Abstract

We demonstrate that multiple spectral-shearing interferometry increases the precision and accuracy of measurements of the spectral phase of a complex pulse (time-bandwidth product = 125) arising from self-phase modulation in a gas filled capillary. We verify that the measured interferometric phase is accurate to 0.1 rad across the full bandwidth by checking the consistency between the spectral phases of each individual shear measurement. The accuracy of extracting pulse parameters (group delay dispersion, pulse duration and peak intensity) for single shear measurements were verified to better than 10% by comparison with the multishear reconstruction. High order space-time coupling is quantified across a single transverse dimension, verifying the suitability of such pulses for use in strong field experiments.

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  1. D. R. Austin, T. Witting, and I. A. Walmsley, “High precision self-referenced phase retrieval of complex pulses with multiple-shearing spectral interferometry,” J. Opt. Soc. Am. B 26, 1818–1830 (2009).
    [CrossRef]
  2. D. R. Austin, T. Witting, and I. A. Walmsley, “Resolution of the relative phase ambiguity in spectral shearing interferometry of ultrashort pulses,” Opt. Lett. 35, 1971–1973 (2010).
    [CrossRef] [PubMed]
  3. I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1, 308–437 (2009).
    [CrossRef]
  4. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, 2002).
    [CrossRef]
  5. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
    [CrossRef]
  6. C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
    [CrossRef]
  7. C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
    [CrossRef]
  8. R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
    [CrossRef]
  9. D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: A study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
    [CrossRef] [PubMed]
  10. B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, 1987–1989 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. F. X. Kärtner, Few-Cycle Laser Pulse Generation and Its Applications (Springer, 2004).
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    [CrossRef]
  14. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
    [CrossRef] [PubMed]
  15. W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. De Silvestri, and 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]
  16. W. Kornelis, M. Bruck, F. W. Helbing, C. P. Hauri, A. Heinrich, J. Biegert, and U. Keller, “Single-shot dynamics of pulses from a gas-filled hollow fiber,” Appl. Phys. B: Lasers Opt. 79, 1033–1039 (2004).
    [CrossRef]
  17. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
    [CrossRef]
  18. L. Gallmann, G. Steinmeyer, D. H. Sutter, T. Rupp, C. Iaconis, I. A. Walmsley, and U. Keller, “Spatially resolved amplitude and phase characterization of femtosecond optical pulses,” Opt. Lett. 26 26, 96–98 (2001).
    [CrossRef]
  19. C. Dorrer and I. A. Walmsley, “Simple linear technique for the measurement of space-time coupling in ultrashort optical pulses,” Opt. Lett. 27, 1947–1949 (2002).
    [CrossRef]
  20. C. Dorrer and 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]
  21. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  22. A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31, 1914–1916 (2006).
    [CrossRef] [PubMed]
  23. C. Dorrer, P. Londero, and I. A. Walmsley, “Homodyne detection in spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 26, 1510–1512 (2001).
    [CrossRef]
  24. J. R. Birge and F. X. Kärtner, “Analysis and mitigation of systematic errors in spectral shearing interferometry of pulses approaching the single-cycle limit,” J. Opt. Soc. Am. B 25, A111–A119 (2008).
    [CrossRef]
  25. A. S. Wyatt, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK, is preparing a manuscript to be called “Generalized multishearing interferometry.”
  26. C. Dorrer and 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]
  27. A. S. Wyatt and I. A. Walmsley, “Analysis of space-time coupling in sea-spider measurements,” in Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference. CLEO Europe - EQEC 2009. European Conference on, Germany, 14–15 June 2009.
  28. P. Gabolde and R. Trebino, “Single-shot measurement of the full spatio-temporal field of ultrashort pulses with multi-spectral digital holography,” Opt. Express 14, 11460–11467 (2006).
    [CrossRef] [PubMed]
  29. P. Bowlan, P. Gabolde, and R. Trebino, “Directly measuring the spatio-temporal electric field of focusing ultra-short pulses,” Opt. Express 15, 10219–10230 (2007).
    [CrossRef] [PubMed]
  30. C. Dorrer, E. M. Kosik, and I. A. Walmsley, “Spatio-temporal characterization of the electric field of ultra-short optical pulses using two-dimensional shearing interferometry,” Appl. Phys. B: Lasers Opt. 74, S209–S217 (2002).
    [CrossRef]
  31. B. Alonso, I. J. Sola, Ö. Varela, J. Hernández-Toro, C. Méndez, J. S. Román, A. Zaïr, and L. Roso, “Spatiotemporal amplitude-and-phase reconstruction by Fourier-transform of interference spectra of high-complex-beams,” J. Opt. Soc. Am. B 27, 933–940 (2010).
    [CrossRef]

2010

2009

2008

2007

2006

2004

W. Kornelis, M. Bruck, F. W. Helbing, C. P. Hauri, A. Heinrich, J. Biegert, and U. Keller, “Single-shot dynamics of pulses from a gas-filled hollow fiber,” Appl. Phys. B: Lasers Opt. 79, 1033–1039 (2004).
[CrossRef]

2003

2002

2001

2000

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
[CrossRef]

1999

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

1998

1997

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

1994

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: A study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

1982

1978

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Alonso, B.

