Abstract

It is demonstrated by numerical simulations that the attosecond chirp of high order harmonic pulses in the 530 to 1000 eV range can be partially compensated by the negative group delay dispersion of unionized molecular hydrogen gas. The transmission of X-rays through gas with the required pressure-length product for optimum chirp compensation is higher than 10% in the photon energy range that covers the K-edge of oxygen and L-edges of iron, cobalt, and nickel.

© 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. J. Breidbach and L. S. Cederbaum, “Migration of holes: Formalism, mechanisms, and illustrative applications,” J. Chem. Phys. 118(9), 3983–3996 (2003).
    [Crossref]
  2. Z. Chang, P. B. Corkum, and S. R. Leone, “Attosecond optics and technology: progress to date and future prospects [Invited],” J. Opt. Soc. Am. B 33(6), 1081–1097 (2016).
    [Crossref]
  3. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994 (2001).
    [Crossref]
  4. K. Schafer, B. Yang, L. DiMauro, and K. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599 (1993).
    [Crossref]
  5. B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65(1), 011804 (2001).
    [Crossref]
  6. X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
    [Crossref]
  7. 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,” Nat. Commun. 8(1), 186 (2017).
    [Crossref]
  8. Y. Yin, J. Li, X. Ren, Y. Wang, A. Chew, and Z. Chang, “High-energy two-cycle pulses at 3.2 μm by a broadband-pumped dual-chirped optical parametric amplification,” Opt. Express 24(22), 24989–24998 (2016).
    [Crossref]
  9. Z. Chang, “Fundamentals of Attosecond Optics,” CRC Press, ISBN 9781420089370 (2011).
  10. K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub− 50− attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69(5), 051805 (2004).
    [Crossref]
  11. Z. Chang, “Attosecond chirp compensation in water window by plasma dispersion,” Opt. Express 26(25), 33238–33244 (2018).
    [Crossref]
  12. E. Gullikson, http://henke.lbl.gov/optical_constants/asf.html .
  13. M. Hoegner, https://github.com/Leberwurscht/HHGmax .
  14. M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photonics 8(3), 178–186 (2014).
    [Crossref]
  15. A. V. Dostovalov, A. A. Wolf, S. A. Babin, M. V. Dubov, and V. K. Mezentsev, “Numerical investigation of the effect of the temporal pulse shape on modification of fused silica by femtosecond pulses,” Quantum Electron. 42(9), 799–804 (2012).
    [Crossref]
  16. Y. Fu, H. Yuan, K. Midorikawa, P. Lan, and E. J. Takahashi, “Towards GW-scale isolated attosecond pulse far beyond carbon K-edge driven by mid-infrared waveform synthesizer,” Appl. Sci. 8(12), 2451 (2018).
    [Crossref]
  17. Z. Zeng, Y. Zheng, Y. Cheng, R. Li, and Z. Xu, “Attosecond pulse generation driven by a synthesized laser field with two pulses of controlled related phase,” J. Phys. B: At., Mol. Opt. Phys. 45(7), 074004 (2012).
    [Crossref]

2018 (3)

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[Crossref]

Z. Chang, “Attosecond chirp compensation in water window by plasma dispersion,” Opt. Express 26(25), 33238–33244 (2018).
[Crossref]

Y. Fu, H. Yuan, K. Midorikawa, P. Lan, and E. J. Takahashi, “Towards GW-scale isolated attosecond pulse far beyond carbon K-edge driven by mid-infrared waveform synthesizer,” Appl. Sci. 8(12), 2451 (2018).
[Crossref]

2017 (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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

2016 (2)

2014 (1)

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photonics 8(3), 178–186 (2014).
[Crossref]

2012 (2)

A. V. Dostovalov, A. A. Wolf, S. A. Babin, M. V. Dubov, and V. K. Mezentsev, “Numerical investigation of the effect of the temporal pulse shape on modification of fused silica by femtosecond pulses,” Quantum Electron. 42(9), 799–804 (2012).
[Crossref]

Z. Zeng, Y. Zheng, Y. Cheng, R. Li, and Z. Xu, “Attosecond pulse generation driven by a synthesized laser field with two pulses of controlled related phase,” J. Phys. B: At., Mol. Opt. Phys. 45(7), 074004 (2012).
[Crossref]

2004 (1)

K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub− 50− attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69(5), 051805 (2004).
[Crossref]

2003 (1)

J. Breidbach and L. S. Cederbaum, “Migration of holes: Formalism, mechanisms, and illustrative applications,” J. Chem. Phys. 118(9), 3983–3996 (2003).
[Crossref]

2001 (2)

B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65(1), 011804 (2001).
[Crossref]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994 (2001).
[Crossref]

1993 (1)

K. Schafer, B. Yang, L. DiMauro, and K. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599 (1993).
[Crossref]

Babin, S. A.

