Abstract

We have measured the performance of a real spectral phase interferometry for direct electric field reconstruction (SPIDER) apparatus operating under suboptimal conditions. We analyzed the errors in SPIDER’s measurements of the temporal phases and intensities of 50-fs ultrashort laser pulses as a function of the additive noise in the detected signal. It was found that SPIDER performs exceptionally well, particularly in the case of additive noise. Specifically, a signal with 10% noise yields a pulse that has a mere 2% error in its intensity profile and a phase that differs from the nominal value by 0.2 rad. Furthermore, we quantified SPIDER’s performance with limited detector resolution and as a function of signal averaging.

© 2004 Optical Society of America

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  1. P. T. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, M. C. Downer, “Frequency-domain interferometric second-harmonic spectroscopy,” Opt. Lett. 24, 496–498 (1999).
    [CrossRef]
  2. H. Kapteyn, M. Murnane, “Ultrashort light pulses: life in the fast lane. Researchers can now routinely use lasers to generate femtosecond light pulses in the lab, making it possible to study processes ranging from photosynthesis to the switching of electronic circuits. How the latest advances could lead to the generation of even shorter pulses,” Phys. World 12, 31–35 (1999).
  3. J.-M. Hopkins, W. Sibbett, “Ultrashort-pulse lasers: big payoffs in a flash-imaging, microelectronic manufacturing, fiber optics and industrial chemistry are eagerly adopting lasers that emit light in powerful bursts lasting only quadrillionths of a second,” Sci. Am. 283, 72–79 (2000).
    [CrossRef] [PubMed]
  4. C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
    [CrossRef] [PubMed]
  5. D. Meshulach, Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature (London) 396, 239–241 (1998).
    [CrossRef]
  6. I. Walmsley, R. Trebino, “Measuring fast pulses with slow detectors,” Opt. Photon. News 7, 23–28 (1996).
    [CrossRef]
  7. D. J. Kane, R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
    [CrossRef]
  8. J. Paye, M. Ramaswamy, J. G. Fujimoto, E. P. Ippen, “Measurement of the amplitude and phase of ultrashort light pulses from spectrally resolved autocorrelation,” Opt. Lett. 18, 1946–1948 (1993).
    [CrossRef] [PubMed]
  9. G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, I. P. Christov, “Ultrashort optical waveform measurements using frequency-resolved optical gating,” Opt. Lett. 20, 743–745 (1995).
    [CrossRef] [PubMed]
  10. K. W. DeLong, R. Trebino, W. E. White, “Simultaneous recovery of two ultrashort laser pulses from a single spectrogram,” J. Opt. Soc. Am. B 12, 2463–2466 (1995).
    [CrossRef]
  11. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
    [CrossRef] [PubMed]
  12. C. W. Siders, J. L. W. Siders, F. G. Omenetto, A. J. Taylor, “Multipulse interferometric frequency-resolved optical gating (invited paper),” IEEE J. Quantum Electron. 35, 432–440 (1999).
    [CrossRef]
  13. R. Trebino, P. O’Shea, M. Kimmel, X. Gu, “Measuring ultrashort laser pulses just got a lot easier,” Opt. Photon. News 12, 22–25 (2001).
    [CrossRef]
  14. M. A. Franco, H. R. Lange, J. F. Ripoche, B. S. Prade, A. Mysyrowicz, “Characterization of ultra-short pulses by cross-phase modulation,” Opt. Commun. 140, 331–340 (1997).
    [CrossRef]
  15. J. W. Nicholson, J. Jasapara, W. Rudolph, F. G. Omenetto, A. J. Taylor, “Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements,” Opt. Lett. 24, 1774–1776 (1999).
    [CrossRef]
  16. K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
    [CrossRef] [PubMed]
  17. I. G. Cormack, W. Sibbett, R. Ortega-Martinez, D. T. Reid, “Ultrashort pulse characterization using a scanning Fabry-Perot etalon enabling rapid acquisition and retrieval of a sonogram at rates up to 1.52 Hz,” Rev. Sci. Instrum. 72, 4071–4079 (2001).
    [CrossRef]
  18. L. Lepetit, G. Cheriaux, M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995).
    [CrossRef]
  19. C. Iaconis, I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
    [CrossRef]
  20. C. Iaconis, I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
    [CrossRef]
  21. M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
    [CrossRef]
  22. C. Dorrer, I. A. Walmsley, “Accuracy criterion for ultrashort pulse characterization techniques: application to spectral phase interferometry for direct electric field reconstruction,” J. Opt. Soc. Am. B 19, 1019–1029 (2002).
    [CrossRef]
  23. T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, I. A. Walmsley, “Real-time SPIDER: ultrashort pulse characterization at 20 Hz,” Opt. Exp. 5, 134–143 (1999), http://www.opticsexpress.org .
    [CrossRef]
  24. W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
    [CrossRef] [PubMed]
  25. C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
    [CrossRef]
  26. L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1314–1316 (1999).
    [CrossRef]
  27. C. Dorrer, “Influence of the calibration of the detector on spectral interferometry,” J. Opt. Soc. Am. B 16, 1160–1168 (1999).
    [CrossRef]
  28. S. Yeremenko, A. Baltuska, M. S. Pshenichnikov, D. A. Wiersma, “The criterion of pulse reconstruction quality based on Wigner representation,” Appl. Phys. B 70, S109–S117 (2000).
    [CrossRef]
  29. C. Dorrer, I. A. Walmsley, “Precision and consistency criteria in spectral phase interferometry for direct electric-field reconstruction,” J. Opt. Soc. Am. B 19, 1030–1038 (2002).
    [CrossRef]
  30. P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, Boston, Mass., 1992).
  31. See, for example, Kapteyn-Murnane Laboratories at http://www.kmlabs.com .
  32. C. Dorrer, Lucent Technologies, Murray Hill, N.J. 07974-0636 (personal communication, 2001).
  33. C. Dorrer, “Implementation of spectral phase interferometry for direct electric-field reconstruction with a simultaneously recorded reference interferogram,” Opt. Lett. 24, 1532–1534 (1999).
    [CrossRef]
  34. D. N. Fittinghoff, K. W. DeLong, R. Trebino, C. L. Ladera, “Noise sensitivity in frequency-resolved optical-gating measurements of ultrashort pulses,” J. Opt. Soc. Am. B 12, 1955–1967 (1995).
    [CrossRef]

