Abstract

Frequency resolved optical gating (FROG) is a popular method for complete characterization of laser pulses. In FROG, a reconstruction algorithm retrieves the pulse from its measured auto-spectrogram (FROG trace). We propose and demonstrate, numerically and experimentally, multiplexed FROG in which several pulses of a pulse–burst are retrieved simultaneously from a single measured trace, which corresponds to the incoherent sum of the FROG traces of the individual pulses. Implementing multiplexed FROG in GRENOUILLE (single-shot FROG) can enable characterization of pulses in non-repetitive pulse-bursts that are currently not measurable.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (3)

2016 (6)

2015 (5)

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91, 021803 (2015).

C. Bourassin-Bouchet and M.-E. Couprie, “Partially coherent ultrafast spectrography,” Nat. Commun. 6, 6465 (2015).
[PubMed]

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6, 8209 (2015).
[PubMed]

M. Lucchini, M. H. Brügmann, A. Ludwig, L. Gallmann, U. Keller, and T. Feurer, “Ptychographic reconstruction of attosecond pulses,” Opt. Express 23(23), 29502–29513 (2015).
[PubMed]

2014 (1)

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[PubMed]

2013 (1)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[PubMed]

2012 (2)

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

2010 (1)

2009 (2)

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[PubMed]

2008 (2)

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).

D. J. Kane, “Principal components generalized projections: a review,” J. Opt. Soc. Am. B 25, A120–A132 (2008).

2006 (2)

A. Gordon, O. Gat, B. Fischer, and F. X. Kärtner, “Self-starting of passive mode locking,” Opt. Express 14(23), 11142–11154 (2006).
[PubMed]

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, and A. W. Miziolek, “Double pulse laser ablation and plasma: Laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta - Part B At. Spectrosc. 61, 999–1014 (2006).

2005 (2)

2001 (1)

1998 (1)

S. Linden, H. Giessen, and J. Kuhl, “XFROG - A New Method for Amplitude and Phase Characterization of Weak Ultrashort Pulses,” Phys. Status Solidi 206, 119–124 (1998).

1997 (2)

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).

D. J. Kane, G. Rodriguez, A. J. Taylor, and T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. B 14, 935 (1997).

1995 (1)

1986 (1)

D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85, 5805–5820 (1986).

1985 (1)

D. J. Tannor and S. A. Rice, “Control of selectivity of chemical reaction via control of wave packet evolution,” J. Chem. Phys. 83, 5013–5018 (1985).

1969 (1)

W. Hoppe and G. Strube, “Beugung in inhomogenen Primärstrahlenwellenfeld. II. Lichtoptische Analogieversuche zur Phasenmessung von Gitterinterferenzen,” Acta Crystallogr. A 25, 502–507 (1969).

Adams, D. E.

Akosman, A. E.

Avnat, Z.

Babushok, V. I.

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, and A. W. Miziolek, “Double pulse laser ablation and plasma: Laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta - Part B At. Spectrosc. 61, 999–1014 (2006).

Barillot, T.

Batey, D. J.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[PubMed]

Bekker, A.

Berger, N. K.

Bourassin-Bouchet, C.

C. Bourassin-Bouchet and M.-E. Couprie, “Partially coherent ultrafast spectrography,” Nat. Commun. 6, 6465 (2015).
[PubMed]

Brügmann, M. H.

D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91, 021803 (2015).

M. Lucchini, M. H. Brügmann, A. Ludwig, L. Gallmann, U. Keller, and T. Feurer, “Ptychographic reconstruction of attosecond pulses,” Opt. Express 23(23), 29502–29513 (2015).
[PubMed]

Bullkich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Cao, S.

S. Cao, P. Kok, P. Li, A. M. Maiden, and J. M. Rodenburg, “Modal decomposition of a propagating matter wave via electron ptychography,” Phys. Rev. A 94, 63621 (2016).

Chen, S.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

Claus, D.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[PubMed]

Clement, T. S.

Cohen, O.

