Abstract

Attosecond light sources have provided insight into the fastest atomic-scale electronic dynamics. True attosecond-pump–attosecond-probe experiments require a single attosecond pulse at high intensity and large photon energy, a challenge that has yet to be conquered. Here we show 100-TW single attosecond x-ray pulses with unprecedented intensity of ${10^{21}}\;{{\rm W/cm}^2}$ and duration 8.0 as can be produced by intense laser irradiation of a capacitor-nanofoil target composed of two separate nanofoils. In the interaction, a strong electrostatic potential develops between the two foils, which drags electrons out of the second foil and piles them up in vacuum, forming an ultradense relativistic electron nanobunch. This nanobunch reaches both high density and high energy in only half a laser cycle and smears out in others, resulting in coherent synchrotron emission of a single, intense attosecond pulse. Such a pulse enables the capture and control of electron motion at the picometer–attosecond scale.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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2016 (1)

F. Krausz, Phys. Scripta 91, 063011 (2016).
[Crossref]

2015 (1)

T. Arber, K. Bennett, C. Brady, A. Lawrence-Douglas, M. Ramsay, N. Sircombe, P. Gillies, R. Evans, H. Schmitz, A. Bell, and C. P. Ridgers, Plasma Phys. Controlled Fusion 57, 113001 (2015).
[Crossref]

2014 (2)

M. Chini, K. Zhao, and Z. Chang, Nat. Photonics 8, 178 (2014).
[Crossref]

W. Ma, J. Bin, H. Wang, M. Yeung, C. Kreuzer, M. Streeter, P. Foster, S. Cousens, D. Kiefer, B. Dromey, and X. Q. Yan, Phys. Rev. Lett. 113, 235002 (2014).
[Crossref]

2012 (2)

J. A. Wheeler, A. Borot, S. Monchocé, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quéré, Nat. Photonics 6, 829 (2012).
[Crossref]

B. Dromey, S. Rykovanov, M. Yeung, R. Hörlein, D. Jung, D. Gautier, T. Dzelzainis, D. Kiefer, S. Palaniyppan, R. Shah, and J. Schreiber, Nat. Phys. 8, 804 (2012).
[Crossref]

2010 (4)

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 822 (2010).
[Crossref]

D. an der Brügge and A. Pukhov, Phys. Plasmas 17, 033110 (2010).
[Crossref]

A. Pukhov, D. An Der Brügge, and I. Kostyukov, Plasma Phys. Controlled Fusion 52, 124039 (2010).
[Crossref]

H. Lu, G. Ni, R. Li, and Z. Xu, J. Chem. Phys. 132, 124303 (2010).
[Crossref]

2009 (4)

H. Lu, J. Liu, C. Wang, W. Wang, Z. Zhou, A. Deng, C. Xia, Y. Xu, X. Lu, Y. Jiang, and Y. X. Leng, Phys. Rev. A 80, 051201 (2009).
[Crossref]

B. Qiao, M. Zepf, M. Borghesi, B. Dromey, and M. Geissler, New J. Phys. 11, 103042 (2009).
[Crossref]

U. Teubner and P. Gibbon, Rev. Mod. Phys. 81, 445 (2009).
[Crossref]

F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009).
[Crossref]

2006 (4)

T. Baeva, S. Gordienko, and A. Pukhov, Phys. Rev. E 74, 046404 (2006).
[Crossref]

F. Quéré, C. Thaury, P. Monot, S. Dobosz, P. Martin, J.-P. Geindre, and P. Audebert, Phys. Rev. Lett. 96, 125004 (2006).
[Crossref]

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, and M. Tampo, Nat. Phys. 2, 456 (2006).
[Crossref]

F. Tavella, A. Marcinkevičius, and F. Krausz, Opt. Express 14, 12822 (2006).
[Crossref]

2005 (1)

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, Phys. Rev. Lett. 94, 103903 (2005).
[Crossref]

2004 (2)

B. Dromey, S. Kar, M. Zepf, and P. Foster, Rev. Sci. Instru. 75, 645 (2004).
[Crossref]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, Phys. Rev. Lett. 93, 115002 (2004).
[Crossref]

1996 (2)

P. Gibbon, Phys. Rev. Lett. 76, 50 (1996).
[Crossref]

R. Lichters, J. Meyer-ter Vehn, and A. Pukhov, Phys. Plasmas 3, 3425 (1996).
[Crossref]

an der Brügge, D.

