Abstract

We investigate, both theoretically and experimentally, the practical use of amplitude and phase pulse shapers to characterize ultrashort optical pulses. Pulse shapers greatly simplify the optical setup required for the SH-FROG and SPIDER measurement techniques, and both methods can even be implemented with a common optical layout. We also introduce, demonstrate, and compare several new interferometric variants of these techniques, which are compatible with a basic setup comprising no more than a pulse shaper, a type I second-harmonic stage, and a spectrometer.

© 2010 Optical Society of America

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  1. P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245-249 (1997).
    [CrossRef]
  2. C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 63-153 (1983).
    [CrossRef]
  3. A. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929-1269 (2000).
    [CrossRef]
  4. A. Monmayrant, M. Joffre, T. Oksenhendler, R. Herzog, D. Kaplan, and P. Tournois, “Time-domain interferometry for direct electric-field reconstruction by use of an acousto-optic programmable filter and a two-photon detector,” Opt. Lett. 28, 278-280 (2003).
    [CrossRef] [PubMed]
  5. N. Forget, M. Joffre, S. Coudreau, and T. Oksenhendler, “Toward programmable ultrashort pulse characterization,” in “CLEO/Europe and IQEC 2007 Conference Digest,” (Optical Society of America, 2007), paper CF-16.
  6. A. Galler and T. Feurer, “Pulse shaper assisted short laser pulse characterization,” Appl. Phys. B 90, 427-430 (2008).
    [CrossRef]
  7. J. Sung, B.-C. Chen, and S.-H. Lim, “Single-beam homodyne SPIDER for multiphoton microscopy,” Opt. Lett. 33, 1404-1406 (2008).
    [CrossRef] [PubMed]
  8. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference IV. ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett. 29, 775-777 (2004).
    [CrossRef] [PubMed]
  9. B. Xu, J. M. Gunn, J. M. D. Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond laser pulses,” J. Opt. Soc. Am. B 23, 750-759 (2006).
    [CrossRef]
  10. V. V. Lozovoy, B. Xu, Y. Coello, and M. Dantus, “Direct measurement of spectral phase for ultrashort laser pulses,” Opt. Express 16, 592-597 (2008).
    [CrossRef] [PubMed]
  11. Y. Coello, V. V. Lozovoy, T. C. Gunaratne, B. Xu, I. Borukhovich, C.-H. Tseng, T. Weinacht, and M. Dantus, “Interference without an interferometer: a different approach to measuring, compressing, and shaping ultrashort laser pulses,” J. Opt. Soc. Am. B 25, A140-A150 (2008).
    [CrossRef]
  12. S. Grabielle, N. Forget, S. Coudreau, T. Oksenhendler, D. Kaplan, J.-F. Hergott, and O. Gobert, “Local spectral compression method for CPA lasers,” in “CLEO/Europe and EQEC 2009 Conference Digest,” (OSA, 2009), pp. CF-P17.
  13. B. von Vacano, T. Buckup, and M. Motzkus, “In situ broadband pulse compression for multiphoton microscopy using a shaper-assisted collinear SPIDER,” Opt. Lett. 31, 1154-1156 (2006).
    [CrossRef] [PubMed]
  14. B. von Vacano, T. Buckup, and M. Motzkus, “Shaper-assisted collinear SPIDER: fast and simple broadband pulse compression in nonlinear microscopy,” J. Opt. Soc. Am. B 24, 1091-1100 (2007).
    [CrossRef]
  15. V. Wong and I. Walmsley, “Linear filter analysis of methods for ultrashort-pulse-shape measurements,” J. Opt. Soc. Am. B 12, 1491-1499 (1995).
    [CrossRef]
  16. I. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Am. J. Optom. Physiol. Opt. 1, 308-437 (2009).
  17. R. Trebino, K. DeLong, D. Fittinghoff, J. Sweetser, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277-3295 (1997).
    [CrossRef]
  18. D. Fittinghoff, J. Squier, C. Barty, J. Sweetser, R. Trebino, and M. Müller, “Collinear type II second-harmonic-generation frequency-resolved optical gating for use with high-numerical-aperture objectives,” Opt. Lett. 23, 1046-1048 (1998).
    [CrossRef]
  19. L. Gallmann, G. Steinmeyer, D. Sutter, N. Matuschek, and U. Keller, “Collinear type II second-harmonic-generation frequency-resolved optical gating for the characterization of sub-10-fs optical pulses,” Opt. Lett. 25, 269-271 (2000).
    [CrossRef]
  20. C. Iaconis and I. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792-794 (1998).
    [CrossRef]
  21. K. DeLong, D. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, “Pulse retrieval in frequency-resolved optical gating based on the method of generalized projections,” Opt. Lett. 19, 2152-2154 (1994).
    [CrossRef] [PubMed]
  22. D. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. 35, 421-431 (1999).
    [CrossRef]
  23. D. Reid, “Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,”IEEE J. Quantum Electron. 35, 1584-1589 (1999).
    [CrossRef]
  24. A. Weiner, “Effect of group velocity mismatch on the measurement of ultrashort optical pulses via second harmonic generation,” IEEE J. Quantum Electron. 19, 1276-1283 (1983).
    [CrossRef]
  25. A. Müller and M. Laubscher, “Spectral phase and amplitude interferometry for direct electric-field reconstruction,”Opt. Lett. 26, 1915-1917 (2001).
    [CrossRef]
  26. I. Amat-Roldán, I. Cormack, P. Loza-Alvarez, and D. Artigas, “Measurement of electric field by interferometric spectral trace observation,” Opt. Lett. 30, 1063-1065 (2005).
    [CrossRef] [PubMed]
  27. I. Amat-Roldán, I. Cormack, P. Loza-Alvarez, E. Gualda, and D. Artigas, “Ultrashort pulse characterisation with SHG collinear-FROG,” Opt. Express 12, 1169-1178 (2004).
    [CrossRef] [PubMed]
  28. G. Stibenz and G. Steinmeyer, “Interferometric frequency-resolved optical gating,” Opt. Express 13, 2617-2626 (2005).
    [CrossRef] [PubMed]
  29. 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]