2003 (1)

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
[CrossRef] [PubMed]

2002 (2)

2001 (2)

I. G. Cormack, W. Sibbett, R. Ortega-Martinez, D. T. Reid, “Ultrashort pulse characterization using a scanning Fabry-Perot etalon enabling rapid acquisition and retrieval of a sonogram at rates up to 1.52 Hz,” Rev. Sci. Instrum. 72, 4071–4079 (2001).
[CrossRef]

R. Trebino, P. O’Shea, M. Kimmel, X. Gu, “Measuring ultrashort laser pulses just got a lot easier,” Opt. Photon. News 12, 22–25 (2001).
[CrossRef]

2000 (3)

J.-M. Hopkins, W. Sibbett, “Ultrashort-pulse lasers: big payoffs in a flash-imaging, microelectronic manufacturing, fiber optics and industrial chemistry are eagerly adopting lasers that emit light in powerful bursts lasting only quadrillionths of a second,” Sci. Am. 283, 72–79 (2000).
[CrossRef] [PubMed]

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

S. Yeremenko, A. Baltuska, M. S. Pshenichnikov, D. A. Wiersma, “The criterion of pulse reconstruction quality based on Wigner representation,” Appl. Phys. B 70, S109–S117 (2000).
[CrossRef]

1999 (10)

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, I. A. Walmsley, “Real-time SPIDER: ultrashort pulse characterization at 20 Hz,” Opt. Exp. 5, 134–143 (1999), http://www.opticsexpress.org .
[CrossRef]

C. Dorrer, “Implementation of spectral phase interferometry for direct electric-field reconstruction with a simultaneously recorded reference interferogram,” Opt. Lett. 24, 1532–1534 (1999).
[CrossRef]

C. Iaconis, I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1314–1316 (1999).
[CrossRef]

C. Dorrer, “Influence of the calibration of the detector on spectral interferometry,” J. Opt. Soc. Am. B 16, 1160–1168 (1999).
[CrossRef]

P. T. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, M. C. Downer, “Frequency-domain interferometric second-harmonic spectroscopy,” Opt. Lett. 24, 496–498 (1999).
[CrossRef]

H. Kapteyn, M. Murnane, “Ultrashort light pulses: life in the fast lane. Researchers can now routinely use lasers to generate femtosecond light pulses in the lab, making it possible to study processes ranging from photosynthesis to the switching of electronic circuits. How the latest advances could lead to the generation of even shorter pulses,” Phys. World 12, 31–35 (1999).