D. an der Brügge and A. Pukhov, Phys. Plasmas 17, 033110 (2010).
[Crossref]

A. Pukhov, D. An Der Brügge, and I. Kostyukov, Plasma Phys. Controlled Fusion 52, 124039 (2010).
[Crossref]

Arber, T.

T. Arber, K. Bennett, C. Brady, A. Lawrence-Douglas, M. Ramsay, N. Sircombe, P. Gillies, R. Evans, H. Schmitz, A. Bell, and C. P. Ridgers, Plasma Phys. Controlled Fusion 57, 113001 (2015).
[Crossref]

Arpin, P.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 822 (2010).
[Crossref]

Audebert, P.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, P. Martin, J.-P. Geindre, and P. Audebert, Phys. Rev. Lett. 96, 125004 (2006).
[Crossref]

Baeva, T.

T. Baeva, S. Gordienko, and A. Pukhov, Phys. Rev. E 74, 046404 (2006).
[Crossref]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, Phys. Rev. Lett. 94, 103903 (2005).
[Crossref]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, Phys. Rev. Lett. 93, 115002 (2004).
[Crossref]

Bell, A.

T. Arber, K. Bennett, C. Brady, A. Lawrence-Douglas, M. Ramsay, N. Sircombe, P. Gillies, R. Evans, H. Schmitz, A. Bell, and C. P. Ridgers, Plasma Phys. Controlled Fusion 57, 113001 (2015).
[Crossref]

Bennett, K.

T. Arber, K. Bennett, C. Brady, A. Lawrence-Douglas, M. Ramsay, N. Sircombe, P. Gillies, R. Evans, H. Schmitz, A. Bell, and C. P. Ridgers, Plasma Phys. Controlled Fusion 57, 113001 (2015).
[Crossref]

Bin, J.

W. Ma, J. Bin, H. Wang, M. Yeung, C. Kreuzer, M. Streeter, P. Foster, S. Cousens, D. Kiefer, B. Dromey, and X. Q. Yan, Phys. Rev. Lett. 113, 235002 (2014).
[Crossref]

Borghesi, M.

B. Qiao, M. Zepf, M. Borghesi, B. Dromey, and M. Geissler, New J. Phys. 11, 103042 (2009).
[Crossref]

Borot, A.

J. A. Wheeler, A. Borot, S. Monchocé, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quéré, Nat. Photonics 6, 829 (2012).
[Crossref]

Brady, C.

T. Arber, K. Bennett, C. Brady, A. Lawrence-Douglas, M. Ramsay, N. Sircombe, P. Gillies, R. Evans, H. Schmitz, A. Bell, and C. P. Ridgers, Plasma Phys. Controlled Fusion 57, 113001 (2015).
[Crossref]

Chang, Z.

M. Chini, K. Zhao, and Z. Chang, Nat. Photonics 8, 178 (2014).
[Crossref]

Chen, M.-C.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 822 (2010).
[Crossref]

Chini, M.

M. Chini, K. Zhao, and Z. Chang, Nat. Photonics 8, 178 (2014).
[Crossref]

Cousens, S.

W. Ma, J. Bin, H. Wang, M. Yeung, C. Kreuzer, M. Streeter, P. Foster, S. Cousens, D. Kiefer, B. Dromey, and X. Q. Yan, Phys. Rev. Lett. 113, 235002 (2014).
[Crossref]

Deng, A.

H. Lu, J. Liu, C. Wang, W. Wang, Z. Zhou, A. Deng, C. Xia, Y. Xu, X. Lu, Y. Jiang, and Y. X. Leng, Phys. Rev. A 80, 051201 (2009).
[Crossref]

Dobosz, S.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, P. Martin, J.-P. Geindre, and P. Audebert, Phys. Rev. Lett. 96, 125004 (2006).
[Crossref]

Dromey, B.

W. Ma, J. Bin, H. Wang, M. Yeung, C. Kreuzer, M. Streeter, P. Foster, S. Cousens, D. Kiefer, B. Dromey, and X. Q. Yan, Phys. Rev. Lett. 113, 235002 (2014).
[Crossref]

B. Dromey, S. Rykovanov, M. Yeung, R. Hörlein, D. Jung, D. Gautier, T. Dzelzainis, D. Kiefer, S. Palaniyppan, R. Shah, and J. Schreiber, Nat. Phys. 8, 804 (2012).
[Crossref]

B. Qiao, M. Zepf, M. Borghesi, B. Dromey, and M. Geissler, New J. Phys. 11, 103042 (2009).
[Crossref]

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, and M. Tampo, Nat. Phys. 2, 456 (2006).
[Crossref]

B. Dromey, S. Kar, M. Zepf, and P. Foster, Rev. Sci. Instru. 75, 645 (2004).
[Crossref]

Dzelzainis, T.

