
[Crossref]

T. Kleine-Ostmann, M. Koch, P. Dawson, “Modulation of THz radiation by semiconductor nanostructures,” Microwave Opt. Technol. Lett. 35, 343–345 (2002).
[Crossref]

2000 (2)

S. Michan, D. Abbott, J. Munch, X.-C. Zhang, T. van Doorn, “Analysis trade-off for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

H. Roskos, “Overview on time-domain terahertz spectroscopy and its applications in atomic and semiconductor physics,” Phys. Scr. T86, 51–54 (2000).
[Crossref]

1999 (4)

S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, A. J. Taylor, “High-power narrow-band terahertz generation using large-aperture photoconductors,” IEEE J. Quantum Electron. 35, 1257–1266 (1999).
[Crossref]

Z. Jiang, X.-C. Zhang, “THz imaging via electro-optic effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[Crossref]

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, D. Grischkowsky, “Measurement of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of the THz radiation,” Appl. Phys. Lett. 74, 3450–3452 (1999).
[Crossref]

D. Dragoman, M. Dragoman, “Implementation of the spatial and the temporal cross-ambiguity functions for waveguide fields and optical pulses,” Appl. Opt. 38, 822–827 (1999).
[Crossref]

1998 (2)

M. Drabbels, G. M. Lankhuijinzen, L. D. Noordam, “Demonstration of a far-infrared streak camera,” IEEE J. Quantum Electron. 34, 2138–2145 (1998).
[Crossref]

D. Dragoman, M. Dragoman, “Temporal implementation of Fourier-related transforms,” Opt. Commun. 145, 33–37 (1998).
[Crossref]

1997 (1)

M. F. Erden, H. M. Ozaktas, A. Sahin, D. Mendlovic, “Design of dynamically adjustable anamorphic fractional Fourier transformer,” Opt. Commun. 136, 52–60 (1997).
[Crossref]

1996 (3)

1995 (1)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[Crossref]

1994 (5)

1989 (1)

L. Cohen, “Time-frequency distributions—A review,” Proc. IEEE 77, 941–981 (1989).
[Crossref]

Abbott, D.

S. Michan, D. Abbott, J. Munch, X.-C. Zhang, T. van Doorn, “Analysis trade-off for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

Auld, B. A.

A. A. Godil, B. A. Auld, D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827–837 (1994).
[Crossref]

Beere, H. E.

R. Köhler, H. E. Beere, D. A. Richie, “Terahertz semiconductor-heterostructure laser,” Nature (London) 417, 156–159 (2002).
[Crossref]

Bloom, D. M.

A. A. Godil, B. A. Auld, D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827–837 (1994).
[Crossref]

Chen, C.-Y.

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, R.-P. Pan, “Room temperature terahertz phase shifter based on magnetically controlled birefringence in liquid crystals,” Appl. Phys. Lett. 83, 4497–4499 (2003).
[Crossref]

Cohen, L.

L. Cohen, “Time-frequency distributions—A review,” Proc. IEEE 77, 941–981 (1989).
[Crossref]

Dawson, P.

T. Kleine-Ostmann, M. Koch, P. Dawson, “Modulation of THz radiation by semiconductor nanostructures,” Microwave Opt. Technol. Lett. 35, 343–345 (2002).
[Crossref]

DeLong, R. W.

Dorsch, R. G.

Drabbels, M.

M. Drabbels, G. M. Lankhuijinzen, L. D. Noordam, “Demonstration of a far-infrared streak camera,” IEEE J. Quantum Electron. 34, 2138–2145 (1998).
[Crossref]

Dragoman, D.

D. Dragoman, M. Dragoman, “Terahertz fields and applications,” Prog. Quantum Electron. 28, 1–66 (2004).
[Crossref]

D. Dragoman, M. Dragoman, “Implementation of the spatial and the temporal cross-ambiguity functions for waveguide fields and optical pulses,” Appl. Opt. 38, 822–827 (1999).
[Crossref]

D. Dragoman, M. Dragoman, “Temporal implementation of Fourier-related transforms,” Opt. Commun. 145, 33–37 (1998).
[Crossref]

D. Dragoman, M. Dragoman, “Wigner-transform implementation in the time-frequency domain,” Appl. Opt. 35, 7025–7030 (1996).
[Crossref] [PubMed]

D. Dragoman, “The Wigner distribution function in optics and optoelectronics” in Progress in Optics, Vol. XXXVII,E. Wolf, ed. (Elsevier, North-Holland, Amsterdam, 1997), pp. 1–56.
[Crossref]

Dragoman, M.