J. W. Nicholson, J. Jasapara, W. Rudolph, F. G. Omenetto, A. J. Taylor, “Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements,” Opt. Lett. 24, 1774–1776 (1999).
[CrossRef]

C. W. Siders, J. L. W. Siders, F. G. Omenetto, A. J. Taylor, “Multipulse interferometric frequency-resolved optical gating (invited paper),” IEEE J. Quantum Electron. 35, 432–440 (1999).
[CrossRef]

1998 (2)

D. Meshulach, Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature (London) 396, 239–241 (1998).
[CrossRef]

C. Iaconis, I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
[CrossRef]

1997 (1)

M. A. Franco, H. R. Lange, J. F. Ripoche, B. S. Prade, A. Mysyrowicz, “Characterization of ultra-short pulses by cross-phase modulation,” Opt. Commun. 140, 331–340 (1997).
[CrossRef]

1996 (3)

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

I. Walmsley, R. Trebino, “Measuring fast pulses with slow detectors,” Opt. Photon. News 7, 23–28 (1996).
[CrossRef]

C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
[CrossRef] [PubMed]

1995 (5)

1993 (2)

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. Paye, M. Ramaswamy, J. G. Fujimoto, E. P. Ippen, “Measurement of the amplitude and phase of ultrashort light pulses from spectrally resolved autocorrelation,” Opt. Lett. 18, 1946–1948 (1993).
[CrossRef] [PubMed]

Aktsipetrov, O. A.

P. T. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, M. C. Downer, “Frequency-domain interferometric second-harmonic spectroscopy,” Opt. Lett. 24, 496–498 (1999).
[CrossRef]

Anderson, M. E.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, I. A. Walmsley, “Real-time SPIDER: ultrashort pulse characterization at 20 Hz,” Opt. Exp. 5, 134–143 (1999), http://www.opticsexpress.org .
[CrossRef]

Babine, A.

C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
[CrossRef] [PubMed]

Baltuska, A.

S. Yeremenko, A. Baltuska, M. S. Pshenichnikov, D. A. Wiersma, “The criterion of pulse reconstruction quality based on Wigner representation,” Appl. Phys. B 70, S109–S117 (2000).
[CrossRef]

Bevington, P. R.

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, Boston, Mass., 1992).

Biegert, J.

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
[CrossRef] [PubMed]

Blanc, S. P. L.

C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
[CrossRef] [PubMed]

Bowie, J. L.

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

Bromage, J.

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, I. A. Walmsley, “Real-time SPIDER: ultrashort pulse characterization at 20 Hz,” Opt. Exp. 5, 134–143 (1999), http://www.opticsexpress.org .
[CrossRef]

Chambaret, J. P.

C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
[CrossRef]

Cheriaux, G.

Christov, I. P.

Chu, K. C.

K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
[CrossRef] [PubMed]

Cormack, I. G.

I. G. Cormack, W. Sibbett, R. Ortega-Martinez, D. T. Reid, “Ultrashort pulse characterization using a scanning Fabry-Perot etalon enabling rapid acquisition and retrieval of a sonogram at rates up to 1.52 Hz,” Rev. Sci. Instrum. 72, 4071–4079 (2001).
[CrossRef]

de Araujo, L. E. E.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

de Beauvoir, B.

C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
[CrossRef]

DeLong, K. W.

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

K. W. DeLong, R. Trebino, W. E. White, “Simultaneous recovery of two ultrashort laser pulses from a single spectrogram,” J. Opt. Soc. Am. B 12, 2463–2466 (1995).
[CrossRef]

G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, I. P. Christov, “Ultrashort optical waveform measurements using frequency-resolved optical gating,” Opt. Lett. 20, 743–745 (1995).
[CrossRef] [PubMed]

D. N. Fittinghoff, K. W. DeLong, R. Trebino, C. L. Ladera, “Noise sensitivity in frequency-resolved optical-gating measurements of ultrashort pulses,” J. Opt. Soc. Am. B 12, 1955–1967 (1995).
[CrossRef]

Dienes, A.

K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
[CrossRef] [PubMed]

Dorrer, C.

C. Dorrer, I. A. Walmsley, “Accuracy criterion for ultrashort pulse characterization techniques: application to spectral phase interferometry for direct electric field reconstruction,” J. Opt. Soc. Am. B 19, 1019–1029 (2002).
[CrossRef]

C. Dorrer, I. A. Walmsley, “Precision and consistency criteria in spectral phase interferometry for direct electric-field reconstruction,” J. Opt. Soc. Am. B 19, 1030–1038 (2002).
[CrossRef]

C. Dorrer, “Implementation of spectral phase interferometry for direct electric-field reconstruction with a simultaneously recorded reference interferogram,” Opt. Lett. 24, 1532–1534 (1999).
[CrossRef]

C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
[CrossRef]

C. Dorrer, “Influence of the calibration of the detector on spectral interferometry,” J. Opt. Soc. Am. B 16, 1160–1168 (1999).
[CrossRef]

C. Dorrer, Lucent Technologies, Murray Hill, N.J. 07974-0636 (personal communication, 2001).

Downer, M. C.