B. Dromey, S. Rykovanov, M. Yeung, R. Hörlein, D. Jung, D. Gautier, T. Dzelzainis, D. Kiefer, S. Palaniyppan, R. Shah, and J. Schreiber, Nat. Phys. 8, 804 (2012).
[Crossref]

Evans, R.

T. Arber, K. Bennett, C. Brady, A. Lawrence-Douglas, M. Ramsay, N. Sircombe, P. Gillies, R. Evans, H. Schmitz, A. Bell, and C. P. Ridgers, Plasma Phys. Controlled Fusion 57, 113001 (2015).
[Crossref]

Foster, P.

W. Ma, J. Bin, H. Wang, M. Yeung, C. Kreuzer, M. Streeter, P. Foster, S. Cousens, D. Kiefer, B. Dromey, and X. Q. Yan, Phys. Rev. Lett. 113, 235002 (2014).
[Crossref]

B. Dromey, S. Kar, M. Zepf, and P. Foster, Rev. Sci. Instru. 75, 645 (2004).
[Crossref]

Gautier, D.

B. Dromey, S. Rykovanov, M. Yeung, R. Hörlein, D. Jung, D. Gautier, T. Dzelzainis, D. Kiefer, S. Palaniyppan, R. Shah, and J. Schreiber, Nat. Phys. 8, 804 (2012).
[Crossref]

Geindre, J.-P.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, P. Martin, J.-P. Geindre, and P. Audebert, Phys. Rev. Lett. 96, 125004 (2006).
[Crossref]

Geissler, M.

B. Qiao, M. Zepf, M. Borghesi, B. Dromey, and M. Geissler, New J. Phys. 11, 103042 (2009).
[Crossref]

Gibbon, P.

U. Teubner and P. Gibbon, Rev. Mod. Phys. 81, 445 (2009).
[Crossref]

P. Gibbon, Phys. Rev. Lett. 76, 50 (1996).
[Crossref]

Gillies, P.

T. Arber, K. Bennett, C. Brady, A. Lawrence-Douglas, M. Ramsay, N. Sircombe, P. Gillies, R. Evans, H. Schmitz, A. Bell, and C. P. Ridgers, Plasma Phys. Controlled Fusion 57, 113001 (2015).
[Crossref]

Gopal, A.

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, and M. Tampo, Nat. Phys. 2, 456 (2006).
[Crossref]

Gordienko, S.

T. Baeva, S. Gordienko, and A. Pukhov, Phys. Rev. E 74, 046404 (2006).
[Crossref]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, Phys. Rev. Lett. 94, 103903 (2005).
[Crossref]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, Phys. Rev. Lett. 93, 115002 (2004).
[Crossref]

Hörlein, R.

B. Dromey, S. Rykovanov, M. Yeung, R. Hörlein, D. Jung, D. Gautier, T. Dzelzainis, D. Kiefer, S. Palaniyppan, R. Shah, and J. Schreiber, Nat. Phys. 8, 804 (2012).
[Crossref]

Ivanov, M.

F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009).
[Crossref]

Jiang, Y.

H. Lu, J. Liu, C. Wang, W. Wang, Z. Zhou, A. Deng, C. Xia, Y. Xu, X. Lu, Y. Jiang, and Y. X. Leng, Phys. Rev. A 80, 051201 (2009).
[Crossref]

Jung, D.

B. Dromey, S. Rykovanov, M. Yeung, R. Hörlein, D. Jung, D. Gautier, T. Dzelzainis, D. Kiefer, S. Palaniyppan, R. Shah, and J. Schreiber, Nat. Phys. 8, 804 (2012).
[Crossref]

Kapteyn, H. C.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 822 (2010).
[Crossref]

Kar, S.

B. Dromey, S. Kar, M. Zepf, and P. Foster, Rev. Sci. Instru. 75, 645 (2004).
[Crossref]

Kiefer, D.

W. Ma, J. Bin, H. Wang, M. Yeung, C. Kreuzer, M. Streeter, P. Foster, S. Cousens, D. Kiefer, B. Dromey, and X. Q. Yan, Phys. Rev. Lett. 113, 235002 (2014).
[Crossref]

B. Dromey, S. Rykovanov, M. Yeung, R. Hörlein, D. Jung, D. Gautier, T. Dzelzainis, D. Kiefer, S. Palaniyppan, R. Shah, and J. Schreiber, Nat. Phys. 8, 804 (2012).
[Crossref]

Kodama, R.