Erden, M. F.

M. F. Erden, H. M. Ozaktas, A. Sahin, D. Mendlovic, “Design of dynamically adjustable anamorphic fractional Fourier transformer,” Opt. Commun. 136, 52–60 (1997).
[Crossref]

Ferreira, C.

Gallot, G.

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, D. Grischkowsky, “Measurement of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of the THz radiation,” Appl. Phys. Lett. 74, 3450–3452 (1999).
[Crossref]

Godil, A. A.

A. A. Godil, B. A. Auld, D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827–837 (1994).
[Crossref]

Grischkowsky, D.

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, D. Grischkowsky, “Measurement of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of the THz radiation,” Appl. Phys. Lett. 74, 3450–3452 (1999).
[Crossref]

Heinz, T. F.

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

Jeon, T.-I.

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, D. Grischkowsky, “Measurement of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of the THz radiation,” Appl. Phys. Lett. 74, 3450–3452 (1999).
[Crossref]

Jiang, Z.

Z. Jiang, X.-C. Zhang, “THz imaging via electro-optic effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[Crossref]

Kane, D. J.

Kersting, R.

R. Kersting, G. Strasser, K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36, 1156–1158 (2002).
[Crossref]

Kleine-Ostmann, T.

T. Kleine-Ostmann, M. Koch, P. Dawson, “Modulation of THz radiation by semiconductor nanostructures,” Microwave Opt. Technol. Lett. 35, 343–345 (2002).
[Crossref]

Koch, M.

T. Kleine-Ostmann, M. Koch, P. Dawson, “Modulation of THz radiation by semiconductor nanostructures,” Microwave Opt. Technol. Lett. 35, 343–345 (2002).
[Crossref]

Köhler, R.

R. Köhler, H. E. Beere, D. A. Richie, “Terahertz semiconductor-heterostructure laser,” Nature (London) 417, 156–159 (2002).
[Crossref]

Kolner, B. H.

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[Crossref]

Lankhuijinzen, G. M.

M. Drabbels, G. M. Lankhuijinzen, L. D. Noordam, “Demonstration of a far-infrared streak camera,” IEEE J. Quantum Electron. 34, 2138–2145 (1998).
[Crossref]

Lohmann, A. W.

McGowan, R. W.

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, D. Grischkowsky, “Measurement of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of the THz radiation,” Appl. Phys. Lett. 74, 3450–3452 (1999).
[Crossref]

Melloch, M. R.

S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, A. J. Taylor, “High-power narrow-band terahertz generation using large-aperture photoconductors,” IEEE J. Quantum Electron. 35, 1257–1266 (1999).
[Crossref]

Mendlovic, D.

M. F. Erden, H. M. Ozaktas, A. Sahin, D. Mendlovic, “Design of dynamically adjustable anamorphic fractional Fourier transformer,” Opt. Commun. 136, 52–60 (1997).
[Crossref]

D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, C. Ferreira, “Optical illustration of a varied fractional Fourier-transform order and the Radon-Wigner display,” Appl. Opt. 35, 3925–3929 (1996).
[Crossref] [PubMed]

A. W. Lohmann, D. Mendlovic, “Fractional Fourier transform: Photonic implementation,” Appl. Opt. 33, 7661–7664 (1994).
[Crossref] [PubMed]

A. W. Lohmann, D. Mendlovic, Z. Zalevsky, “Fractional transformations in optics,” in Progress in Optics, Vol. XXXVIII, E. Wolf, ed. (Elsevier, North-Holland, Amsterdam, 1998), pp. 263–342.
[Crossref]

Michan, S.

S. Michan, D. Abbott, J. Munch, X.-C. Zhang, T. van Doorn, “Analysis trade-off for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

Munch, J.

S. Michan, D. Abbott, J. Munch, X.-C. Zhang, T. van Doorn, “Analysis trade-off for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

Nahata, A.

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

Noordam, L. D.

M. Drabbels, G. M. Lankhuijinzen, L. D. Noordam, “Demonstration of a far-infrared streak camera,” IEEE J. Quantum Electron. 34, 2138–2145 (1998).
[Crossref]

Ozaktas, H. M.

M. F. Erden, H. M. Ozaktas, A. Sahin, D. Mendlovic, “Design of dynamically adjustable anamorphic fractional Fourier transformer,” Opt. Commun. 136, 52–60 (1997).
[Crossref]

Pan, C.-L.

