Abstract

We propose an optical time-to-two-dimensional (2-D)-space-to-time-to-2-D-space conversion technique for ultrafast image transmission with ultrashort-pulse lasers. The proposed technique is based on the concepts of the time–space transform, the spatial time–frequency transform, and their inverses. We describe and analyze the proposed technique for ultrafast all-optical processors that can convert an input 2-D spatial object into a modulated ultrafast optical pulse sequence and can retrieve the original 2-D spatial image from the temporal signals transmitted through the optical fiber channel with ultrahigh bandwidth. To verify the proposed technique, we report preliminary experimental results.

© 1999 Optical Society of America

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  1. C. A. Brackett, “Is there an emerging consensus on WDM networking?” J. Lightwave Technol. 14, 936–941 (1996).
  2. H. Taga, “Long distance transmission experiments using the WDM technology,” J. Lightwave Technol. 14, 1287–1298 (1996).
    [CrossRef]
  3. V. P. Heuring, H. F. Jordan, J. P. Pratt, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
    [CrossRef]
  4. H. Hatami-Hanza, A. Mostofi, P. L. Chu, “A multilevel soliton communication system,” J. Lightwave Technol. 15, 6–19 (1997).
    [CrossRef]
  5. S. Baroni, P. Bayvel, “Wavelength requirements in arbitrarily connected wavelength-routed optical networks,” J. Lightwave Technol. 15, 242–251 (1997).
    [CrossRef]
  6. Y. T. Mazurenko, “Reconstruction of a nonstationary wave field by holography in a 3-D medium,” Opt. Spectrosc. (USSR) 57, 343–344 (1984).
  7. P. C. Sun, Y. T. Mazurenko, W. S. C. Chang, P. K. L. Yu, Y. Fainman, “All-optical parallel-to-serial conversion by holographic spatial-to-temporal frequency encoding,” Opt. Lett. 20, 1728–1730 (1995).
    [CrossRef] [PubMed]
  8. P. C. Sun, Y. T. Mazurenko, Y. Fainman, “Femtosecond pulse imaging: ultrafast optical oscilloscope,” J. Opt. Soc. Am. A 14, 1159–1170 (1997).
    [CrossRef]
  9. R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlonson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682–696 (1986).
    [CrossRef]
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    [CrossRef]
  11. M. M. Wefers, K. A. Nelson, “Analysis of programmable ultrashort waveform generation using liquid-crystal spatial light-modulators,” J. Opt. Soc. Am. B 12, 1343–1362 (1995).
    [CrossRef]
  12. M. M. Wefers, K. A. Nelson, A. M. Weiner, “Multidimensional shaping of ultrafast optical waveforms,” Opt. Lett. 21, 746–748 (1996).
    [CrossRef] [PubMed]
  13. H. M. Ozaktas, M. C. Nuss, “Time-variant linear pulse processing,” Opt. Commun. 131, 114–118 (1996).
    [CrossRef]
  14. L. Cohen, “Time–frequency distribution,” Proc. IEEE 77, 941–981 (1989).
    [CrossRef]
  15. L. Cohen, Time–Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1995).
  16. A. Cohen, J. Kovacevic, “Wavelets: the mathematical background,” Proc. IEEE 84, 514–522 (1996).
    [CrossRef]
  17. Y. Zhang, Y. Li, E. G. Kanterakis, A. Katz, X. J. Lu, R. Tolimieri, N. P. Caviris, “Optical realization of wavelet transform for a one-dimensional signal,” Opt. Lett. 17, 210–212 (1992).
    [CrossRef] [PubMed]
  18. K. G. Purchase, D. J. Brady, K. Wagner, “Time-of-flight cross correlation on a detector array for ultrafast packet detection,” Opt. Lett. 18, 2129–2131 (1993).
    [CrossRef] [PubMed]
  19. D. J. Kane, R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
    [CrossRef]

1997 (3)