2009 (1)

I. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Am. J. Optom. Physiol. Opt. 1, 308-437 (2009).

2008 (4)

2007 (1)

2006 (2)

2005 (2)

2004 (2)

2003 (1)

2001 (2)

2000 (2)

1999 (2)

D. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. 35, 421-431 (1999).
[CrossRef]

D. Reid, “Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,”IEEE J. Quantum Electron. 35, 1584-1589 (1999).
[CrossRef]

1998 (2)

1997 (2)

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

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245-249 (1997).
[CrossRef]

1995 (1)

1994 (1)

1983 (2)

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 63-153 (1983).
[CrossRef]

A. Weiner, “Effect of group velocity mismatch on the measurement of ultrashort optical pulses via second harmonic generation,” IEEE J. Quantum Electron. 19, 1276-1283 (1983).
[CrossRef]

Amat-Roldán, I.

Artigas, D.

Barty, C.

Borukhovich, I.

Buckup, T.

Chen, B.-C.

Coello, Y.

Colombeau, B.

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 63-153 (1983).
[CrossRef]

Cormack, I.

Coudreau, S.

N. Forget, M. Joffre, S. Coudreau, and T. Oksenhendler, “Toward programmable ultrashort pulse characterization,” in “CLEO/Europe and IQEC 2007 Conference Digest,” (Optical Society of America, 2007), paper CF-16.

S. Grabielle, N. Forget, S. Coudreau, T. Oksenhendler, D. Kaplan, J.-F. Hergott, and O. Gobert, “Local spectral compression method for CPA lasers,” in “CLEO/Europe and EQEC 2009 Conference Digest,” (OSA, 2009), pp. CF-P17.

Cruz, J. M. D.

Dantus, M.

DeLong, K.

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

K. DeLong, D. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, “Pulse retrieval in frequency-resolved optical gating based on the method of generalized projections,” Opt. Lett. 19, 2152-2154 (1994).
[CrossRef] [PubMed]

Dorrer, C.

I. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Am. J. Optom. Physiol. Opt. 1, 308-437 (2009).

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]

Feurer, T.

A. Galler and T. Feurer, “Pulse shaper assisted short laser pulse characterization,” Appl. Phys. B 90, 427-430 (2008).
[CrossRef]

Fittinghoff, D.

Forget, N.

S. Grabielle, N. Forget, S. Coudreau, T. Oksenhendler, D. Kaplan, J.-F. Hergott, and O. Gobert, “Local spectral compression method for CPA lasers,” in “CLEO/Europe and EQEC 2009 Conference Digest,” (OSA, 2009), pp. CF-P17.