P. T. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, M. C. Downer, “Frequency-domain interferometric second-harmonic spectroscopy,” Opt. Lett. 24, 496–498 (1999).
[CrossRef]

C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
[CrossRef] [PubMed]

Fisher, D.

C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
[CrossRef] [PubMed]

Fittinghoff, D. N.

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

D. N. Fittinghoff, K. W. DeLong, R. Trebino, C. L. Ladera, “Noise sensitivity in frequency-resolved optical-gating measurements of ultrashort pulses,” J. Opt. Soc. Am. B 12, 1955–1967 (1995).
[CrossRef]

Franco, M. A.

M. A. Franco, H. R. Lange, J. F. Ripoche, B. S. Prade, A. Mysyrowicz, “Characterization of ultra-short pulses by cross-phase modulation,” Opt. Commun. 140, 331–340 (1997).
[CrossRef]

Fujimoto, J. G.

Gallmann, L.

Grant, R. S.

K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
[CrossRef] [PubMed]

Gu, X.

R. Trebino, P. O’Shea, M. Kimmel, X. Gu, “Measuring ultrashort laser pulses just got a lot easier,” Opt. Photon. News 12, 22–25 (2001).
[CrossRef]

Heritage, J. P.

K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
[CrossRef] [PubMed]

Hopkins, J.-M.

J.-M. Hopkins, W. Sibbett, “Ultrashort-pulse lasers: big payoffs in a flash-imaging, microelectronic manufacturing, fiber optics and industrial chemistry are eagerly adopting lasers that emit light in powerful bursts lasting only quadrillionths of a second,” Sci. Am. 283, 72–79 (2000).
[CrossRef] [PubMed]

Iaconis, C.

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, I. A. Walmsley, “Real-time SPIDER: ultrashort pulse characterization at 20 Hz,” Opt. Exp. 5, 134–143 (1999), http://www.opticsexpress.org .
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1314–1316 (1999).
[CrossRef]

C. Iaconis, I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

C. Iaconis, I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
[CrossRef]

Ippen, E. P.

Jasapara, J.

Jennings, R. T.

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

Jiang, Y.

P. T. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, M. C. Downer, “Frequency-domain interferometric second-harmonic spectroscopy,” Opt. Lett. 24, 496–498 (1999).
[CrossRef]

Joffre, M.

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]

Kapteyn, H.

H. Kapteyn, M. Murnane, “Ultrashort light pulses: life in the fast lane. Researchers can now routinely use lasers to generate femtosecond light pulses in the lab, making it possible to study processes ranging from photosynthesis to the switching of electronic circuits. How the latest advances could lead to the generation of even shorter pulses,” Phys. World 12, 31–35 (1999).

Kapteyn, H. C.

Keller, U.

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
[CrossRef] [PubMed]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1314–1316 (1999).
[CrossRef]

Kimmel, M.

R. Trebino, P. O’Shea, M. Kimmel, X. Gu, “Measuring ultrashort laser pulses just got a lot easier,” Opt. Photon. News 12, 22–25 (2001).
[CrossRef]

Kornelis, W.

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
[CrossRef] [PubMed]

Kosik, E. M.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

Krumbugel, M. A.

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

Ladera, C. L.

Lange, H. R.

M. A. Franco, H. R. Lange, J. F. Ripoche, B. S. Prade, A. Mysyrowicz, “Characterization of ultra-short pulses by cross-phase modulation,” Opt. Commun. 140, 331–340 (1997).
[CrossRef]

LeBlanc, C.

C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
[CrossRef]

Lepetit, L.

Liu, K. X.

K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
[CrossRef] [PubMed]

Matuschek, N.

Meshulach, D.

D. Meshulach, Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature (London) 396, 239–241 (1998).
[CrossRef]

Mishina, E. D.

P. T. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, M. C. Downer, “Frequency-domain interferometric second-harmonic spectroscopy,” Opt. Lett. 24, 496–498 (1999).
[CrossRef]

Murnane, M.

H. Kapteyn, M. Murnane, “Ultrashort light pulses: life in the fast lane. Researchers can now routinely use lasers to generate femtosecond light pulses in the lab, making it possible to study processes ranging from photosynthesis to the switching of electronic circuits. How the latest advances could lead to the generation of even shorter pulses,” Phys. World 12, 31–35 (1999).