A. V. Dostovalov, A. A. Wolf, S. A. Babin, M. V. Dubov, and V. K. Mezentsev, “Numerical investigation of the effect of the temporal pulse shape on modification of fused silica by femtosecond pulses,” Quantum Electron. 42(9), 799–804 (2012).
[Crossref]

Baik, M.-G.

K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub− 50− attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69(5), 051805 (2004).
[Crossref]

Breidbach, J.

J. Breidbach and L. S. Cederbaum, “Migration of holes: Formalism, mechanisms, and illustrative applications,” J. Chem. Phys. 118(9), 3983–3996 (2003).
[Crossref]

Cederbaum, L. S.

J. Breidbach and L. S. Cederbaum, “Migration of holes: Formalism, mechanisms, and illustrative applications,” J. Chem. Phys. 118(9), 3983–3996 (2003).
[Crossref]

Chang, Z.

Z. Chang, “Attosecond chirp compensation in water window by plasma dispersion,” Opt. Express 26(25), 33238–33244 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

Z. Chang, P. B. Corkum, and S. R. Leone, “Attosecond optics and technology: progress to date and future prospects [Invited],” J. Opt. Soc. Am. B 33(6), 1081–1097 (2016).
[Crossref]

Y. Yin, J. Li, X. Ren, Y. Wang, A. Chew, and Z. Chang, “High-energy two-cycle pulses at 3.2 μm by a broadband-pumped dual-chirped optical parametric amplification,” Opt. Express 24(22), 24989–24998 (2016).
[Crossref]

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photonics 8(3), 178–186 (2014).
[Crossref]

B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65(1), 011804 (2001).
[Crossref]

Z. Chang, “Fundamentals of Attosecond Optics,” CRC Press, ISBN 9781420089370 (2011).

Cheng, Y.

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

Z. Zeng, Y. Zheng, Y. Cheng, R. Li, and Z. Xu, “Attosecond pulse generation driven by a synthesized laser field with two pulses of controlled related phase,” J. Phys. B: At., Mol. Opt. Phys. 45(7), 074004 (2012).
[Crossref]

Chew, A.

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

Y. Yin, J. Li, X. Ren, Y. Wang, A. Chew, and Z. Chang, “High-energy two-cycle pulses at 3.2 μm by a broadband-pumped dual-chirped optical parametric amplification,” Opt. Express 24(22), 24989–24998 (2016).
[Crossref]

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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photonics 8(3), 178–186 (2014).
[Crossref]

Corkum, P. B.

Cunningham, E.

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

DiMauro, L.

K. Schafer, B. Yang, L. DiMauro, and K. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599 (1993).
[Crossref]

Dostovalov, A. V.

A. V. Dostovalov, A. A. Wolf, S. A. Babin, M. V. Dubov, and V. K. Mezentsev, “Numerical investigation of the effect of the temporal pulse shape on modification of fused silica by femtosecond pulses,” Quantum Electron. 42(9), 799–804 (2012).
[Crossref]

Dubov, M. V.

A. V. Dostovalov, A. A. Wolf, S. A. Babin, M. V. Dubov, and V. K. Mezentsev, “Numerical investigation of the effect of the temporal pulse shape on modification of fused silica by femtosecond pulses,” Quantum Electron. 42(9), 799–804 (2012).
[Crossref]

Fu, Y.

Y. Fu, H. Yuan, K. Midorikawa, P. Lan, and E. J. Takahashi, “Towards GW-scale isolated attosecond pulse far beyond carbon K-edge driven by mid-infrared waveform synthesizer,” Appl. Sci. 8(12), 2451 (2018).
[Crossref]

Gullikson, E.

E. Gullikson, http://henke.lbl.gov/optical_constants/asf.html .

Hoegner, M.