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, and M. Tampo, Nat. Phys. 2, 456 (2006).
[Crossref]

Kostyukov, I.

A. Pukhov, D. An Der Brügge, and I. Kostyukov, Plasma Phys. Controlled Fusion 52, 124039 (2010).
[Crossref]

Krausz, F.

F. Krausz, Phys. Scripta 91, 063011 (2016).
[Crossref]

F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009).
[Crossref]

F. Tavella, A. Marcinkevičius, and F. Krausz, Opt. Express 14, 12822 (2006).
[Crossref]

Kreuzer, C.

W. Ma, J. Bin, H. Wang, M. Yeung, C. Kreuzer, M. Streeter, P. Foster, S. Cousens, D. Kiefer, B. Dromey, and X. Q. Yan, Phys. Rev. Lett. 113, 235002 (2014).
[Crossref]

Krushelnick, K.

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, and M. Tampo, Nat. Phys. 2, 456 (2006).
[Crossref]

Lancaster, K.

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, and M. Tampo, Nat. Phys. 2, 456 (2006).
[Crossref]

Lawrence-Douglas, A.

T. Arber, K. Bennett, C. Brady, A. Lawrence-Douglas, M. Ramsay, N. Sircombe, P. Gillies, R. Evans, H. Schmitz, A. Bell, and C. P. Ridgers, Plasma Phys. Controlled Fusion 57, 113001 (2015).
[Crossref]

Leng, Y. X.

H. Lu, J. Liu, C. Wang, W. Wang, Z. Zhou, A. Deng, C. Xia, Y. Xu, X. Lu, Y. Jiang, and Y. X. Leng, Phys. Rev. A 80, 051201 (2009).
[Crossref]

Li, R.

H. Lu, G. Ni, R. Li, and Z. Xu, J. Chem. Phys. 132, 124303 (2010).
[Crossref]

Lichters, R.

R. Lichters, J. Meyer-ter Vehn, and A. Pukhov, Phys. Plasmas 3, 3425 (1996).
[Crossref]

Liu, J.

H. Lu, J. Liu, C. Wang, W. Wang, Z. Zhou, A. Deng, C. Xia, Y. Xu, X. Lu, Y. Jiang, and Y. X. Leng, Phys. Rev. A 80, 051201 (2009).
[Crossref]

Lopez-Martens, R.

J. A. Wheeler, A. Borot, S. Monchocé, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quéré, Nat. Photonics 6, 829 (2012).
[Crossref]

Lu, H.

H. Lu, G. Ni, R. Li, and Z. Xu, J. Chem. Phys. 132, 124303 (2010).
[Crossref]

H. Lu, J. Liu, C. Wang, W. Wang, Z. Zhou, A. Deng, C. Xia, Y. Xu, X. Lu, Y. Jiang, and Y. X. Leng, Phys. Rev. A 80, 051201 (2009).
[Crossref]

Lu, X.

H. Lu, J. Liu, C. Wang, W. Wang, Z. Zhou, A. Deng, C. Xia, Y. Xu, X. Lu, Y. Jiang, and Y. X. Leng, Phys. Rev. A 80, 051201 (2009).
[Crossref]

Ma, W.

W. Ma, J. Bin, H. Wang, M. Yeung, C. Kreuzer, M. Streeter, P. Foster, S. Cousens, D. Kiefer, B. Dromey, and X. Q. Yan, Phys. Rev. Lett. 113, 235002 (2014).
[Crossref]

Malvache, A.

J. A. Wheeler, A. Borot, S. Monchocé, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quéré, Nat. Photonics 6, 829 (2012).
[Crossref]

Marcinkevicius, A.

Martin, P.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, P. Martin, J.-P. Geindre, and P. Audebert, Phys. Rev. Lett. 96, 125004 (2006).
[Crossref]

Meyer-ter Vehn, J.

R. Lichters, J. Meyer-ter Vehn, and A. Pukhov, Phys. Plasmas 3, 3425 (1996).
[Crossref]

Monchocé, S.

J. A. Wheeler, A. Borot, S. Monchocé, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quéré, Nat. Photonics 6, 829 (2012).
[Crossref]

Monot, P.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, P. Martin, J.-P. Geindre, and P. Audebert, Phys. Rev. Lett. 96, 125004 (2006).
[Crossref]

Moustaizis, S.

B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, and M. Tampo, Nat. Phys. 2, 456 (2006).
[Crossref]

Murnane, M. M.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 822 (2010).
[Crossref]

Ni, G.