Murnane, M. M.

Mysyrowicz, A.

M. A. Franco, H. R. Lange, J. F. Ripoche, B. S. Prade, A. Mysyrowicz, “Characterization of ultra-short pulses by cross-phase modulation,” Opt. Commun. 140, 331–340 (1997).
[CrossRef]

Nicholson, J. W.

Nisoli, M.

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
[CrossRef] [PubMed]

O’Shea, P.

R. Trebino, P. O’Shea, M. Kimmel, X. Gu, “Measuring ultrashort laser pulses just got a lot easier,” Opt. Photon. News 12, 22–25 (2001).
[CrossRef]

Omenetto, F. G.

C. W. Siders, J. L. W. Siders, F. G. Omenetto, A. J. Taylor, “Multipulse interferometric frequency-resolved optical gating (invited paper),” IEEE J. Quantum Electron. 35, 432–440 (1999).
[CrossRef]

J. W. Nicholson, J. Jasapara, W. Rudolph, F. G. Omenetto, A. J. Taylor, “Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements,” Opt. Lett. 24, 1774–1776 (1999).
[CrossRef]

Ortega-Martinez, R.

I. G. Cormack, W. Sibbett, R. Ortega-Martinez, D. T. Reid, “Ultrashort pulse characterization using a scanning Fabry-Perot etalon enabling rapid acquisition and retrieval of a sonogram at rates up to 1.52 Hz,” Rev. Sci. Instrum. 72, 4071–4079 (2001).
[CrossRef]

Paye, J.

Prade, B. S.

M. A. Franco, H. R. Lange, J. F. Ripoche, B. S. Prade, A. Mysyrowicz, “Characterization of ultra-short pulses by cross-phase modulation,” Opt. Commun. 140, 331–340 (1997).
[CrossRef]

Pshenichnikov, M. S.

S. Yeremenko, A. Baltuska, M. S. Pshenichnikov, D. A. Wiersma, “The criterion of pulse reconstruction quality based on Wigner representation,” Appl. Phys. B 70, S109–S117 (2000).
[CrossRef]

Ramaswamy, M.

Ranc, S.

C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
[CrossRef]

Reid, D. T.

I. G. Cormack, W. Sibbett, R. Ortega-Martinez, D. T. Reid, “Ultrashort pulse characterization using a scanning Fabry-Perot etalon enabling rapid acquisition and retrieval of a sonogram at rates up to 1.52 Hz,” Rev. Sci. Instrum. 72, 4071–4079 (2001).
[CrossRef]

Ripoche, J. F.

M. A. Franco, H. R. Lange, J. F. Ripoche, B. S. Prade, A. Mysyrowicz, “Characterization of ultra-short pulses by cross-phase modulation,” Opt. Commun. 140, 331–340 (1997).
[CrossRef]

Robinson, D. K.

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, Boston, Mass., 1992).

Rousseau, J. P.

C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
[CrossRef]

Rousseau, P.

C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
[CrossRef]

Rudolph, W.

Rundquist, A.

Salin, F.

C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
[CrossRef]

Sansone, G.

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
[CrossRef] [PubMed]

Sergeev, A.

C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
[CrossRef] [PubMed]

Shuman, T. M.

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, I. A. Walmsley, “Real-time SPIDER: ultrashort pulse characterization at 20 Hz,” Opt. Exp. 5, 134–143 (1999), http://www.opticsexpress.org .
[CrossRef]

Sibbett, W.

I. G. Cormack, W. Sibbett, R. Ortega-Martinez, D. T. Reid, “Ultrashort pulse characterization using a scanning Fabry-Perot etalon enabling rapid acquisition and retrieval of a sonogram at rates up to 1.52 Hz,” Rev. Sci. Instrum. 72, 4071–4079 (2001).
[CrossRef]

J.-M. Hopkins, W. Sibbett, “Ultrashort-pulse lasers: big payoffs in a flash-imaging, microelectronic manufacturing, fiber optics and industrial chemistry are eagerly adopting lasers that emit light in powerful bursts lasting only quadrillionths of a second,” Sci. Am. 283, 72–79 (2000).
[CrossRef] [PubMed]

Siders, C. W.

C. W. Siders, J. L. W. Siders, F. G. Omenetto, A. J. Taylor, “Multipulse interferometric frequency-resolved optical gating (invited paper),” IEEE J. Quantum Electron. 35, 432–440 (1999).
[CrossRef]

C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
[CrossRef] [PubMed]

Siders, J. L. W.