N. Forget, M. Joffre, S. Coudreau, and T. Oksenhendler, “Toward programmable ultrashort pulse characterization,” in “CLEO/Europe and IQEC 2007 Conference Digest,” (Optical Society of America, 2007), paper CF-16.

Froehly, C.

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 63-153 (1983).
[CrossRef]

Galler, A.

A. Galler and T. Feurer, “Pulse shaper assisted short laser pulse characterization,” Appl. Phys. B 90, 427-430 (2008).
[CrossRef]

Gallmann, L.

Gobert, O.

S. Grabielle, N. Forget, S. Coudreau, T. Oksenhendler, D. Kaplan, J.-F. Hergott, and O. Gobert, “Local spectral compression method for CPA lasers,” in “CLEO/Europe and EQEC 2009 Conference Digest,” (OSA, 2009), pp. CF-P17.

Grabielle, S.

S. Grabielle, N. Forget, S. Coudreau, T. Oksenhendler, D. Kaplan, J.-F. Hergott, and O. Gobert, “Local spectral compression method for CPA lasers,” in “CLEO/Europe and EQEC 2009 Conference Digest,” (OSA, 2009), pp. CF-P17.

Gualda, E.

Gunaratne, T. C.

Gunn, J. M.

Hergott, J.-F.

S. Grabielle, N. Forget, S. Coudreau, T. Oksenhendler, D. Kaplan, J.-F. Hergott, and O. Gobert, “Local spectral compression method for CPA lasers,” in “CLEO/Europe and EQEC 2009 Conference Digest,” (OSA, 2009), pp. CF-P17.

Herzog, R.

Iaconis, C.

Joffre, M.

A. Monmayrant, M. Joffre, T. Oksenhendler, R. Herzog, D. Kaplan, and P. Tournois, “Time-domain interferometry for direct electric-field reconstruction by use of an acousto-optic programmable filter and a two-photon detector,” Opt. Lett. 28, 278-280 (2003).
[CrossRef] [PubMed]

N. Forget, M. Joffre, S. Coudreau, and T. Oksenhendler, “Toward programmable ultrashort pulse characterization,” in “CLEO/Europe and IQEC 2007 Conference Digest,” (Optical Society of America, 2007), paper CF-16.

Kane, D.

D. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. 35, 421-431 (1999).
[CrossRef]

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

Kaplan, D.

A. Monmayrant, M. Joffre, T. Oksenhendler, R. Herzog, D. Kaplan, and P. Tournois, “Time-domain interferometry for direct electric-field reconstruction by use of an acousto-optic programmable filter and a two-photon detector,” Opt. Lett. 28, 278-280 (2003).
[CrossRef] [PubMed]

S. Grabielle, N. Forget, S. Coudreau, T. Oksenhendler, D. Kaplan, J.-F. Hergott, and O. Gobert, “Local spectral compression method for CPA lasers,” in “CLEO/Europe and EQEC 2009 Conference Digest,” (OSA, 2009), pp. CF-P17.

Keller, U.

Kohler, B.

Krumbügel, M.

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

Laubscher, M.

Lim, S.-H.

Londero, P.

Loza-Alvarez, P.

Lozovoy, V.

Lozovoy, V. V.

Matuschek, N.

Monmayrant, A.

Motzkus, M.

Müller, A.

Müller, M.

Oksenhendler, T.

A. Monmayrant, M. Joffre, T. Oksenhendler, R. Herzog, D. Kaplan, and P. Tournois, “Time-domain interferometry for direct electric-field reconstruction by use of an acousto-optic programmable filter and a two-photon detector,” Opt. Lett. 28, 278-280 (2003).
[CrossRef] [PubMed]

N. Forget, M. Joffre, S. Coudreau, and T. Oksenhendler, “Toward programmable ultrashort pulse characterization,” in “CLEO/Europe and IQEC 2007 Conference Digest,” (Optical Society of America, 2007), paper CF-16.

S. Grabielle, N. Forget, S. Coudreau, T. Oksenhendler, D. Kaplan, J.-F. Hergott, and O. Gobert, “Local spectral compression method for CPA lasers,” in “CLEO/Europe and EQEC 2009 Conference Digest,” (OSA, 2009), pp. CF-P17.

Pastirk, I.

Reid, D.

