Abstract

A new method for retrieving the spectral phase of isolated attosecond X-ray pulses from streaking traces is explored. The neural network method shows the potential for nearly instantaneous attosecond streaking phase retrieval, without use of the central momentum approximation. A neural network is trained with computer generated data that contain statistical noise and shown to correctly retrieve the phase of both computer generated and experimental attosecond streaking traces.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
    [Crossref]
  2. M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nature Photonics 8, 178–186 (2014).
    [Crossref]
  3. Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Physical Review A 71, 011401 (2005).
    [Crossref]
  4. D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE Journal of Quantum Electronics 29, 571–579 (1993).
    [Crossref]
  5. M. Chini, S. Gilbertson, S. D. Khan, and Z. Chang, “Characterizing ultrabroadband attosecond lasers,” Opt. Express 18, 13006–13016 (2010).
    [Crossref] [PubMed]
  6. X. Zhao, H. Wei, Y. Wu, and C. D. Lin, “Phase-retrieval algorithm for the characterization of broadband single attosecond pulses,” Physical Review A 95, 043407 (2017).
    [Crossref]
  7. P. Keathley, S. Bhardwaj, J. Moses, G. Laurent, and F. Kärtner, “Volkov transform generalized projection algorithm for attosecond pulse characterization,” New Journal of Physics 18, 073009 (2016).
    [Crossref]
  8. T. Zahavy, A. Dikopoltsev, D. Moss, G. I. Haham, O. Cohen, S. Mannor, and M. Segev, “Deep learning reconstruction of ultrashort pulses,” Optica 5, 666–673 (2018).
    [Crossref]
  9. A. Géron, Hands-On Machine Learning with Scikit-Learn and TensorFlow (O’Reilly Media, 2017).
  10. J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Physical Review Letters 88, 173903 (2002).
    [Crossref] [PubMed]
  11. J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
    [Crossref] [PubMed]
  12. Li Jie, “Generation and characterization of isolated attosecond pulse in the soft X-ray region,” PhD thesis, University of Central Florida (2017). http://ifast.ucf.edu/Publications.aspx?Type=8&Header=Dissertations
  13. D. Kingma and J. Ba, “Adam: a method for stochastic optimization” (2014). arXiv preprint, arXiv preprint arXiv:1412.6980.
  14. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
    [Crossref] [PubMed]

2018 (1)

2017 (2)

X. Zhao, H. Wei, Y. Wu, and C. D. Lin, “Phase-retrieval algorithm for the characterization of broadband single attosecond pulses,” Physical Review A 95, 043407 (2017).
[Crossref]

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

2016 (1)

P. Keathley, S. Bhardwaj, J. Moses, G. Laurent, and F. Kärtner, “Volkov transform generalized projection algorithm for attosecond pulse characterization,” New Journal of Physics 18, 073009 (2016).
[Crossref]

2014 (2)

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nature Photonics 8, 178–186 (2014).
[Crossref]

2010 (1)

2006 (1)

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

2005 (1)

Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Physical Review A 71, 011401 (2005).
[Crossref]

2002 (1)

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Physical Review Letters 88, 173903 (2002).
[Crossref] [PubMed]

1993 (1)

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE Journal of Quantum Electronics 29, 571–579 (1993).
[Crossref]

Altucci, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Avaldi, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Ba, J.

D. Kingma and J. Ba, “Adam: a method for stochastic optimization” (2014). arXiv preprint, arXiv preprint arXiv:1412.6980.

Benedetti, E.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Bhardwaj, S.

P. Keathley, S. Bhardwaj, J. Moses, G. Laurent, and F. Kärtner, “Volkov transform generalized projection algorithm for attosecond pulse characterization,” New Journal of Physics 18, 073009 (2016).
[Crossref]

Burgdörfer, J.

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

Calegari, F.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Cederbaum, L. S.