P. Sidorenko, O. Lahav, and O. Cohen, “Ptychographic ultrahigh-speed imaging,” Opt. Express 25(10), 10997–11008 (2017).
[PubMed]

P. Sidorenko, O. Lahav, Z. Avnat, and O. Cohen, “Ptychographic reconstruction algorithm for frequency-resolved optical gating: super-resolution and supreme robustness,” Optica 3, 1320–1330 (2016).

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6, 8209 (2015).
[PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Cohen-Hyams, T.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Couprie, M.-E.

C. Bourassin-Bouchet and M.-E. Couprie, “Partially coherent ultrafast spectrography,” Nat. Commun. 6, 6465 (2015).
[PubMed]

Dana, H.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

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).

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

DeLucia, F. C.

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, and A. W. Miziolek, “Double pulse laser ablation and plasma: Laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta - Part B At. Spectrosc. 61, 999–1014 (2006).

Eldar, Y. C.

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6, 8209 (2015).
[PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[PubMed]

Escoto, E.

Feurer, T.

M. Lucchini, M. H. Brügmann, A. Ludwig, L. Gallmann, U. Keller, and T. Feurer, “Ptychographic reconstruction of attosecond pulses,” Opt. Express 23(23), 29502–29513 (2015).
[PubMed]

D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91, 021803 (2015).

Fischer, B.

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).

Fleischer, A.

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6, 8209 (2015).
[PubMed]

Gallmann, L.

Gardner, D. F.

Gat, O.

Gavartin, E.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).

Gazit, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[PubMed]

Giessen, H.

S. Linden, H. Giessen, and J. Kuhl, “XFROG - A New Method for Amplitude and Phase Characterization of Weak Ultrashort Pulses,” Phys. Status Solidi 206, 119–124 (1998).

Gordon, A.

Gorodetsky, M. L.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).

Gottfried, J. L.

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, and A. W. Miziolek, “Double pulse laser ablation and plasma: Laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta - Part B At. Spectrosc. 61, 999–1014 (2006).

Greening, D.

Gu, X.

Hartinger, K.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).

Herink, G.

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot,” Nat. Photonics 10, 321–326 (2016).

Herr, T.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).

Holzwarth, R.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).

Hoppe, W.

W. Hoppe and G. Strube, “Beugung in inhomogenen Primärstrahlenwellenfeld. II. Lichtoptische Analogieversuche zur Phasenmessung von Gitterinterferenzen,” Acta Crystallogr. A 25, 502–507 (1969).

Hu, G.

Hyyti, J.

Jalali, B.

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot,” Nat. Photonics 10, 321–326 (2016).

Kane, D. J.

D. J. Kane, “Principal components generalized projections: a review,” J. Opt. Soc. Am. B 25, A120–A132 (2008).

D. J. Kane, G. Rodriguez, A. J. Taylor, and T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. B 14, 935 (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).

Kapteyn, H. C.

Karl, R.

Kärtner, F. X.

Keller, U.

Kfir, O.

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6, 8209 (2015).
[PubMed]

Kimmel, M.

Kippenberg, T. J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).

Kley, E. B.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Kok, P.

S. Cao, P. Kok, P. Li, A. M. Maiden, and J. M. Rodenburg, “Modal decomposition of a propagating matter wave via electron ptychography,” Phys. Rev. A 94, 63621 (2016).

Kosloff, R.

D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85, 5805–5820 (1986).

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).

Kuhl, J.

S. Linden, H. Giessen, and J. Kuhl, “XFROG - A New Method for Amplitude and Phase Characterization of Weak Ultrashort Pulses,” Phys. Status Solidi 206, 119–124 (1998).

Lahav, O.

Leaird, D. E.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

Li, C.

Li, H.

Li, P.

S. Cao, P. Kok, P. Li, A. M. Maiden, and J. M. Rodenburg, “Modal decomposition of a propagating matter wave via electron ptychography,” Phys. Rev. A 94, 63621 (2016).

Linden, S.