H. Hatami-Hanza, A. Mostofi, P. L. Chu, “A multilevel soliton communication system,” J. Lightwave Technol. 15, 6–19 (1997).
[CrossRef]

S. Baroni, P. Bayvel, “Wavelength requirements in arbitrarily connected wavelength-routed optical networks,” J. Lightwave Technol. 15, 242–251 (1997).
[CrossRef]

P. C. Sun, Y. T. Mazurenko, Y. Fainman, “Femtosecond pulse imaging: ultrafast optical oscilloscope,” J. Opt. Soc. Am. A 14, 1159–1170 (1997).
[CrossRef]

1996 (6)

A. Cohen, J. Kovacevic, “Wavelets: the mathematical background,” Proc. IEEE 84, 514–522 (1996).
[CrossRef]

M. M. Wefers, K. A. Nelson, A. M. Weiner, “Multidimensional shaping of ultrafast optical waveforms,” Opt. Lett. 21, 746–748 (1996).
[CrossRef] [PubMed]

C. A. Brackett, “Is there an emerging consensus on WDM networking?” J. Lightwave Technol. 14, 936–941 (1996).

H. Taga, “Long distance transmission experiments using the WDM technology,” J. Lightwave Technol. 14, 1287–1298 (1996).
[CrossRef]

V. P. Heuring, H. F. Jordan, J. P. Pratt, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
[CrossRef]

H. M. Ozaktas, M. C. Nuss, “Time-variant linear pulse processing,” Opt. Commun. 131, 114–118 (1996).
[CrossRef]

1995 (2)

1993 (2)

K. G. Purchase, D. J. Brady, K. Wagner, “Time-of-flight cross correlation on a detector array for ultrafast packet detection,” Opt. Lett. 18, 2129–2131 (1993).
[CrossRef] [PubMed]

D. J. Kane, R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

1992 (2)

Y. Zhang, Y. Li, E. G. Kanterakis, A. Katz, X. J. Lu, R. Tolimieri, N. P. Caviris, “Optical realization of wavelet transform for a one-dimensional signal,” Opt. Lett. 17, 210–212 (1992).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

1989 (1)

L. Cohen, “Time–frequency distribution,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

1986 (1)

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlonson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682–696 (1986).
[CrossRef]

1984 (1)

Y. T. Mazurenko, “Reconstruction of a nonstationary wave field by holography in a 3-D medium,” Opt. Spectrosc. (USSR) 57, 343–344 (1984).

Baroni, S.

S. Baroni, P. Bayvel, “Wavelength requirements in arbitrarily connected wavelength-routed optical networks,” J. Lightwave Technol. 15, 242–251 (1997).
[CrossRef]

Bayvel, P.

S. Baroni, P. Bayvel, “Wavelength requirements in arbitrarily connected wavelength-routed optical networks,” J. Lightwave Technol. 15, 242–251 (1997).
[CrossRef]

Brackett, C. A.

C. A. Brackett, “Is there an emerging consensus on WDM networking?” J. Lightwave Technol. 14, 936–941 (1996).

Brady, D. J.

Caviris, N. P.

Chang, W. S. C.

Chu, P. L.

H. Hatami-Hanza, A. Mostofi, P. L. Chu, “A multilevel soliton communication system,” J. Lightwave Technol. 15, 6–19 (1997).
[CrossRef]

Cohen, A.

A. Cohen, J. Kovacevic, “Wavelets: the mathematical background,” Proc. IEEE 84, 514–522 (1996).
[CrossRef]

Cohen, L.

L. Cohen, “Time–frequency distribution,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

L. Cohen, Time–Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1995).

Fainman, Y.

Hatami-Hanza, H.

H. Hatami-Hanza, A. Mostofi, P. L. Chu, “A multilevel soliton communication system,” J. Lightwave Technol. 15, 6–19 (1997).
[CrossRef]

Heritage, J. P.

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlonson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682–696 (1986).
[CrossRef]

Heuring, V. P.