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

Chang, Z.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nature Photonics 8, 178–186 (2014).
[Crossref]

M. Chini, S. Gilbertson, S. D. Khan, and Z. Chang, “Characterizing ultrabroadband attosecond lasers,” Opt. Express 18, 13006–13016 (2010).
[Crossref] [PubMed]

Cheng, Y.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

Chew, A.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

Chini, M.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nature Photonics 8, 178–186 (2014).
[Crossref]

M. Chini, S. Gilbertson, S. D. Khan, and Z. Chang, “Characterizing ultrabroadband attosecond lasers,” Opt. Express 18, 13006–13016 (2010).
[Crossref] [PubMed]

Cohen, O.

Corkum, P. B.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Physical Review Letters 88, 173903 (2002).
[Crossref] [PubMed]

Cunningham, E.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

Dikopoltsev, A.

Dudovich, N.

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

Feist, J.

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

Flammini, R.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Géron, A.

A. Géron, Hands-On Machine Learning with Scikit-Learn and TensorFlow (O’Reilly Media, 2017).

Gilbertson, S.

Greene, C. H.

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

Haham, G. I.

Hu, S.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

Itatani, J.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Physical Review Letters 88, 173903 (2002).
[Crossref] [PubMed]

Ivanov, M.

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

Ivanov, M. Y.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Physical Review Letters 88, 173903 (2002).
[Crossref] [PubMed]

Jie, Li

Li Jie, “Generation and characterization of isolated attosecond pulse in the soft X-ray region,” PhD thesis, University of Central Florida (2017). http://ifast.ucf.edu/Publications.aspx?Type=8&Header=Dissertations

Kane, D. J.

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE Journal of Quantum Electronics 29, 571–579 (1993).
[Crossref]

Kärtner, F.

P. Keathley, S. Bhardwaj, J. Moses, G. Laurent, and F. Kärtner, “Volkov transform generalized projection algorithm for attosecond pulse characterization,” New Journal of Physics 18, 073009 (2016).
[Crossref]

Keathley, P.

P. Keathley, S. Bhardwaj, J. Moses, G. Laurent, and F. Kärtner, “Volkov transform generalized projection algorithm for attosecond pulse characterization,” New Journal of Physics 18, 073009 (2016).
[Crossref]

Khan, S. D.

Kienberger, R.

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

Kingma, D.

D. Kingma and J. Ba, “Adam: a method for stochastic optimization” (2014). arXiv preprint, arXiv preprint arXiv:1412.6980.

Krausz, F.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Physical Review Letters 88, 173903 (2002).
[Crossref] [PubMed]

Laurent, G.

P. Keathley, S. Bhardwaj, J. Moses, G. Laurent, and F. Kärtner, “Volkov transform generalized projection algorithm for attosecond pulse characterization,” New Journal of Physics 18, 073009 (2016).
[Crossref]

Leone, S. R.

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

Li, J.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

Lin, C. D.

X. Zhao, H. Wei, Y. Wu, and C. D. Lin, “Phase-retrieval algorithm for the characterization of broadband single attosecond pulses,” Physical Review A 95, 043407 (2017).
[Crossref]

Mairesse, Y.

Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Physical Review A 71, 011401 (2005).
[Crossref]

Mannor, S.

McCurdy, C. W.

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

Moses, J.

P. Keathley, S. Bhardwaj, J. Moses, G. Laurent, and F. Kärtner, “Volkov transform generalized projection algorithm for attosecond pulse characterization,” New Journal of Physics 18, 073009 (2016).
[Crossref]

Moss, D.

Nisoli, M.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Poletto, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Quéré, F.

Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Physical Review A 71, 011401 (2005).
[Crossref]

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Physical Review Letters 88, 173903 (2002).
[Crossref] [PubMed]

Ren, X.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

Sansone, G.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Segev, M.

Silvestri, S. De

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Stagira, S.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Trebino, R.

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE Journal of Quantum Electronics 29, 571–579 (1993).
[Crossref]

Velotta, R.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Villoresi, P.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Vozzi, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Wang, Y.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

Wei, H.

X. Zhao, H. Wei, Y. Wu, and C. D. Lin, “Phase-retrieval algorithm for the characterization of broadband single attosecond pulses,” Physical Review A 95, 043407 (2017).
[Crossref]

Wu, Y.