C. W. Siders, J. L. W. Siders, F. G. Omenetto, A. J. Taylor, “Multipulse interferometric frequency-resolved optical gating (invited paper),” IEEE J. Quantum Electron. 35, 432–440 (1999).
[CrossRef]

Silberberg, Y.

D. Meshulach, Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature (London) 396, 239–241 (1998).
[CrossRef]

Silvestri, S. D.

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
[CrossRef] [PubMed]

Steinmeyer, G.

Stepanov, A.

C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
[CrossRef] [PubMed]

Sullivan, A.

K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
[CrossRef] [PubMed]

Sutter, D. H.

Sweetser, J. N.

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

Taft, G.

Tajima, T.

C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
[CrossRef] [PubMed]

Taylor, A. J.

C. W. Siders, J. L. W. Siders, F. G. Omenetto, A. J. Taylor, “Multipulse interferometric frequency-resolved optical gating (invited paper),” IEEE J. Quantum Electron. 35, 432–440 (1999).
[CrossRef]

J. W. Nicholson, J. Jasapara, W. Rudolph, F. G. Omenetto, A. J. Taylor, “Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements,” Opt. Lett. 24, 1774–1776 (1999).
[CrossRef]

Tisch, J. W. G.

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
[CrossRef] [PubMed]

Trebino, R.

R. Trebino, P. O’Shea, M. Kimmel, X. Gu, “Measuring ultrashort laser pulses just got a lot easier,” Opt. Photon. News 12, 22–25 (2001).
[CrossRef]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

I. Walmsley, R. Trebino, “Measuring fast pulses with slow detectors,” Opt. Photon. News 7, 23–28 (1996).
[CrossRef]

K. W. DeLong, R. Trebino, W. E. White, “Simultaneous recovery of two ultrashort laser pulses from a single spectrogram,” J. Opt. Soc. Am. B 12, 2463–2466 (1995).
[CrossRef]

G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, I. P. Christov, “Ultrashort optical waveform measurements using frequency-resolved optical gating,” Opt. Lett. 20, 743–745 (1995).
[CrossRef] [PubMed]

D. N. Fittinghoff, K. W. DeLong, R. Trebino, C. L. Ladera, “Noise sensitivity in frequency-resolved optical-gating measurements of ultrashort pulses,” J. Opt. Soc. Am. B 12, 1955–1967 (1995).
[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]

Vozzi, C.

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
[CrossRef] [PubMed]

Walmsley, I.

I. Walmsley, R. Trebino, “Measuring fast pulses with slow detectors,” Opt. Photon. News 7, 23–28 (1996).
[CrossRef]

Walmsley, I. A.

C. Dorrer, I. A. Walmsley, “Precision and consistency criteria in spectral phase interferometry for direct electric-field reconstruction,” J. Opt. Soc. Am. B 19, 1030–1038 (2002).
[CrossRef]

C. Dorrer, I. A. Walmsley, “Accuracy criterion for ultrashort pulse characterization techniques: application to spectral phase interferometry for direct electric field reconstruction,” J. Opt. Soc. Am. B 19, 1019–1029 (2002).
[CrossRef]

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

C. Iaconis, I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1314–1316 (1999).
[CrossRef]

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, I. A. Walmsley, “Real-time SPIDER: ultrashort pulse characterization at 20 Hz,” Opt. Exp. 5, 134–143 (1999), http://www.opticsexpress.org .
[CrossRef]

C. Iaconis, I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
[CrossRef]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

Waxer, L.

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, I. A. Walmsley, “Real-time SPIDER: ultrashort pulse characterization at 20 Hz,” Opt. Exp. 5, 134–143 (1999), http://www.opticsexpress.org .
[CrossRef]

White, W. E.

K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
[CrossRef] [PubMed]

K. W. DeLong, R. Trebino, W. E. White, “Simultaneous recovery of two ultrashort laser pulses from a single spectrogram,” J. Opt. Soc. Am. B 12, 2463–2466 (1995).
[CrossRef]

Wiersma, D. A.

S. Yeremenko, A. Baltuska, M. S. Pshenichnikov, D. A. Wiersma, “The criterion of pulse reconstruction quality based on Wigner representation,” Appl. Phys. B 70, S109–S117 (2000).
[CrossRef]

Wilson, P. T.

P. T. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, M. C. Downer, “Frequency-domain interferometric second-harmonic spectroscopy,” Opt. Lett. 24, 496–498 (1999).
[CrossRef]

Yeremenko, S.