M. Hoegner, https://github.com/Leberwurscht/HHGmax .

Hu, S.

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

Kim, C. M.

K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub− 50− attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69(5), 051805 (2004).
[Crossref]

Kim, K. T.

K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub− 50− attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69(5), 051805 (2004).
[Crossref]

Kulander, K.

K. Schafer, B. Yang, L. DiMauro, and K. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599 (1993).
[Crossref]

Lan, P.

Y. Fu, H. Yuan, K. Midorikawa, P. Lan, and E. J. Takahashi, “Towards GW-scale isolated attosecond pulse far beyond carbon K-edge driven by mid-infrared waveform synthesizer,” Appl. Sci. 8(12), 2451 (2018).
[Crossref]

Leone, S. R.

Li, J.

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

Y. Yin, J. Li, X. Ren, Y. Wang, A. Chew, and Z. Chang, “High-energy two-cycle pulses at 3.2 μm by a broadband-pumped dual-chirped optical parametric amplification,” Opt. Express 24(22), 24989–24998 (2016).
[Crossref]

Li, R.

Z. Zeng, Y. Zheng, Y. Cheng, R. Li, and Z. Xu, “Attosecond pulse generation driven by a synthesized laser field with two pulses of controlled related phase,” J. Phys. B: At., Mol. Opt. Phys. 45(7), 074004 (2012).
[Crossref]

Mezentsev, V. K.

A. V. Dostovalov, A. A. Wolf, S. A. Babin, M. V. Dubov, and V. K. Mezentsev, “Numerical investigation of the effect of the temporal pulse shape on modification of fused silica by femtosecond pulses,” Quantum Electron. 42(9), 799–804 (2012).
[Crossref]

Midorikawa, K.

Y. Fu, H. Yuan, K. Midorikawa, P. Lan, and E. J. Takahashi, “Towards GW-scale isolated attosecond pulse far beyond carbon K-edge driven by mid-infrared waveform synthesizer,” Appl. Sci. 8(12), 2451 (2018).
[Crossref]

Nam, C. H.

K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub− 50− attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69(5), 051805 (2004).
[Crossref]

Ren, X.

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

Y. Yin, J. Li, X. Ren, Y. Wang, A. Chew, and Z. Chang, “High-energy two-cycle pulses at 3.2 μm by a broadband-pumped dual-chirped optical parametric amplification,” Opt. Express 24(22), 24989–24998 (2016).
[Crossref]

Schafer, K.

K. Schafer, B. Yang, L. DiMauro, and K. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599 (1993).
[Crossref]

Shan, B.

B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65(1), 011804 (2001).
[Crossref]

Takahashi, E. J.

Y. Fu, H. Yuan, K. Midorikawa, P. Lan, and E. J. Takahashi, “Towards GW-scale isolated attosecond pulse far beyond carbon K-edge driven by mid-infrared waveform synthesizer,” Appl. Sci. 8(12), 2451 (2018).
[Crossref]

Umesh, G.

K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub− 50− attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69(5), 051805 (2004).
[Crossref]

Wang, Y.

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

Y. Yin, J. Li, X. Ren, Y. Wang, A. Chew, and Z. Chang, “High-energy two-cycle pulses at 3.2 μm by a broadband-pumped dual-chirped optical parametric amplification,” Opt. Express 24(22), 24989–24998 (2016).
[Crossref]

Wolf, A. A.

A. V. Dostovalov, A. A. Wolf, S. A. Babin, M. V. Dubov, and V. K. Mezentsev, “Numerical investigation of the effect of the temporal pulse shape on modification of fused silica by femtosecond pulses,” Quantum Electron. 42(9), 799–804 (2012).
[Crossref]

Wu, Y.

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

Xu, Z.

Z. Zeng, Y. Zheng, Y. Cheng, R. Li, and Z. Xu, “Attosecond pulse generation driven by a synthesized laser field with two pulses of controlled related phase,” J. Phys. B: At., Mol. Opt. Phys. 45(7), 074004 (2012).
[Crossref]

Yang, B.

K. Schafer, B. Yang, L. DiMauro, and K. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599 (1993).
[Crossref]

Yin, Y.