X. Zhao, H. Wei, Y. Wu, and C. D. Lin, “Phase-retrieval algorithm for the characterization of broadband single attosecond pulses,” Physical Review A 95, 043407 (2017).
[Crossref]

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

Yin, Y.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

Yudin, G. L.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Physical Review Letters 88, 173903 (2002).
[Crossref] [PubMed]

Zahavy, T.

Zhao, K.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nature Photonics 8, 178–186 (2014).
[Crossref]

Zhao, X.

X. Zhao, H. Wei, Y. Wu, and C. D. Lin, “Phase-retrieval algorithm for the characterization of broadband single attosecond pulses,” Physical Review A 95, 043407 (2017).
[Crossref]

IEEE Journal of Quantum Electronics (1)

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE Journal of Quantum Electronics 29, 571–579 (1993).
[Crossref]

Nature Communications (1)

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nature Communications 8, 186 (2017).
[Crossref] [PubMed]

Nature Photonics (2)

S. R. Leone, C. W. McCurdy, J. Burgdörfer, L. S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C. H. Greene, M. Ivanov, and R. Kienberger, “What will it take to observe processes in’real time’?” Nature Photonics 8, 162–166 (2014).
[Crossref]

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nature Photonics 8, 178–186 (2014).
[Crossref]

New Journal of Physics (1)

P. Keathley, S. Bhardwaj, J. Moses, G. Laurent, and F. Kärtner, “Volkov transform generalized projection algorithm for attosecond pulse characterization,” New Journal of Physics 18, 073009 (2016).
[Crossref]

Opt. Express (1)

Optica (1)

Physical Review A (2)

X. Zhao, H. Wei, Y. Wu, and C. D. Lin, “Phase-retrieval algorithm for the characterization of broadband single attosecond pulses,” Physical Review A 95, 043407 (2017).
[Crossref]

Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Physical Review A 71, 011401 (2005).
[Crossref]

Physical Review Letters (1)

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Physical Review Letters 88, 173903 (2002).
[Crossref] [PubMed]

Science (1)

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Other (3)

A. Géron, Hands-On Machine Learning with Scikit-Learn and TensorFlow (O’Reilly Media, 2017).

Li Jie, “Generation and characterization of isolated attosecond pulse in the soft X-ray region,” PhD thesis, University of Central Florida (2017). http://ifast.ucf.edu/Publications.aspx?Type=8&Header=Dissertations

D. Kingma and J. Ba, “Adam: a method for stochastic optimization” (2014). arXiv preprint, arXiv preprint arXiv:1412.6980.

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Figures (4)

Fig. 1
Fig. 1 The MSE cost function is evaluated on 500 samples from the training set after each epoch to evaluate the accuracy of the network on the training data set of 80,000 samples.
Fig. 2
Fig. 2 (a) Input streaking trace. (b) True XUV spectrum and phase corresponding to the streaking trace. (c) Streaking trace from the predicted XUV field (d) Predicted XUV from the neural network output.
Fig. 3
Fig. 3 Several streaking traces are generated and input to the network to test the accuracy of the network with computer generated data. The MSE values of the output field vectors for these traces are similar to the training error shown in Fig. 1.
Fig. 4
Fig. 4 (a) Input measured streaking trace. (b) Reconstructed Streaking Trace. (c) Predicted XUV spectral phase.

Equations (7)

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s ( K , τ d ) = | ε X ( t τ d ) d [ v + A L ( t ) ] e i Φ G ( v , t ) e i ( K + I p ) t d t | 2
Φ G ( v , t ) = t v A L ( t ) d t
K = 1 2 v 2
Out i Supervised = ( E r e a l X U V o u t E i m a g X U V o u t E r e a l I R o u t E i m a g I R o u t ) y i = ( E r e a l X U V y E i m a g X U V y E r e a l I R y E i m a g I R y )
Out i Unsupervised = ( S o u t ( K , τ d ) ) y i = ( S y ( K , τ d ) )
C = 1 n i = 1 n ( Out i y i ) 2 f
θ n e x t = θ η θ C