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, R.-P. Pan, “Room temperature terahertz phase shifter based on magnetically controlled birefringence in liquid crystals,” Appl. Phys. Lett. 83, 4497–4499 (2003).
[Crossref]

Pan, R.-P.

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, R.-P. Pan, “Room temperature terahertz phase shifter based on magnetically controlled birefringence in liquid crystals,” Appl. Phys. Lett. 83, 4497–4499 (2003).
[Crossref]

Park, S.-G.

S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, A. J. Taylor, “High-power narrow-band terahertz generation using large-aperture photoconductors,” IEEE J. Quantum Electron. 35, 1257–1266 (1999).
[Crossref]

Richie, D. A.

R. Köhler, H. E. Beere, D. A. Richie, “Terahertz semiconductor-heterostructure laser,” Nature (London) 417, 156–159 (2002).
[Crossref]

Roskos, H.

H. Roskos, “Overview on time-domain terahertz spectroscopy and its applications in atomic and semiconductor physics,” Phys. Scr. T86, 51–54 (2000).
[Crossref]

Sahin, A.

M. F. Erden, H. M. Ozaktas, A. Sahin, D. Mendlovic, “Design of dynamically adjustable anamorphic fractional Fourier transformer,” Opt. Commun. 136, 52–60 (1997).
[Crossref]

Siders, C. W.

S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, A. J. Taylor, “High-power narrow-band terahertz generation using large-aperture photoconductors,” IEEE J. Quantum Electron. 35, 1257–1266 (1999).
[Crossref]

Siders, J. L. W.

S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, A. J. Taylor, “High-power narrow-band terahertz generation using large-aperture photoconductors,” IEEE J. Quantum Electron. 35, 1257–1266 (1999).
[Crossref]

Soffer, B.

Strasser, G.

R. Kersting, G. Strasser, K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36, 1156–1158 (2002).
[Crossref]

Taylor, A. J.

S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, A. J. Taylor, “High-power narrow-band terahertz generation using large-aperture photoconductors,” IEEE J. Quantum Electron. 35, 1257–1266 (1999).
[Crossref]

D. J. Kane, A. J. Taylor, R. Trebino, R. W. DeLong, “Single-shot measurement of the intensity and phase of a femtosecond UV laser pulse with frequency-resolved optical gating,” Opt. Lett. 19, 1061–1063 (1994).
[Crossref] [PubMed]

Trebino, R.

Tsai, T.-R.

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, R.-P. Pan, “Room temperature terahertz phase shifter based on magnetically controlled birefringence in liquid crystals,” Appl. Phys. Lett. 83, 4497–4499 (2003).
[Crossref]

Unterrainer, K.

R. Kersting, G. Strasser, K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36, 1156–1158 (2002).
[Crossref]

van Doorn, T.

S. Michan, D. Abbott, J. Munch, X.-C. Zhang, T. van Doorn, “Analysis trade-off for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

Weiner, A. M.

S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, A. J. Taylor, “High-power narrow-band terahertz generation using large-aperture photoconductors,” IEEE J. Quantum Electron. 35, 1257–1266 (1999).
[Crossref]

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[Crossref]

Weling, A. S.

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

Zalevsky, Z.

D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, C. Ferreira, “Optical illustration of a varied fractional Fourier-transform order and the Radon-Wigner display,” Appl. Opt. 35, 3925–3929 (1996).
[Crossref] [PubMed]

A. W. Lohmann, D. Mendlovic, Z. Zalevsky, “Fractional transformations in optics,” in Progress in Optics, Vol. XXXVIII, E. Wolf, ed. (Elsevier, North-Holland, Amsterdam, 1998), pp. 263–342.
[Crossref]

Zhang, J.

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, D. Grischkowsky, “Measurement of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of the THz radiation,” Appl. Phys. Lett. 74, 3450–3452 (1999).
[Crossref]

Zhang, X.-C.