V. P. Heuring, H. F. Jordan, J. P. Pratt, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
[CrossRef]

Jordan, H. F.

V. P. Heuring, H. F. Jordan, J. P. Pratt, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
[CrossRef]

Kane, D. J.

D. J. Kane, R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

Kanterakis, E. G.

Katz, A.

Kovacevic, J.

A. Cohen, J. Kovacevic, “Wavelets: the mathematical background,” Proc. IEEE 84, 514–522 (1996).
[CrossRef]

Leaird, D. E.

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

Li, Y.

Lu, X. J.

Mazurenko, Y. T.

Mostofi, A.

H. Hatami-Hanza, A. Mostofi, P. L. Chu, “A multilevel soliton communication system,” J. Lightwave Technol. 15, 6–19 (1997).
[CrossRef]

Nelson, K. A.

Nuss, M. C.

H. M. Ozaktas, M. C. Nuss, “Time-variant linear pulse processing,” Opt. Commun. 131, 114–118 (1996).
[CrossRef]

Ozaktas, H. M.

H. M. Ozaktas, M. C. Nuss, “Time-variant linear pulse processing,” Opt. Commun. 131, 114–118 (1996).
[CrossRef]

Patel, J. S.

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

Pratt, J. P.

V. P. Heuring, H. F. Jordan, J. P. Pratt, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
[CrossRef]

Purchase, K. G.

Sun, P. C.

Taga, H.

H. Taga, “Long distance transmission experiments using the WDM technology,” J. Lightwave Technol. 14, 1287–1298 (1996).
[CrossRef]

Thurston, R. N.

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlonson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682–696 (1986).
[CrossRef]

Tolimieri, R.

Tomlonson, W. J.

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlonson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682–696 (1986).
[CrossRef]

Trebino, R.

D. J. Kane, R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

Wagner, K.

Wefers, M. M.

Weiner, A. M.

M. M. Wefers, K. A. Nelson, A. M. Weiner, “Multidimensional shaping of ultrafast optical waveforms,” Opt. Lett. 21, 746–748 (1996).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlonson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682–696 (1986).
[CrossRef]

Wullert, J. R.

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

Yu, P. K. L.

Zhang, Y.

IEEE J. Quantum Electron. (3)

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlonson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682–696 (1986).
[CrossRef]

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

D. J. Kane, R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

J. Lightwave Technol. (5)

C. A. Brackett, “Is there an emerging consensus on WDM networking?” J. Lightwave Technol. 14, 936–941 (1996).

H. Taga, “Long distance transmission experiments using the WDM technology,” J. Lightwave Technol. 14, 1287–1298 (1996).
[CrossRef]

V. P. Heuring, H. F. Jordan, J. P. Pratt, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
[CrossRef]

H. Hatami-Hanza, A. Mostofi, P. L. Chu, “A multilevel soliton communication system,” J. Lightwave Technol. 15, 6–19 (1997).
[CrossRef]

S. Baroni, P. Bayvel, “Wavelength requirements in arbitrarily connected wavelength-routed optical networks,” J. Lightwave Technol. 15, 242–251 (1997).
[CrossRef]

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

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

Opt. Commun. (1)

H. M. Ozaktas, M. C. Nuss, “Time-variant linear pulse processing,” Opt. Commun. 131, 114–118 (1996).
[CrossRef]

Opt. Lett. (4)

Opt. Spectrosc. (USSR) (1)

Y. T. Mazurenko, “Reconstruction of a nonstationary wave field by holography in a 3-D medium,” Opt. Spectrosc. (USSR) 57, 343–344 (1984).

Proc. IEEE (2)

L. Cohen, “Time–frequency distribution,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

A. Cohen, J. Kovacevic, “Wavelets: the mathematical background,” Proc. IEEE 84, 514–522 (1996).
[CrossRef]

Other (1)

L. Cohen, Time–Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1995).

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