H. Lu, G. Ni, R. Li, and Z. Xu, J. Chem. Phys. 132, 124303 (2010).
[Crossref]

Palaniyppan, S.

B. Dromey, S. Rykovanov, M. Yeung, R. Hörlein, D. Jung, D. Gautier, T. Dzelzainis, D. Kiefer, S. Palaniyppan, R. Shah, and J. Schreiber, Nat. Phys. 8, 804 (2012).
[Crossref]

Popmintchev, T.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 822 (2010).
[Crossref]

Pukhov, A.

D. an der Brügge and A. Pukhov, Phys. Plasmas 17, 033110 (2010).
[Crossref]

A. Pukhov, D. An Der Brügge, and I. Kostyukov, Plasma Phys. Controlled Fusion 52, 124039 (2010).
[Crossref]

T. Baeva, S. Gordienko, and A. Pukhov, Phys. Rev. E 74, 046404 (2006).
[Crossref]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, Phys. Rev. Lett. 94, 103903 (2005).
[Crossref]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, Phys. Rev. Lett. 93, 115002 (2004).
[Crossref]

R. Lichters, J. Meyer-ter Vehn, and A. Pukhov, Phys. Plasmas 3, 3425 (1996).
[Crossref]

Qiao, B.

B. Qiao, M. Zepf, M. Borghesi, B. Dromey, and M. Geissler, New J. Phys. 11, 103042 (2009).
[Crossref]

Quéré, F.

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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. Schematic for the mechanism of a single attosecond x-ray pulse generation by an intense laser irradiating a capacitor-nanofoil target composed of two separate nanofoils. (a) Electrons of the first nanofoil are blown out at the peak laser cycle, forming a flying relativistic electron mirror, which rapidly impacts the second nanofoil. (b) The second nanofoil acquires significant negative charges, developing a strong electrostatic potential (green) between two foils. This potential drags a large number of electrons out of the second foil and piles them up, forming a dense relativistic electron nanobunch for enhanced CSE of attosecond x-ray pulse.
Fig. 2.
Fig. 2. 1D PIC simulation. (a) Electron longitudinal energy density distribution map $ {n_e}{\gamma _x} $ evolving with time from $ t = 26 $ to $ 29{T_0} $. Square of the corresponding reflected radiation field amplitude $ E_{\text{ref}}^2 $ (orange, red, and green lines) is also plotted. (b), (c) Electron $ {\gamma _x} $ distributions at $ t = 27.57{T_0} $ around the peak of the laser and $ 28.08{T_0} $ of the next laser cycle, respectively. (d)–(f) Electron density distributions of the first (purple, $ {n_1} $) and second (red, $ {n_2} $) foils, electrostatic force (blue), and laser ponderomotive force (green) at $ t = 27.48 $, 27.57, and $ 28.08{T_0} $. The initial positions of the two foils are marked with dashed lines. (g) Velocity $ {v_x} $ of one representative electron, for the capacitor-nanofoil target (CNT) and the single foil target (SFT) cases. (h) Harmonic spectrum for radiation in the reflected direction. (i) Obtained radiation pulse amplitude $ E_{\text{atto}}^2 $ versus position $ x $ by applying a spectral filter to select $ \omega \gt 100{\omega _0} $. The inset shows the zoomed single pulse with an envelope fitting (red).
Fig. 3.
Fig. 3. 2D PIC results. (a), (b) Normalized electron density ($ {n_e}/{n_c} $) and longitudinal momentum ($ {\gamma _x} $) maps, respectively, at $ t = 27.57{T_0} $ around the peak laser intensity. (c) By selecting harmonics above $ 100{\omega _0} $, a single attosecond x-ray pulse is produced with $ {I_{\text{rad}}} = 2.7 \times {10^{19}}\;{\rm W}/{{\rm cm}^2} $ ($ E_{\text{atto}}^2 = 12.6 $) and $ {\tau _{\text{rad}}} = 14\;{\rm as} $ (see the inset for its longitudinal profile).
Fig. 4.
Fig. 4. Demonstrative experimental design for the proposed scheme by using petawatt–femtosecond lasers. (a) Experimental setup. (b), (c) 1D PIC simulation result: (b) compressed ultradense relativistic electron nanobunch of density $ 2500{n_c} $ (red line for the electron density of the second foil) is formed, where the blue line is that of the first foil; (c) single attosecond x-ray pulse with intensity $ I = 7.3 \times {10^{19}}\;{\rm W}/{{\rm cm}^2} $ and duration $ \tau = 24\;{\rm as} $ is obtained with the same filter, where the inset shows the zoomed attosecond pulse with an envelope fitting (red).

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