S. Michan, D. Abbott, J. Munch, X.-C. Zhang, T. van Doorn, “Analysis trade-off for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

Z. Jiang, X.-C. Zhang, “THz imaging via electro-optic effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (3)

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, R.-P. Pan, “Room temperature terahertz phase shifter based on magnetically controlled birefringence in liquid crystals,” Appl. Phys. Lett. 83, 4497–4499 (2003).
[Crossref]

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

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, D. Grischkowsky, “Measurement of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of the THz radiation,” Appl. Phys. Lett. 74, 3450–3452 (1999).
[Crossref]

Electron. Lett. (1)

R. Kersting, G. Strasser, K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36, 1156–1158 (2002).
[Crossref]

IEEE J. Quantum Electron. (4)

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[Crossref]

A. A. Godil, B. A. Auld, D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827–837 (1994).
[Crossref]

S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, A. J. Taylor, “High-power narrow-band terahertz generation using large-aperture photoconductors,” IEEE J. Quantum Electron. 35, 1257–1266 (1999).
[Crossref]

M. Drabbels, G. M. Lankhuijinzen, L. D. Noordam, “Demonstration of a far-infrared streak camera,” IEEE J. Quantum Electron. 34, 2138–2145 (1998).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

Z. Jiang, X.-C. Zhang, “THz imaging via electro-optic effect,” IEEE Trans. Microwave Theory Tech. 47, 2644–2650 (1999).
[Crossref]

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

Microelectron. J. (1)

S. Michan, D. Abbott, J. Munch, X.-C. Zhang, T. van Doorn, “Analysis trade-off for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

Microwave Opt. Technol. Lett. (1)

T. Kleine-Ostmann, M. Koch, P. Dawson, “Modulation of THz radiation by semiconductor nanostructures,” Microwave Opt. Technol. Lett. 35, 343–345 (2002).
[Crossref]

Nature (London) (1)

R. Köhler, H. E. Beere, D. A. Richie, “Terahertz semiconductor-heterostructure laser,” Nature (London) 417, 156–159 (2002).
[Crossref]

Opt. Commun. (2)

D. Dragoman, M. Dragoman, “Temporal implementation of Fourier-related transforms,” Opt. Commun. 145, 33–37 (1998).
[Crossref]

M. F. Erden, H. M. Ozaktas, A. Sahin, D. Mendlovic, “Design of dynamically adjustable anamorphic fractional Fourier transformer,” Opt. Commun. 136, 52–60 (1997).
[Crossref]

Opt. Lett. (1)

Phys. Scr. (1)

H. Roskos, “Overview on time-domain terahertz spectroscopy and its applications in atomic and semiconductor physics,” Phys. Scr. T86, 51–54 (2000).
[Crossref]

Proc. IEEE (1)

L. Cohen, “Time-frequency distributions—A review,” Proc. IEEE 77, 941–981 (1989).
[Crossref]

Prog. Quantum Electron. (2)

D. Dragoman, M. Dragoman, “Terahertz fields and applications,” Prog. Quantum Electron. 28, 1–66 (2004).
[Crossref]

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[Crossref]

Other (3)

D. Dragoman, “The Wigner distribution function in optics and optoelectronics” in Progress in Optics, Vol. XXXVII,E. Wolf, ed. (Elsevier, North-Holland, Amsterdam, 1997), pp. 1–56.
[Crossref]

D. Mittleman, ed., Sensing with Terahertz Radiation, Vol. 85 of the Springer Series in Optical Sciences (Springer, Berlin, New York, 2003).
[Crossref]

A. W. Lohmann, D. Mendlovic, Z. Zalevsky, “Fractional transformations in optics,” in Progress in Optics, Vol. XXXVIII, E. Wolf, ed. (Elsevier, North-Holland, Amsterdam, 1998), pp. 263–342.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

(a), (b) Setups for the implementation of the spatial FRFT of the order of α; (c), (d) the corresponding set-ups for the implementation of the temporal FRFT of the order of -α.

Fig. 2
Fig. 2

Setup for the simultaneous display of spatial FRFTs with different degrees of fractionality α.

Fig. 3
Fig. 3

Phase modulator that allows the simultaneously implementation of temporal lenses with different focal lengths.

Fig. 4
Fig. 4

Setup for the implementation of the spatial spectrogram.

Fig. 5
Fig. 5

Temporal analog of the setup in Fig. 4.

Equations (7)

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E/z=i/2k2E/x2,
A/z=iβ2/22A/τ2
fT=ω0/πV0/Vπωm2,
n2=289.27-6f2/29.16-f2,
β2=1c2 dndω+ω d2ndω2
Fαp=expiπαˆ/4-α/22π|sin α|exp-i p22cot α×expi pxk0sin α-i x2k022cot αΦxdx
Sx, p= ΦxFx-xexp-ik0xpdx2,

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