Abstract

A key requirement for femtosecond spectroscopy measurements is to compress the laser pulse to its transform-limited duration. In particular, for few-cycle laser pulses, the compression process is time-consuming using conventional algorithms that converge statistically. Here we show that machine learning can accelerate the process of pulse compression: we have developed an adaptive neural-network algorithm to control a deformable-mirror–based pulse shaper that converges 100× faster than a standard evolutionary algorithm.

© 2018 Optical Society of America

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References

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2016 (1)

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, Nature 530, 66 (2016).
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2015 (1)

L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, J. Chem. Phys. 143, 164203 (2015).
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2012 (1)

M. T. Hassan, A. Wirth, I. Grguraš, T. Moulet, T. T. Luu, J. Gagnon, V. Pervak, and E. Goulielmakis, Rev. Sci. Instrum. 83, 111301 (2012).
[Crossref]

2011 (2)

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-C. Chen, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, Nat. Photonics 5, 475 (2011).
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A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, Science 334, 195 (2011).
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2008 (1)

R. Selle, T. Brixner, M. Wollenhaupt, and T. Baumert, J. Phys. B 41, 074019 (2008).
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2007 (1)

R. Selle, G. Vogt, T. Brixner, G. Gerber, R. Metzler, and W. Kinzel, Phys. Rev. A 76, 023810 (2007).
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2006 (1)

2005 (1)

V. I. Prokhorenko, A. M. Nagy, and R. Miller, J. Chem. Phys. 122, 184502 (2005).
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2004 (1)

2002 (1)

2001 (1)

2000 (1)

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1999 (2)

1997 (1)

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
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1995 (1)

G. V. Vdovin, Opt. Eng. 34, 3249 (1995).
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1994 (1)

A. Y. Zomaya, IEEE Trans. Syst. Man Cybernet. 24, 357 (1994).
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1993 (2)

T. H. Lee and W. K. Tan, Mechatronics 3, 705 (1993).
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1992 (1)

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1990 (1)

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1987 (1)

1984 (1)

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A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, Science 334, 195 (2011).
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Angelow, G.

Azzeer, A. M.

A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, Science 334, 195 (2011).
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Backus, S.

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Baumert, T.

R. Selle, T. Brixner, M. Wollenhaupt, and T. Baumert, J. Phys. B 41, 074019 (2008).
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T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
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S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-C. Chen, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, Nat. Photonics 5, 475 (2011).
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Boiko, A.

Brazard, J.

L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, J. Chem. Phys. 143, 164203 (2015).
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Brito Cruz, C. H.

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R. Selle, T. Brixner, M. Wollenhaupt, and T. Baumert, J. Phys. B 41, 074019 (2008).
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L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, J. Chem. Phys. 143, 164203 (2015).
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Chen, L.-C.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-C. Chen, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, Nat. Photonics 5, 475 (2011).
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Chen, Y.

Z. Sun, Y. Chen, X. Li, X. Qin, and H. Wang, Opt. Commun. 382, 519 (2017).
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Cirmi, G.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-C. Chen, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, Nat. Photonics 5, 475 (2011).
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I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT, 2016).

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De Jesús, O.

M. T. Hagan, H. B. Demuth, M. H. Beale, and O. De Jesús, Neural Network Design, 2nd ed. (2014).

Demuth, H. B.

M. T. Hagan, H. B. Demuth, M. H. Beale, and O. De Jesús, Neural Network Design, 2nd ed. (2014).

Diaz-Pernas, F. J.

C. Gonzalez-Gutierrez, J. D. Santos, M. Martinez-Zarzuela, A. G. Basden, J. Osborn, F. J. Diaz-Pernas, and F. Javier de Cos Juez, Sensors 17, 1263 (2017).
[Crossref]

DiMauro, L. F.