D. Reid, “Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,”IEEE J. Quantum Electron. 35, 1584-1589 (1999).
[CrossRef]

Richman, B.

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

Squier, J.

Steinmeyer, G.

Stibenz, G.

Sung, J.

Sutter, D.

Sweetser, J.

D. Fittinghoff, J. Squier, C. Barty, J. Sweetser, R. Trebino, and M. Müller, “Collinear type II second-harmonic-generation frequency-resolved optical gating for use with high-numerical-aperture objectives,” Opt. Lett. 23, 1046-1048 (1998).
[CrossRef]

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

Tournois, P.

Trebino, R.

Tseng, C.-H.

Vampouille, M.

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 63-153 (1983).
[CrossRef]

von Vacano, B.

Walmsley, I.

Walmsley, I. A.

Weinacht, T.

Weiner, A.

A. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929-1269 (2000).
[CrossRef]

A. Weiner, “Effect of group velocity mismatch on the measurement of ultrashort optical pulses via second harmonic generation,” IEEE J. Quantum Electron. 19, 1276-1283 (1983).
[CrossRef]

Wilson, K.

Wong, V.

Xu, B.

Am. J. Optom. Physiol. Opt. (1)

I. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Am. J. Optom. Physiol. Opt. 1, 308-437 (2009).

Appl. Phys. B (1)

A. Galler and T. Feurer, “Pulse shaper assisted short laser pulse characterization,” Appl. Phys. B 90, 427-430 (2008).
[CrossRef]

IEEE J. Quantum Electron. (3)

D. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. 35, 421-431 (1999).
[CrossRef]

D. Reid, “Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,”IEEE J. Quantum Electron. 35, 1584-1589 (1999).
[CrossRef]

A. Weiner, “Effect of group velocity mismatch on the measurement of ultrashort optical pulses via second harmonic generation,” IEEE J. Quantum Electron. 19, 1276-1283 (1983).
[CrossRef]

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

Opt. Commun. (1)

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245-249 (1997).
[CrossRef]

Opt. Express (3)

Opt. Lett. (11)

I. Amat-Roldán, I. Cormack, P. Loza-Alvarez, and D. Artigas, “Measurement of electric field by interferometric spectral trace observation,” Opt. Lett. 30, 1063-1065 (2005).
[CrossRef] [PubMed]

B. von Vacano, T. Buckup, and M. Motzkus, “In situ broadband pulse compression for multiphoton microscopy using a shaper-assisted collinear SPIDER,” Opt. Lett. 31, 1154-1156 (2006).
[CrossRef] [PubMed]

V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference IV. ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett. 29, 775-777 (2004).
[CrossRef] [PubMed]

J. Sung, B.-C. Chen, and S.-H. Lim, “Single-beam homodyne SPIDER for multiphoton microscopy,” Opt. Lett. 33, 1404-1406 (2008).
[CrossRef] [PubMed]

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

D. Fittinghoff, J. Squier, C. Barty, J. Sweetser, R. Trebino, and M. Müller, “Collinear type II second-harmonic-generation frequency-resolved optical gating for use with high-numerical-aperture objectives,” Opt. Lett. 23, 1046-1048 (1998).
[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]

A. Müller and M. Laubscher, “Spectral phase and amplitude interferometry for direct electric-field reconstruction,”Opt. Lett. 26, 1915-1917 (2001).
[CrossRef]

A. Monmayrant, M. Joffre, T. Oksenhendler, R. Herzog, D. Kaplan, and P. Tournois, “Time-domain interferometry for direct electric-field reconstruction by use of an acousto-optic programmable filter and a two-photon detector,” Opt. Lett. 28, 278-280 (2003).
[CrossRef] [PubMed]

L. Gallmann, G. Steinmeyer, D. Sutter, N. Matuschek, and U. Keller, “Collinear type II second-harmonic-generation frequency-resolved optical gating for the characterization of sub-10-fs optical pulses,” Opt. Lett. 25, 269-271 (2000).
[CrossRef]

K. DeLong, D. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, “Pulse retrieval in frequency-resolved optical gating based on the method of generalized projections,” Opt. Lett. 19, 2152-2154 (1994).
[CrossRef] [PubMed]

Prog. Opt. (1)

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 63-153 (1983).
[CrossRef]

Rev. Sci. Instrum. (2)

A. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929-1269 (2000).
[CrossRef]

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

Other (2)

S. Grabielle, N. Forget, S. Coudreau, T. Oksenhendler, D. Kaplan, J.-F. Hergott, and O. Gobert, “Local spectral compression method for CPA lasers,” in “CLEO/Europe and EQEC 2009 Conference Digest,” (OSA, 2009), pp. CF-P17.