S. Linden, H. Giessen, and J. Kuhl, “XFROG - A New Method for Amplitude and Phase Characterization of Weak Ultrashort Pulses,” Phys. Status Solidi 206, 119–124 (1998).

Liu, Y.

Y. Liu, X. Zhao, G. Hu, C. Li, B. Zhao, and Z. Zheng, “Unidirectional, dual-comb lasing under multiple pulse formation mechanisms in a passively mode-locked fiber ring laser,” Opt. Express 24(19), 21392–21398 (2016).
[PubMed]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

Lucchini, M.

Ludwig, A.

Maiden, A. M.

S. Cao, P. Kok, P. Li, A. M. Maiden, and J. M. Rodenburg, “Modal decomposition of a propagating matter wave via electron ptychography,” Phys. Rev. A 94, 63621 (2016).

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[PubMed]

Mairesse, Y.

Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Phys. Rev. A 71, 011401 (2005).

Mancuso, C. A.

Marangos, J. P.

Matia-Hernando, P.

Menzel, A.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[PubMed]

Miziolek, A. W.

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, and A. W. Miziolek, “Double pulse laser ablation and plasma: Laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta - Part B At. Spectrosc. 61, 999–1014 (2006).

Munson, C. A.

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, and A. W. Miziolek, “Double pulse laser ablation and plasma: Laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta - Part B At. Spectrosc. 61, 999–1014 (2006).

Murnane, M. M.

Neethling, P.

D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91, 021803 (2015).

O’Shea, P.

Osherovich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Ouzounov, D. G.

Porter, C. L.

Qi, M.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

Quéré, F.

Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Phys. Rev. A 71, 011401 (2005).

Rice, S. A.

D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85, 5805–5820 (1986).

D. J. Tannor and S. A. Rice, “Control of selectivity of chemical reaction via control of wave packet evolution,” J. Chem. Phys. 83, 5013–5018 (1985).

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).

Riemensberger, J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).

Rodenburg, J. M.

S. Cao, P. Kok, P. Li, A. M. Maiden, and J. M. Rodenburg, “Modal decomposition of a propagating matter wave via electron ptychography,” Phys. Rev. A 94, 63621 (2016).

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[PubMed]

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).

Rodriguez, G.

Rohwer, E.

D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91, 021803 (2015).

Ropers, C.

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot,” Nat. Photonics 10, 321–326 (2016).

Sander, M. Y.

Seaberg, M. H.

Segev, M.

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6, 8209 (2015).
[PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[PubMed]

Shanblatt, E. R.

Shechtman, Y.

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6, 8209 (2015).
[PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Shoham, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Sidorenko, P.

P. Sidorenko, O. Lahav, and O. Cohen, “Ptychographic ultrahigh-speed imaging,” Opt. Express 25(10), 10997–11008 (2017).
[PubMed]

P. Sidorenko, O. Lahav, Z. Avnat, and O. Cohen, “Ptychographic reconstruction algorithm for frequency-resolved optical gating: super-resolution and supreme robustness,” Optica 3, 1320–1330 (2016).

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6, 8209 (2015).
[PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Smulakovsky, V.

Solli, D. R.

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot,” Nat. Photonics 10, 321–326 (2016).

Spangenberg, D.

D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91, 021803 (2015).

Steiner, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Steinmeyer, G.

Strube, G.

W. Hoppe and G. Strube, “Beugung in inhomogenen Primärstrahlenwellenfeld. II. Lichtoptische Analogieversuche zur Phasenmessung von Gitterinterferenzen,” Acta Crystallogr. A 25, 502–507 (1969).

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).

Szameit, A.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[PubMed]

Tannor, D. J.

D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85, 5805–5820 (1986).

D. J. Tannor and S. A. Rice, “Control of selectivity of chemical reaction via control of wave packet evolution,” J. Chem. Phys. 83, 5013–5018 (1985).

Taylor, A. J.

Thibault, P.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[PubMed]

Tisch, J. W. G.

Trebino, R.

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort-pulse measurement,” Opt. Lett. 26(12), 932–934 (2001).
[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).