André, Y.-B.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Austin, D. R.

Biegert, J.

Birge, J. R.

Bourayou, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Bowlan, P.

Brabec, T.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
[CrossRef]

Bruck, M.

W. Kornelis, M. Bruck, F. W. Helbing, C. P. Hauri, A. Heinrich, J. Biegert, and U. Keller, “Single-shot dynamics of pulses from a gas-filled hollow fiber,” Appl. Phys. B: Lasers Opt. 79, 1033–1039 (2004).
[CrossRef]

Bucksbaum, P. H.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: A study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

De Silvestri, S.

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Dorrer, C.

Dudley, J. M.

J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fiber,” Nat. Photonics 3, 85–90 (2009).
[CrossRef]

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Frey, S.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Gabolde, P.

Gallmann, L.

Hauri, C. P.

W. Kornelis, M. Bruck, F. W. Helbing, C. P. Hauri, A. Heinrich, J. Biegert, and U. Keller, “Single-shot dynamics of pulses from a gas-filled hollow fiber,” Appl. Phys. B: Lasers Opt. 79, 1033–1039 (2004).
[CrossRef]

Heinrich, A.

W. Kornelis, M. Bruck, F. W. Helbing, C. P. Hauri, A. Heinrich, J. Biegert, and U. Keller, “Single-shot dynamics of pulses from a gas-filled hollow fiber,” Appl. Phys. B: Lasers Opt. 79, 1033–1039 (2004).
[CrossRef]

Helbing, F. W.

W. Kornelis, M. Bruck, F. W. Helbing, C. P. Hauri, A. Heinrich, J. Biegert, and U. Keller, “Single-shot dynamics of pulses from a gas-filled hollow fiber,” Appl. Phys. B: Lasers Opt. 79, 1033–1039 (2004).
[CrossRef]

Hernández-Toro, J.

Iaconis, C.

Ina, H.

Jalali, B.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
[CrossRef]

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Kärtner, F. X.

Kasparian, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Keller, U.

Kobayashi, S.

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
[CrossRef]

Kornelis, W.

W. Kornelis, M. Bruck, F. W. Helbing, C. P. Hauri, A. Heinrich, J. Biegert, and U. Keller, “Single-shot dynamics of pulses from a gas-filled hollow fiber,” Appl. Phys. B: Lasers Opt. 79, 1033–1039 (2004).
[CrossRef]

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. De Silvestri, and 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.

C. Dorrer, E. M. Kosik, and I. A. Walmsley, “Spatio-temporal characterization of the electric field of ultra-short optical pulses using two-dimensional shearing interferometry,” Appl. Phys. B: Lasers Opt. 74, S209–S217 (2002).
[CrossRef]

Krausz, F.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
[CrossRef]

Krumbügel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Lin, C.

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Londero, P.

Méjean, G.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Méndez, C.

Muller, H. G.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: A study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

Mysyrowicz, A.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Nisoli, M.

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Rodriguez, M.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Román, J. S.

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
[CrossRef]

Roso, L.

Rupp, T.

Salmon, E.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Sansone, G.

Sauerbrey, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Schenkel, B.

Schumacher, D. W.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: A study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

Sola, I. J.

Solli, D. R.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
[CrossRef]

Stagira, S.

Steinmeyer, G.

Stibenz, G.

Stolen, R. H.

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Sutter, D. H.

Svelto, O.

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Takeda, M.

Taylor, J. R.

J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fiber,” Nat. Photonics 3, 85–90 (2009).
[CrossRef]

Tisch, J. W. G.

Trebino, R.

P. Bowlan, P. Gabolde, and R. Trebino, “Directly measuring the spatio-temporal electric field of focusing ultra-short pulses,” Opt. Express 15, 10219–10230 (2007).
[CrossRef] [PubMed]

P. Gabolde and R. Trebino, “Single-shot measurement of the full spatio-temporal field of ultrashort pulses with multi-spectral digital holography,” Opt. Express 14, 11460–11467 (2006).
[CrossRef] [PubMed]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, 2002).
[CrossRef]

Varela, Ö.