S. Yeremenko, A. Baltuska, M. S. Pshenichnikov, D. A. Wiersma, “The criterion of pulse reconstruction quality based on Wigner representation,” Appl. Phys. B 70, S109–S117 (2000).
[CrossRef]

Appl. Phys. B (2)

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[CrossRef]

S. Yeremenko, A. Baltuska, M. S. Pshenichnikov, D. A. Wiersma, “The criterion of pulse reconstruction quality based on Wigner representation,” Appl. Phys. B 70, S109–S117 (2000).
[CrossRef]

IEEE J. Quantum Electron. (3)

C. Iaconis, I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[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]

C. W. Siders, J. L. W. Siders, F. G. Omenetto, A. J. Taylor, “Multipulse interferometric frequency-resolved optical gating (invited paper),” IEEE J. Quantum Electron. 35, 432–440 (1999).
[CrossRef]

J. Opt. Soc. Am. B (2)

K. W. DeLong, R. Trebino, W. E. White, “Simultaneous recovery of two ultrashort laser pulses from a single spectrogram,” J. Opt. Soc. Am. B 12, 2463–2466 (1995).
[CrossRef]

C. Dorrer, “Influence of the calibration of the detector on spectral interferometry,” J. Opt. Soc. Am. B 16, 1160–1168 (1999).
[CrossRef]

J. Opt. Soc. Am. B (4)

Nature (London) (1)

D. Meshulach, Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature (London) 396, 239–241 (1998).
[CrossRef]

Opt. Commun. (1)

M. A. Franco, H. R. Lange, J. F. Ripoche, B. S. Prade, A. Mysyrowicz, “Characterization of ultra-short pulses by cross-phase modulation,” Opt. Commun. 140, 331–340 (1997).
[CrossRef]

Opt. Exp. (1)

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, I. A. Walmsley, “Real-time SPIDER: ultrashort pulse characterization at 20 Hz,” Opt. Exp. 5, 134–143 (1999), http://www.opticsexpress.org .
[CrossRef]

Opt. Lett. (5)

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28, 281–283 (2003).
[CrossRef] [PubMed]

C. Dorrer, B. de Beauvoir, C. LeBlanc, S. Ranc, J. P. Rousseau, P. Rousseau, J. P. Chambaret, F. Salin, “Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24, 1644–1646 (1999).
[CrossRef]

K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
[CrossRef] [PubMed]

P. T. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, M. C. Downer, “Frequency-domain interferometric second-harmonic spectroscopy,” Opt. Lett. 24, 496–498 (1999).
[CrossRef]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

Opt. Lett. (6)

Opt. Photon. News (1)

R. Trebino, P. O’Shea, M. Kimmel, X. Gu, “Measuring ultrashort laser pulses just got a lot easier,” Opt. Photon. News 12, 22–25 (2001).
[CrossRef]

Opt. Photon. News (1)

I. Walmsley, R. Trebino, “Measuring fast pulses with slow detectors,” Opt. Photon. News 7, 23–28 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

C. W. Siders, S. P. L. Blanc, D. Fisher, T. Tajima, M. C. Downer, A. Babine, A. Stepanov, A. Sergeev, “Laser wakefield excitation and measurement by femtosecond longitudinal interferometry,” Phys. Rev. Lett. 76, 3570–3573 (1996).
[CrossRef] [PubMed]

Phys. World (1)

H. Kapteyn, M. Murnane, “Ultrashort light pulses: life in the fast lane. Researchers can now routinely use lasers to generate femtosecond light pulses in the lab, making it possible to study processes ranging from photosynthesis to the switching of electronic circuits. How the latest advances could lead to the generation of even shorter pulses,” Phys. World 12, 31–35 (1999).

Rev. Sci. Instrum. (1)

I. G. Cormack, W. Sibbett, R. Ortega-Martinez, D. T. Reid, “Ultrashort pulse characterization using a scanning Fabry-Perot etalon enabling rapid acquisition and retrieval of a sonogram at rates up to 1.52 Hz,” Rev. Sci. Instrum. 72, 4071–4079 (2001).
[CrossRef]

Sci. Am. (1)

J.-M. Hopkins, W. Sibbett, “Ultrashort-pulse lasers: big payoffs in a flash-imaging, microelectronic manufacturing, fiber optics and industrial chemistry are eagerly adopting lasers that emit light in powerful bursts lasting only quadrillionths of a second,” Sci. Am. 283, 72–79 (2000).
[CrossRef] [PubMed]

Other (3)

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, Boston, Mass., 1992).

See, for example, Kapteyn-Murnane Laboratories at http://www.kmlabs.com .