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

Vodonos, B.

Walke, D.

Wang, C. Y.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).

Wang, J.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

Wang, P.-H.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

Weiner, A. M.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

White, W. E.

Wise, F. W.

Witting, T.

Xuan, Y.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

Xue, X.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

Yavneh, I.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Zhang, B.

Zhao, B.

Zhao, X.

Zheng, Z.

Zibulevsky, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Acta Crystallogr. A (1)

W. Hoppe and G. Strube, “Beugung in inhomogenen Primärstrahlenwellenfeld. II. Lichtoptische Analogieversuche zur Phasenmessung von Gitterinterferenzen,” Acta Crystallogr. A 25, 502–507 (1969).

Adv. Imaging Electron Phys. (1)

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).

J. Chem. Phys. (2)

D. J. Tannor and S. A. Rice, “Control of selectivity of chemical reaction via control of wave packet evolution,” J. Chem. Phys. 83, 5013–5018 (1985).

D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85, 5805–5820 (1986).

J. Opt. Soc. Am. B (3)

Nat. Commun. (2)

C. Bourassin-Bouchet and M.-E. Couprie, “Partially coherent ultrafast spectrography,” Nat. Commun. 6, 6465 (2015).
[PubMed]

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6, 8209 (2015).
[PubMed]

Nat. Mater. (1)

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[PubMed]

Nat. Photonics (3)

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot,” Nat. Photonics 10, 321–326 (2016).

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).

Nature (1)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[PubMed]

Opt. Express (7)

Opt. Lett. (5)

Optica (1)

Phys. Rev. A (3)

Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Phys. Rev. A 71, 011401 (2005).

S. Cao, P. Kok, P. Li, A. M. Maiden, and J. M. Rodenburg, “Modal decomposition of a propagating matter wave via electron ptychography,” Phys. Rev. A 94, 63621 (2016).

D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91, 021803 (2015).

Phys. Status Solidi (1)

S. Linden, H. Giessen, and J. Kuhl, “XFROG - A New Method for Amplitude and Phase Characterization of Weak Ultrashort Pulses,” Phys. Status Solidi 206, 119–124 (1998).

Rev. Sci. Instrum. (1)

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).

Spectrochim. Acta - Part B At. Spectrosc. (1)

V. I. Babushok, F. C. DeLucia, J. L. Gottfried, C. A. Munson, and A. W. Miziolek, “Double pulse laser ablation and plasma: Laser induced breakdown spectroscopy signal enhancement,” Spectrochim. Acta - Part B At. Spectrosc. 61, 999–1014 (2006).

Ultramicroscopy (2)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[PubMed]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[PubMed]

Other (2)

T. Bendory, D. Edidin, and Y. C. Eldar, “On Signal Reconstruction from FROG Measurements,” https://arxiv.org/abs/1706.08494v1 (2017).

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer US, 2000).

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Figures (6)