N. Forget, M. Joffre, S. Coudreau, and T. Oksenhendler, “Toward programmable ultrashort pulse characterization,” in “CLEO/Europe and IQEC 2007 Conference Digest,” (Optical Society of America, 2007), paper CF-16.

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Figures (9)

Fig. 1
Fig. 1

(a) Optical setup. (b) Principle of polarization multiplexing.

Fig. 2
Fig. 2

(a) Experimental FROG trace. (b) Reconstructed FROG trace. (c) Retrieved spectrum and spectral phase. (d) Retrieved time intensity ( 123 fs FWHM).  

Fig. 3
Fig. 3

(a) Experimental single-shot SPIDER spectrum. (b) Extracted spectral amplitude and phase. Retrieved pulse duration was 28 fs FWHM.

Fig. 4
Fig. 4

(a) Experimental iFROG trace. (b) Experimental iFROG autocorrelation. (c) Filtered FROG trace. (d) Retrieved FROG trace. (e) Retrieved spectral phase and intensity. (f) Retrieved time intensity.

Fig. 5
Fig. 5

(a) Experimental bFROG trace. (b) Experimental bFROG autocorrelation. (c) Retrieved bFROG trace. (d) Retrieved spectral phase and intensity. (e) Retrieved time intensity.

Fig. 6
Fig. 6

cSPIDER experimental results. (a) I + + ( ω ) (solid curve) and I ( ω ) (dashed curve). (b) I + ( ω ) (solid curve) and I + ( ω ) (dashed curve). (c) extracted SPIDER signal. (d) Retrieved spectrum and spectral phase. (e) Retrieved time intensity.

Fig. 7
Fig. 7

hSPIDER experimental results. (a) I + 1 ( ω ) (solid curve) and I 1 ( ω ) (dashed curve). (b) I + 2 ( ω ) (solid curve) and I 2 ( ω ) (dashed curve). (c)Extracted homodyne signals. (d) Retrieved spectral phase and intensity. (e) Retrieved time intensity.

Fig. 8
Fig. 8

Compared time intensities retrieved by bFROG, iFROG, cSPIDER and hSPIDER.

Fig. 9
Fig. 9

(a) Experimental FROG traces. (b) Experimental SPIDER spectrum. (c) Compared retrieved time intensities (FROG: solid curve. SPIDER: dots).

Equations (33)

