Abstract

A new self-referencing technique to characterize the temporal electric field of a short optical pulse is presented. The group delay of the pulse is directly obtained from two projections of the Wigner–Ville function after rotation of the pulse in chronocyclic space. Implementation of the technique requires only quadratic temporal phase modulation and two spectrum measurements, from which the electric field is directly and unambiguously reconstructed without any assumption. A device based on these principles is used to characterize the electric field of a 2-ps optical pulse.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. Walmsley and V. Wong, J. Opt. Soc. Am. B 13, 2453 (1996).
    [CrossRef]
  2. R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
    [CrossRef]
  3. V. Wong and I. Walmsley, J. Opt. Soc. Am. B 14, 944 (1997).
    [CrossRef]
  4. C. Dorrer and I. Kang, Opt. Lett. 27, 1315 (2002).
    [CrossRef]
  5. C. Iaconis and I. A. Walmsley, Opt. Lett. 23, 792 (1998).
    [CrossRef]
  6. C. Dorrer and I. Kang, Opt. Lett. 28, 477 (2003).
    [CrossRef] [PubMed]
  7. M. Beck, M. Raymer, I. Walmsley, and V. Wong, Opt. Lett. 18, 2041 (1993).
    [CrossRef]
  8. M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, J. Opt. (Paris) 15, 385 (1984).
    [CrossRef]
  9. M. Kaufman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
    [CrossRef]
  10. T. Alieva, M. J. Bastiaans, and L. J. Stankovic, in 11th IEEE Workshop on Signal Process, Statistical Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), pp. 325–328.
    [CrossRef]
  11. T. Alieva, M. J. Bastiaans, and L. J. Stankovic, IEEE Trans. Signal Process. 51, 112 (2003).
    [CrossRef]
  12. L. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, IEEE J. Quantum Electron. 36, 795 (2000).
    [CrossRef]
  13. C. V. Bennet and B. H. Kolner, Opt. Lett. 24, 783 (1999).
    [CrossRef]

2003

T. Alieva, M. J. Bastiaans, and L. J. Stankovic, IEEE Trans. Signal Process. 51, 112 (2003).
[CrossRef]

C. Dorrer and I. Kang, Opt. Lett. 28, 477 (2003).
[CrossRef] [PubMed]

2002

2001

T. Alieva, M. J. Bastiaans, and L. J. Stankovic, in 11th IEEE Workshop on Signal Process, Statistical Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), pp. 325–328.
[CrossRef]

2000

L. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, IEEE J. Quantum Electron. 36, 795 (2000).
[CrossRef]

1999

1998

1997

V. Wong and I. Walmsley, J. Opt. Soc. Am. B 14, 944 (1997).
[CrossRef]

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

1996

1994

M. Kaufman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

1993

1984

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, J. Opt. (Paris) 15, 385 (1984).
[CrossRef]

Alieva, T.

T. Alieva, M. J. Bastiaans, and L. J. Stankovic, IEEE Trans. Signal Process. 51, 112 (2003).
[CrossRef]

T. Alieva, M. J. Bastiaans, and L. J. Stankovic, in 11th IEEE Workshop on Signal Process, Statistical Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), pp. 325–328.
[CrossRef]

Banyai, W.

M. Kaufman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Barthélémy, A.

L. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, IEEE J. Quantum Electron. 36, 795 (2000).
[CrossRef]

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, J. Opt. (Paris) 15, 385 (1984).
[CrossRef]

Bastiaans, M. J.

T. Alieva, M. J. Bastiaans, and L. J. Stankovic, IEEE Trans. Signal Process. 51, 112 (2003).
[CrossRef]

T. Alieva, M. J. Bastiaans, and L. J. Stankovic, in 11th IEEE Workshop on Signal Process, Statistical Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), pp. 325–328.
[CrossRef]

Beck, M.

Bennet, C. V.

Bloom, D.

M. Kaufman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Colombeau, B.

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, J. Opt. (Paris) 15, 385 (1984).
[CrossRef]

Delong, K. W.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Dorrer, C.

Fittinghoff, D. N.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Froehly, C.

L. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, IEEE J. Quantum Electron. 36, 795 (2000).
[CrossRef]

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, J. Opt. (Paris) 15, 385 (1984).
[CrossRef]

Godil, A.

M. Kaufman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Iaconis, C.

Kane, D. J.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Kang, I.

Kaufman, M.

M. Kaufman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Kolner, B. H.

Krumbugel, M. A.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Louradour, F.

L. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, IEEE J. Quantum Electron. 36, 795 (2000).
[CrossRef]

Messager, V.

L. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, IEEE J. Quantum Electron. 36, 795 (2000).
[CrossRef]

Mouradian, L.

L. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, IEEE J. Quantum Electron. 36, 795 (2000).
[CrossRef]

Raymer, M.

Richman, B. A.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Stankovic, L. J.

T. Alieva, M. J. Bastiaans, and L. J. Stankovic, IEEE Trans. Signal Process. 51, 112 (2003).
[CrossRef]

T. Alieva, M. J. Bastiaans, and L. J. Stankovic, in 11th IEEE Workshop on Signal Process, Statistical Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), pp. 325–328.
[CrossRef]

Sweetser, J. N.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Trebino, R.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Vampouille, M.

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, J. Opt. (Paris) 15, 385 (1984).
[CrossRef]

Walmsley, I.

Walmsley, I. A.

Wong, V.

Appl. Phys. Lett.

M. Kaufman, W. Banyai, A. Godil, and D. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

IEEE J. Quantum Electron.

L. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, IEEE J. Quantum Electron. 36, 795 (2000).
[CrossRef]

IEEE Trans. Signal Process.

T. Alieva, M. J. Bastiaans, and L. J. Stankovic, IEEE Trans. Signal Process. 51, 112 (2003).
[CrossRef]

J. Opt. (Paris)

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, J. Opt. (Paris) 15, 385 (1984).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Rev. Sci. Instrum.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Other

T. Alieva, M. J. Bastiaans, and L. J. Stankovic, in 11th IEEE Workshop on Signal Process, Statistical Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), pp. 325–328.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) W-V distribution of the pulse, rotation (Rot.) in chronocyclic space, and projection (Proj.) on the frequency axis. (b) Chronocyclic tomography uses a large number of projections, (c) the time-to-frequency converter uses the projection for α=π/2, and (d) simplified chronocyclic tomography uses the projections for two small angles.

Fig. 2
Fig. 2

Implementation of simplified chronocyclic tomography by use of a temporal phase modulator. A first spectrum is measured when the pulse is synchronized with the maximum of the phase modulation. A second spectrum is measured when the pulse is synchronized with the minimum of the modulation.

Fig. 3
Fig. 3

Spectrum and phase of the initial pulse (respectively, solid and dashed curves) of the pulse after 179 m (respectively, upward-pointing triangles and circles) and 330 m (respectively, downward-pointing triangles and squares) of standard single-mode fiber. The spectral intensities are identical, but the spectral phases differ by a quadratic phase.

Fig. 4
Fig. 4

Second-order intensity autocorrelation calculated from the measured electric fields (circles) and measured with a second-order autocorrelator (solid curves) for the initial pulse on (a) a linear and (b) a logarithmic scale.

Equations (7)

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

Wt,ω=E˜ω+ω2E˜*ω-ω2exp-iωtdω2π.
Iαω=Wt cosα+ω sinα, ω cosα-t sinαdt.
Iαω=Wt+ωα, ω-tαdt.
Iαα=ωWt-tWωdt=-ωtWdt.
Iαα=-ωIφω.
Etexpiψ2t2
Iψψ=ωIφω,

Metrics