Fig. 1
Fig. 1 Principle of the multiplexed FROG trace. (a) A burst of three pulses. The duration of each pulse is much shorter than the time interval between them. (b) SHG-FROG traces which are generated from each pulse separately. (c) A multiplexed FROG trace, that corresponds to the sum of the three individual traces depicted in (b).
Fig. 2
Fig. 2 Numerical example of characterization of three pulses from a single multiplexed FROG trace. (a-c) original (solid) and reconstructed (dashed) amplitudes and phases of the three simulated pulses, as well as calculated δ. The inset in each graph is the corresponding FROG traces. (d) Multiplexed FROG trace, corresponding to the sum of the individual FROG traces. (e) The multiplexed trace with white Gaussian noise at 10dB SNR. (f) Reconstructed multiplexed trace.
Fig. 3
Fig. 3 Statistical investigation of multiplexed FROG. Mean (over 50 realizations of multiplexed FROG traces) of the δ max in a burst as a function of the number of pulses for different noise levels. (a) Without and (b) with using power spectra constraint of the pulses.
Fig. 4
Fig. 4 Experimental demonstration of multiplexed FROG. (a) Measured multiplexed FROG trace of a two-pulse burst. (b) and (c) Measured FROG traces for each pulse in the burst. (d) Reconstructed multiplexed FROG trace. (e) and (f) Reconstructed pulses using multiplexed FROG (dashed curves) and ordinary FROG (solid curves).
Fig. 5
Fig. 5 Example for deducing the correct number of pulses in the burst. Trace reconstruction NMSE and reconstruction maximal δ max as a function of the number of assumed pulses (the original burst which contains 3 pulses is shown in Fig. 2). The correct number of pulses is identified by the knee in the curve of reconstructed trace NMSE vs number of pulses.
Fig. 6
Fig. 6 Multiplexed Blind FROG: concept and numerical demonstration. (a) Each pulse in the burst interacts only with its consecutive pulses. (b) The complete FROG trace of the burst. The multiplexed blind FROG trace corresponds to the side lobe marked with the dashed red box. (c) The blind FROG traces, which are the components of the multiplexed blind FROG. (d) The multiplexed blind FROG trace. (e) The multiplexed blind FROG trace with white Gaussian noise at 10dB SNR. (f-h) original and reconstructed amplitudes and phases of the three simulated pulses.

Equations (13)

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I MFROG N ( ω,τ )= n=1 N | E ( n ) ( t ) E ( n ) ( tτ ) e iωt dt | 2
I j N ( ω )= n=1 N | F( χ j ( n ) ( t ) ) | 2 ,
ψ j ( n ) ( t )= E ( n ) ( t ) E ( n ) ( ts( j )Δτ ).
Φ j ( n ) ( ω )= I s( j ) N F[ ψ j ( n ) ( t ) ] n | F[ ψ j ( n ) ( t ) ] | 2 .
ψ ˜ j ( n ) ( t )= F 1 [ Φ j ( n ) ( ω ) ].
E j+1 ( n ) ( t )= E j ( n ) ( t )+α E j ( n )* ( ts( j )Δτ ) | E j ( n ) ( ts( j )Δτ ) | max 2 ( ψ ˜ j ( n ) ( t ) ψ j ( n ) ( t ) ).
E ^ j+1 ( n ) ( ω )= S ^ j ( n ) F[ E j+1 ( n ) ( t ) ] | F[ E j+1 ( n ) ( t ) ] | .
E ^ j+1 ( n ) ( t )= F 1 [ E ^ j+1 ( n ) ( ω ) ].
δ( E, E ^ )=arcos( | E ^ ( t )| E( t ) | E ^ ( t )| E ^ ( t ) E( t )| E( t ) ),
ψ j ( n ) ( t )= E ( n ) ( t ) E ( n+1 ) ( ts( j )Δτ ).
E j+1 ( n ) ( t )= E j ( n ) ( t )+α E j ( n+1 )* ( ts( j )Δτ ) | E j ( n+1 ) ( ts( j )Δτ ) | max 2 ( ψ ˜ j ( n ) ( t ) ψ j ( n ) ( t ) )+ α E j ( n1 )* ( t+s( j )Δτ ) | E j ( n1 ) ( t+s( j )Δτ ) | max 2 ( ψ ˜ j ( n1 ) ( t+s( j )Δτ ) ψ j ( n1 ) ( t+s( j )Δτ ) )
E j+1 ( N ) ( t )= E j ( N ) ( t )+α E j ( N1 )* ( t+s( j )Δτ ) | E j ( N1 ) ( t+s( j )Δτ ) | max 2 , ( ψ ˜ j ( N1 ) ( t+s( j )Δτ ) ψ j ( N1 ) ( t+s( j )Δτ ) )
E j+1 ( 1 ) ( t )= E j ( 1 ) ( t )+α E j ( 2 )* ( ts( j )Δτ ) | E j ( 2 ) ( ts( j )Δτ ) | max 2 ( ψ ˜ j ( 1 ) ( t ) ψ j ( 1 ) ( t ) ).

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