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E ( t ) = Re { E ( t ) } with E ( t ) = A ( t ) e + i ω 0 t ,
H ( ω ) = 1 + e i π 4 e i ( ω ω 0 ) τ ,
H ( t ) = δ ( t ) + e i π 4 e i ω 0 τ δ ( t τ ) ,
I ( ω ) | [ H ( t ) A ( t ) ] 2 e 2 i ω 0 t e i ω t d t | 2 ,
H ( ω ) = H 1 ( ω ) + H 2 ( ω ) e i ω τ c .
I ( ω ) | [ H 1 ( t ) A ( t ) ] [ H 2 ( t ) A ( t ) ] e 2 i ω 0 t e i ω t d t | 2 ,
I FROG ( τ , ω ) | A ( t ) A ( t τ ) e 2 i ω 0 t e i ω t d t | 2 .
H FROG ( τ , ω ) = 1 + e i ω ( τ + τ c ) ,
τ k = τ max ( k N ) N with k = 1 . . 2 N 1 .
ν k = 2 ν 0 + Δ ν ( k N ) N with k = 1 . . 2 N 1 ,
S ( ω ) = I ( ω ) + I ( ω + δ ω ) + 2 I ( ω ) I ( ω + δ ω ) cos [ φ ( ω ) φ ( ω + δ ω ) ] .
ϕ SPIDER ( ω ) = ω τ + φ ( ω + ω 0 ) φ ( ω + ω 0 + δ ω ) .
I iFROG ( τ , ω ) | ( A ( t ) + A ( t τ ) e i ω 0 τ ) 2 e 2 i ω 0 t e i ω t d t | 2 ,
H iFROG ( ω ) = 1 + exp { i [ ( ω ω 0 ) τ ] } .
H Ω ( ω , τ ) = 1 + exp { i [ ( ω Ω ) τ ] } .
I iFROG ( τ , ω ) 4 I SH ( ω ) cos 2 ( δ ω τ 2 Ω τ ) ,
E FROG c ( τ , ω ) = A ( t τ 2 ) A ( t + τ 2 ) e i ( 2 ω 0 ω ) t d t .
I iFROG ( τ , ω ) I SH ( ω ) cos 2 ( δ ω τ 2 Ω τ ) + 4 I FROG c ( τ , ω ) + 8 cos ( δ ω τ 2 Ω τ ) Re [ E SH ( ω ) E FROG c ( τ , ω ) ] .
I bFROG ( τ , ω ) | ( A ( t ) + A ( t τ ) ) 2 e 2 i ω 0 t e i ω t d t | 2 .
E tot ( t ) = { E ( t ) + M 1 ( t ) e i δ ω t + E ( t τ ) + M 2 ( t τ ) e i δ ω t } e i ω 0 t ,
E SPIDER ( t ) = E ( t ) M 1 ( t ) e i δ ω t + E ( t τ ) M 2 ( t τ ) e i δ ω t ,
I tot ( 2 ω 0 + Ω ) = { 4 | E 2 ˆ | 2 cos 2 ( Ω τ ) + | M 1 2 ˆ | 2 + | M 1 2 ˆ | 2 ( SHG ) + 4 | E ̂ SPIDER | 2 ( SPIDER ) + 2 Re { E 2 ˆ ( 1 + e i Ω τ ) ( M 1 2 ˆ + M 2 2 ˆ e i 2 Ω τ i 2 δ ω τ ) } ( cross-term ) + 4 Re { E ̂ SPIDER [ E 2 ˆ ( 1 + e i Ω τ ) + M 1 2 ˆ + M 2 2 ˆ e i ( Ω + 2 δ ω ) τ ] } ( cross-term ) } ,
E ± ± = E ( t ) ± M 1 ( t ) + E ( t τ ) ± M 2 ( t τ ) .
Δ I = 32 Re { E ̂ ( Ω ) M 1 ˆ ( Ω δ ω ) × E ̂ ( Ω ) M 2 ˆ ( Ω + δ ω ) e i Ω τ } .
Δ I = 32 E ̂ ( Ω + δ ω ) E ̂ ( Ω δ ω ) cos ( Ω τ + φ ( Ω + δ ω ) φ ( Ω δ ω ) ) .
H ± ± ( ω ) = ± exp ( i Ω τ 2 ) ± exp ( + i Ω τ 2 ) + Rect ( ω 0 , Δ ω ) exp ( i ϕ ( 2 ) Ω 2 2 ) .
ϕ hSPIDER , 1 ( ω ) = ω τ + φ ( ω + ω 1 ) φ SHG ( ω ) .
Δ ϕ ( ω ) = ϕ hSPIDER , 2 ( ω ) ϕ hSPIDER , 1 ( ω ) = φ ( ω + ω 2 ) φ ( ω + ω 1 ) ,
E ± 1 ( t ) = { E ( t ) + E ( t τ ) ± M 1 ( t τ ) e i δ ω 1 t } e i ω 0 t .
I ± 1 ( 2 ω 0 + Ω ) = { | E 2 ˆ ( Ω ) ± 2 E ̂ ( Ω ) M 1 ˆ ( Ω δ ω 1 ) e i Ω τ | 2 + | M 1 2 ˆ ( Ω 2 δ ω 1 ) e i Ω τ + E 2 ˆ ( Ω ) e i Ω τ | 2 + 2 Re { ( E 2 ˆ ( Ω ) ± 2 E ̂ ( Ω ) M 1 ˆ ( Ω 2 δ ω 1 ) e i Ω τ ) } × { ( M 1 2 ˆ ( Ω δ ω 1 ) + E 2 ˆ ( Ω ) ) e i Ω τ } } .
ϕ hSPIDER , 1 ( ω ) = Ω τ + φ ( ω + ω 1 ) φ SHG ( ω ) .
E ± , 2 ( t ) = { E ( t ) + E ( t τ ) ± M 2 ( t τ ) e i δ ω 2 t } e i ω 0 t ,
ϕ hSPIDER , 2 ( ω ) = Ω τ + φ ( ω + ω 2 ) φ SHG ( ω ) .

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