H. Liang, P. Krogen, Z. Wang, H. Park, T. Kroh, K. Zawilski, P. Schunemann, J. Moses, L. F. DiMauro, F. X. Kärtner, and K.-H. Hong, Nat. Commun. 8, 141 (2017).
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Eggleton, B. J.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-C. Chen, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, Nat. Photonics 5, 475 (2011).
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Ell, R.

Feurer, T.

Flemens, N.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K.-H. Hong, F. X. Kärtner, and J. Moses, Nat. Photonics 11, 222 (2017).
[Crossref]

Fork, R. L.

Fujimoto, J. G.

Gagnon, J.

M. T. Hassan, A. Wirth, I. Grguraš, T. Moulet, T. T. Luu, J. Gagnon, V. Pervak, and E. Goulielmakis, Rev. Sci. Instrum. 83, 111301 (2012).
[Crossref]

A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, Science 334, 195 (2011).
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Garg, M.

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K. J. Hunt, D. Sbarbaro, R. Zbikowski, and P. J. Gawthrop, Automatica 28, 1083 (1992).
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L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, J. Chem. Phys. 143, 164203 (2015).
[Crossref]

Gerber, G.

R. Selle, G. Vogt, T. Brixner, G. Gerber, R. Metzler, and W. Kinzel, Phys. Rev. A 76, 023810 (2007).
[Crossref]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[Crossref]

Gonzalez-Gutierrez, C.

C. Gonzalez-Gutierrez, J. D. Santos, M. Martinez-Zarzuela, A. G. Basden, J. Osborn, F. J. Diaz-Pernas, and F. Javier de Cos Juez, Sensors 17, 1263 (2017).
[Crossref]

Goodfellow, I.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT, 2016).

Gordon, J. P.

Goulielmakis, E.

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, Nature 530, 66 (2016).
[Crossref]

M. T. Hassan, A. Wirth, I. Grguraš, T. Moulet, T. T. Luu, J. Gagnon, V. Pervak, and E. Goulielmakis, Rev. Sci. Instrum. 83, 111301 (2012).
[Crossref]

A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, Science 334, 195 (2011).
[Crossref]

Greenaway, A. H.

Grguraš, I.

M. T. Hassan, A. Wirth, I. Grguraš, T. Moulet, T. T. Luu, J. Gagnon, V. Pervak, and E. Goulielmakis, Rev. Sci. Instrum. 83, 111301 (2012).
[Crossref]

A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, Science 334, 195 (2011).
[Crossref]

Hagan, M. T.

M. T. Hagan, H. B. Demuth, M. H. Beale, and O. De Jesús, Neural Network Design, 2nd ed. (2014).

Hassan, M. T.

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, Nature 530, 66 (2016).
[Crossref]

M. T. Hassan, A. Wirth, I. Grguraš, T. Moulet, T. T. Luu, J. Gagnon, V. Pervak, and E. Goulielmakis, Rev. Sci. Instrum. 83, 111301 (2012).
[Crossref]

A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, Science 334, 195 (2011).
[Crossref]

Hong, K.-H.

H. Liang, P. Krogen, Z. Wang, H. Park, T. Kroh, K. Zawilski, P. Schunemann, J. Moses, L. F. DiMauro, F. X. Kärtner, and K.-H. Hong, Nat. Commun. 8, 141 (2017).
[Crossref]

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K.-H. Hong, F. X. Kärtner, and J. Moses, Nat. Photonics 11, 222 (2017).
[Crossref]

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-C. Chen, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, Nat. Photonics 5, 475 (2011).
[Crossref]

Huang, S.-W.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-C. Chen, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, Nat. Photonics 5, 475 (2011).
[Crossref]

Hunt, K. J.

K. J. Hunt, D. Sbarbaro, R. Zbikowski, and P. J. Gawthrop, Automatica 28, 1083 (1992).
[Crossref]

Ippen, E. P.

Javier de Cos Juez, F.

C. Gonzalez-Gutierrez, J. D. Santos, M. Martinez-Zarzuela, A. G. Basden, J. Osborn, F. J. Diaz-Pernas, and F. Javier de Cos Juez, Sensors 17, 1263 (2017).
[Crossref]

Kapteyn, H.