Vozzi, C.

Walmsley, I. A.

D. R. Austin, T. Witting, and I. A. Walmsley, “Resolution of the relative phase ambiguity in spectral shearing interferometry of ultrashort pulses,” Opt. Lett. 35, 1971–1973 (2010).
[CrossRef] [PubMed]

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1, 308–437 (2009).
[CrossRef]

D. R. Austin, T. Witting, and I. A. Walmsley, “High precision self-referenced phase retrieval of complex pulses with multiple-shearing spectral interferometry,” J. Opt. Soc. Am. B 26, 1818–1830 (2009).
[CrossRef]

A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31, 1914–1916 (2006).
[CrossRef] [PubMed]

C. Dorrer and I. A. Walmsley, “Simple linear technique for the measurement of space-time coupling in ultrashort optical pulses,” Opt. Lett. 27, 1947–1949 (2002).
[CrossRef]

C. Dorrer, E. M. Kosik, and I. A. Walmsley, “Spatio-temporal characterization of the electric field of ultra-short optical pulses using two-dimensional shearing interferometry,” Appl. Phys. B: Lasers Opt. 74, S209–S217 (2002).
[CrossRef]

C. Dorrer and 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 and 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, P. Londero, and I. A. Walmsley, “Homodyne detection in spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 26, 1510–1512 (2001).
[CrossRef]

L. Gallmann, G. Steinmeyer, D. H. Sutter, T. Rupp, C. Iaconis, I. A. Walmsley, and U. Keller, “Spatially resolved amplitude and phase characterization of femtosecond optical pulses,” Opt. Lett. 26 26, 96–98 (2001).
[CrossRef]

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

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

A. S. Wyatt and I. A. Walmsley, “Analysis of space-time coupling in sea-spider measurements,” in Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference. CLEO Europe - EQEC 2009. European Conference on, Germany, 14–15 June 2009.

Weihe, F.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: A study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

Wille, H.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Witting, T.

Wolf, J.-P.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Wöste, L.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Wyatt, A. S.

A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31, 1914–1916 (2006).
[CrossRef] [PubMed]

A. S. Wyatt, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK, is preparing a manuscript to be called “Generalized multishearing interferometry.”

A. S. Wyatt and I. A. Walmsley, “Analysis of space-time coupling in sea-spider measurements,” in Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference. CLEO Europe - EQEC 2009. European Conference on, Germany, 14–15 June 2009.

Yu, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Zaïr, A.

Adv. Opt. Photon.

Appl. Phys. B: Lasers Opt.

W. Kornelis, M. Bruck, F. W. Helbing, C. P. Hauri, A. Heinrich, J. Biegert, and U. Keller, “Single-shot dynamics of pulses from a gas-filled hollow fiber,” Appl. Phys. B: Lasers Opt. 79, 1033–1039 (2004).
[CrossRef]

C. Dorrer, E. M. Kosik, and I. A. Walmsley, “Spatio-temporal characterization of the electric field of ultra-short optical pulses using two-dimensional shearing interferometry,” Appl. Phys. B: Lasers Opt. 74, S209–S217 (2002).
[CrossRef]

IEEE J. Quantum Electron.

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Nat. Photonics

J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fiber,” Nat. Photonics 3, 85–90 (2009).
[CrossRef]

Nature (London)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

C. Dorrer and I. A. Walmsley, “Simple linear technique for the measurement of space-time coupling in ultrashort optical pulses,” Opt. Lett. 27, 1947–1949 (2002).
[CrossRef]

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. De Silvestri, and 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]

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, 1987–1989 (2003).
[CrossRef] [PubMed]

A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31, 1914–1916 (2006).
[CrossRef] [PubMed]

D. R. Austin, T. Witting, and I. A. Walmsley, “Resolution of the relative phase ambiguity in spectral shearing interferometry of ultrashort pulses,” Opt. Lett. 35, 1971–1973 (2010).
[CrossRef] [PubMed]

L. Gallmann, G. Steinmeyer, D. H. Sutter, T. Rupp, C. Iaconis, I. A. Walmsley, and U. Keller, “Spatially resolved amplitude and phase characterization of femtosecond optical pulses,” Opt. Lett. 26 26, 96–98 (2001).
[CrossRef]

C. Dorrer, P. Londero, and I. A. Walmsley, “Homodyne detection in spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 26, 1510–1512 (2001).
[CrossRef]

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

Phys. Rev. A

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Phys. Rev. Lett.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: A study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

Rev. Mod. Phys.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
[CrossRef]

Rev. Sci. Instrum.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Science

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Other

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, 2002).
[CrossRef]

F. X. Kärtner, Few-Cycle Laser Pulse Generation and Its Applications (Springer, 2004).

A. S. Wyatt, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK, is preparing a manuscript to be called “Generalized multishearing interferometry.”