C. Dorrer, Lucent Technologies, Murray Hill, N.J. 07974-0636 (personal communication, 2001).

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Figures (13)

Fig. 1
Fig. 1

SPIDER apparatus (a) An ultrashort laser pulse enters through a pinhole in the top left corner and strikes an etalon where it is separated into three pulses. (b) Two of these pulses travel down one arm of SPIDER to the type I β-barium borate crystal. (c) The third pulse travels to a pair of diffraction gratings and is temporally stretched before meeting the pulse pair at the crystal. (d) The crystal spectrally shears the pulse pair and doubles their frequencies before they enter the spectrometer. (e) Inside the spectrometer the pulses spread out and interfere with each other. (f) The interference pattern, or interferogram, is detected by an array of photodiode detectors and exported to a computer for mathematical analysis. (g) The entire apparatus fits on a bread board that is 12 in. (31 cm) wide by 18 in. (46 cm) long.

Fig. 2
Fig. 2

Measured interferogram with the highest possible SNR.

Fig. 3
Fig. 3

Five separate measurements of the spectral phase of an ultrashort laser pulse. (a) The five measurements are indistinguishable on this scale. (b) The difference between each individual phase and the average of all five phases.

Fig. 4
Fig. 4

Three pulses used in this study. (a) The spectral phases were positive quadratic, flat, and negative quadratic. (b) The corresponding temporal profiles for positive quadratic (dashed curve), flat (solid curve), and negative quadratic (dotted curve). (The positive quadratic pulse actually contained some cubic terms as well, which leads to the interesting temporal profile.)

Fig. 5
Fig. 5

Measured interferogram with 10% noise.

Fig. 6
Fig. 6

Average error in reconstructed temporal intensity (lower curve) and phase (upper curve) versus noise fraction.

Fig. 7
Fig. 7

Reconstructed pulse intensity and phase from interferograms recorded under optimum conditions (dashed curves) and with 10% noise fraction (solid curves).

Fig. 8
Fig. 8

Interferogram rounded to 2 bits (four levels).

Fig. 9
Fig. 9

Average error in reconstructed pulse intensity (solid circles) and phase (open circles) versus quantization bit depth.

Fig. 10
Fig. 10

Measured interferogram (solid curve), 1-bit round off (dashed horizontal line), and Gaussian threshold (dotted curve).

Fig. 11
Fig. 11

Two techniques used to retrieve 1-bit interferograms: (a) bit rounding and (b) Gaussian thresholding.

Fig. 12
Fig. 12

Reconstructed pulses from an optimal interferogram (solid curves) and the Gaussian threshold interferogram of Fig. 11(a) (dashed curves).

Fig. 13
Fig. 13

Average error in reconstructed pulse intensity (solid circles) and phase (open circles) versus number of interferogram averages. The solid curves are fits to Eq. (14).

Equations (14)

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E ω exp - i ϕ ω
  E 1 ω = | E 1 ω | exp - i ϕ ω ,   E 2 ω - Ω = | E 2 ω - Ω | exp - i ϕ ω - Ω + ω τ ,
S ω =   | E 1 ω | 2 +   | E 1 ω E 2 ω - Ω   | exp i ϕ ω - ϕ ω - Ω + ω τ +   | E 1 ω   E 2 ω - Ω   | × exp - i ϕ ω - ϕ ω - Ω + ω τ +   | E 2 ω - Ω   | 2 .
F S ω =   - d ω exp i ω t | E 1 ω | 2 + | E 2 ω - Ω | 2 +   - d ω exp i ω t + τ | E 1 ω E 2 ω - Ω | exp i ϕ ω - ϕ ω - Ω +   - d ω exp i ω t - τ | E 1 ω E 2 ω - Ω | exp - i ϕ ω - ϕ ω - Ω .
exp i ϕ ω - ϕ ω - Ω + ω τ .
θ ω = ϕ ω - ϕ ω - Ω Ω   d ϕ ω d ω ,
ϕ ω =   1 Ω θ ω d ω .
E t =   1 2 π -   | E ω | exp - i ϕ ω exp i ω τ d ω .
  S noisy ω i =   S input ω i +   σ elec ω i ,
S quant ω i =   1 2 bit   depth - 1 2 bit   depth - 1 S input ω i ,
ε I = 1 N j = 1 N I ref t j - I   t j 2 1 / 2 ,
ε ϕ = 1 N j = 1 N I 2 t j ϕ ref t j - ϕ t j 2 1 / 2 1 N j = 1 N I 2 t j 1 / 2 ,
rms σ elec = rms α n   η i ,
ε = γ + β /   N ,

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