Karpowicz, N.

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, Nature 530, 66 (2016).
[Crossref]

Kärtner, F. X.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K.-H. Hong, F. X. Kärtner, and J. Moses, Nat. Photonics 11, 222 (2017).
[Crossref]

H. Liang, P. Krogen, Z. Wang, H. Park, T. Kroh, K. Zawilski, P. Schunemann, J. Moses, L. F. DiMauro, F. X. Kärtner, and K.-H. Hong, Nat. Commun. 8, 141 (2017).
[Crossref]

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-C. Chen, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, Nat. Photonics 5, 475 (2011).
[Crossref]

R. Ell, U. Morgner, F. X. Kärtner, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, M. J. Lederer, A. Boiko, and B. Luther-Davies, Opt. Lett. 26, 373 (2001).
[Crossref]

Kinzel, W.

R. Selle, G. Vogt, T. Brixner, G. Gerber, R. Metzler, and W. Kinzel, Phys. Rev. A 76, 023810 (2007).
[Crossref]

Koehl, R. M.

Krausz, F.

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, Nature 530, 66 (2016).
[Crossref]

A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, Science 334, 195 (2011).
[Crossref]

Krogen, P.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K.-H. Hong, F. X. Kärtner, and J. Moses, Nat. Photonics 11, 222 (2017).
[Crossref]

H. Liang, P. Krogen, Z. Wang, H. Park, T. Kroh, K. Zawilski, P. Schunemann, J. Moses, L. F. DiMauro, F. X. Kärtner, and K.-H. Hong, Nat. Commun. 8, 141 (2017).
[Crossref]

Kroh, T.

H. Liang, P. Krogen, Z. Wang, H. Park, T. Kroh, K. Zawilski, P. Schunemann, J. Moses, L. F. DiMauro, F. X. Kärtner, and K.-H. Hong, Nat. Commun. 8, 141 (2017).
[Crossref]

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Nature (1)

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Opt. Express (1)

Opt. Lett. (5)

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Science (1)

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Sensors (1)

C. Gonzalez-Gutierrez, J. D. Santos, M. Martinez-Zarzuela, A. G. Basden, J. Osborn, F. J. Diaz-Pernas, and F. Javier de Cos Juez, Sensors 17, 1263 (2017).
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S. Shalev-Shwartz and S. Ben-David, Understanding Machine Learning: From Theory to Algorithms (Cambridge University, 2014).

M. T. Hagan, H. B. Demuth, M. H. Beale, and O. De Jesús, Neural Network Design, 2nd ed. (2014).

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Figures (3)

Fig. 1.
Fig. 1. (a) NNA iteration sequence: the iterative feedback loop executed by the NNA is composed of steps 1–5 (detailed in the text). In summary, the neural network selects the DM actuator positions ( actu ( t ) ) that will modulate the pulse to produce an ideal goal signal ( int P ( t ) ) , which the prediction function calculates based on the current nonresonant response signal ( int A ( t ) ) induced by the pulse. (b) Prediction function (description in text) implements a variation of reinforcement learning: it assesses the total summed intensity value as an indicator of the success of the previous iteration to respond to the system in executing the next iteration.
Fig. 2.
Fig. 2. Normalized, summed intensity values are plotted versus iterations of EA (red) and NNA (blue) optimization. (Each point of the EA curve represents one generation, equivalent to 60 iterations; each point of the NNA curve represents one iteration.) The NNA converges to an optimized pulse in approximately 100 × fewer iterations than the EA, as demonstrated here with representative samples: the NNA converged in 13 iterations, while the EA converged in 1021 iterations.
Fig. 3.
Fig. 3. TG–FROG scan demonstrates the resulting pulse compression after pulse optimization with the NNA. The NNA converged to the optimized 6.1 fs pulse shown after 42 iterations in this experiment.

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