A. S. Wyatt and I. A. Walmsley, “Analysis of space-time coupling in sea-spider measurements,” in Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference. CLEO Europe - EQEC 2009. European Conference on, Germany, 14–15 June 2009.

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Figures (5)

Fig. 1
Fig. 1

SEA-SPIDER concept. The two signal pulses (SP1 & SP2) are created via type II sum frequency generation (SFG) in a χ(2) nonlinear crystal (e.g. 30 μm BBO) of the test pulse (TP) with two spatially tilted and highly chirped ancillary pulses (CP1 & CP2) separated in time by a delay τ. During the SFG, the TP interacts with two different quasi-monochromatic frequencies, resulting in two spectrally sheared replicas of the test pulse centered near twice the fundamental frequency. The upconverted interference pattern is filtered using a blue filter (BF) and spatial filter (SF), then imaged onto the entrance slit of an imaging spectrometer. The spatial tilt results in spatial fringes, enabling the extraction of the spatially-dependent spectral phase. Experimentally, focusing mirrors are used for f1 and f2 to prevent chromatic aberration and dispersion of the TP.

Fig. 2
Fig. 2

Pulse spectrum variation during measurement acquisition. (a) Intensity error between measured spectrum and ensemble average. (b) Histogram of spectral error (counts along horizontal axis). (c) Measured spectra (blue=zero intensity, red=maximum intensity, smoothed to remove electronic read-out noise); the pulse’s spectral moment (black dots) and RMS width (white dots) are superimposed. (d) Ensemble average (black line) and standard deviation (red band).

Fig. 3
Fig. 3

Spectral and temporal reconstructions; the probability that the phase/intensity is a given value is represented by the intensity of the line at that value. (a) Spectral intensity and phase. The phases have been offset from each other for clarity. The SP spectrum has been shifted in wavelength to overlap with the fundamental. (b) Temporal intensity reconstructions and FWHM pulse durations after phase compensation — see text; the color scheme is the same as in (a). The Fourier transform limited temporal profile (dark red) is calculated from the fundamental spectrum.

Fig. 4
Fig. 4

Extracted SPIDER phases for the different shear measurements. The intensity of each line represents the probability distribution calculated from 100 measurements for each individual shear. For each shear, the SPIDER phase has also been calculated using the TP spectral phase reconstructed via the multishear algorithm and is superimposed as a black dotted line. The RMS phase error between the measured and reconstructed SPIDER phase for each shear is written above each measurement. The SPIDER phases have been offset from each other for clarity.

Fig. 5
Fig. 5

Space-time temporal reconstruction of the test pulse with the first order (linear) pulse-front tilt removed. The spatially dependent time of arrival of the peak (dotted) and of the pulse and half-maximum intensities (dashed) are overlaid.

Tables (1)

Tables Icon

Table 1 Quantitative results from multishear, concatenation (top line for each shear) and integration (bottom line for each shear) methods. Three quantities of interest have been chosen: (1) the GDD (ϕ(2), calculated via a weighted polynomial fit about the center of mass of the fundamental spectrum) of the pulse before compensating the optical path to the experiment, (2) the pulse duration measured at FWHM (ΔtFWHM) and (3) the peak power (I0) of the pulse after compensating the optical path to the experiment. In each case, the mean values from the sample distributions are shown along with the standard deviation of the sample estimate in brackets, and hence the precision of the estimated value (note this is not the standard error in the estimate of the mean). The percentage error (Δ) has been calculated with respect to the multishear value, since this is deemed as the best estimate of the true value from our experimental data. The precision (σ) is a measure of the standard deviation of the RMS pulse error for the sample distribution [20]. The accuracy (ɛ) is calculated from the RMS error between the pulse means reconstructed from the multishear algorithm and the individual shear reconstructions [26].

Equations (4)

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θ ( ω , Ω ) = arg [ D ( ω + ω CP , Ω ) D cal * ( ω + ω CP ) ] = ϕ TP ( ω Ω ) ϕ TP ( ω ) .
θ ( m + M s ) = n = 0 N 1 [ A ( m + M s ) n B ( m + M s ) n ] ϕ n ,
η ( Ω ) = { | D ( ω , Ω ) | 2 [ θ ms ( ω , Ω ) θ meas ( ω , Ω ) ] 2 d ω | D ( ω , Ω ) | 2 d ω } 1 / 2 .
N dB = B T 2 π ,

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