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

Y. Yin, J. Li, X. Ren, Y. Wang, A. Chew, and Z. Chang, “High-energy two-cycle pulses at 3.2 μm by a broadband-pumped dual-chirped optical parametric amplification,” Opt. Express 24(22), 24989–24998 (2016).
[Crossref]

Yuan, H.

Y. Fu, H. Yuan, K. Midorikawa, P. Lan, and E. J. Takahashi, “Towards GW-scale isolated attosecond pulse far beyond carbon K-edge driven by mid-infrared waveform synthesizer,” Appl. Sci. 8(12), 2451 (2018).
[Crossref]

Zeng, Z.

Z. Zeng, Y. Zheng, Y. Cheng, R. Li, and Z. Xu, “Attosecond pulse generation driven by a synthesized laser field with two pulses of controlled related phase,” J. Phys. B: At., Mol. Opt. Phys. 45(7), 074004 (2012).
[Crossref]

Zhao, K.

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photonics 8(3), 178–186 (2014).
[Crossref]

Zheng, Y.

Z. Zeng, Y. Zheng, Y. Cheng, R. Li, and Z. Xu, “Attosecond pulse generation driven by a synthesized laser field with two pulses of controlled related phase,” J. Phys. B: At., Mol. Opt. Phys. 45(7), 074004 (2012).
[Crossref]

Appl. Sci. (1)

Y. Fu, H. Yuan, K. Midorikawa, P. Lan, and E. J. Takahashi, “Towards GW-scale isolated attosecond pulse far beyond carbon K-edge driven by mid-infrared waveform synthesizer,” Appl. Sci. 8(12), 2451 (2018).
[Crossref]

J. Chem. Phys. (1)

J. Breidbach and L. S. Cederbaum, “Migration of holes: Formalism, mechanisms, and illustrative applications,” J. Chem. Phys. 118(9), 3983–3996 (2003).
[Crossref]

J. Opt. (1)

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, and Y. Wu, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. B: At., Mol. Opt. Phys. (1)

Z. Zeng, Y. Zheng, Y. Cheng, R. Li, and Z. Xu, “Attosecond pulse generation driven by a synthesized laser field with two pulses of controlled related phase,” J. Phys. B: At., Mol. Opt. Phys. 45(7), 074004 (2012).
[Crossref]

Nat. Commun. (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,” Nat. Commun. 8(1), 186 (2017).
[Crossref]

Nat. Photonics (1)

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photonics 8(3), 178–186 (2014).
[Crossref]

Opt. Express (2)

Phys. Rev. A (2)

B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65(1), 011804 (2001).
[Crossref]

K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub− 50− attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69(5), 051805 (2004).
[Crossref]

Phys. Rev. Lett. (2)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994 (2001).
[Crossref]

K. Schafer, B. Yang, L. DiMauro, and K. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599 (1993).
[Crossref]

Quantum Electron. (1)

A. V. Dostovalov, A. A. Wolf, S. A. Babin, M. V. Dubov, and V. K. Mezentsev, “Numerical investigation of the effect of the temporal pulse shape on modification of fused silica by femtosecond pulses,” Quantum Electron. 42(9), 799–804 (2012).
[Crossref]

Other (3)

E. Gullikson, http://henke.lbl.gov/optical_constants/asf.html .

M. Hoegner, https://github.com/Leberwurscht/HHGmax .

Z. Chang, “Fundamentals of Attosecond Optics,” CRC Press, ISBN 9781420089370 (2011).

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Figures (3)

Fig. 1.
Fig. 1. Single-cycle mid-infrared driving laser field centered at 3.2 μm. The peak intensity is 4 × 1014 W/cm2. The carrier envelope phase is 5π/8 rad.
Fig. 2.
Fig. 2. (a) Power spectrum of the X-ray pulse. (b) Transmission of molecular hydrogen gas with pressure and length required for atto-chirp compensation. (c) Phases of X-rays with and without chirp compensation by the gas.
Fig. 3.
Fig. 3. Electric fields of the X-ray pulses. (a) Without chirp compensation. (b) With chirp compensation by hydrogen gas. (c) Transform-limited.

Equations (7)

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C h i r p = 1.63 × 10 18 1 I 0 λ 0 .
n ~ ( λ x ) = 1 1 2 π N r 0 λ x 2 [ f 1 ( λ x ) + i f 2 ( λ x ) ] ,
n ~ ( ω x ) = 1 + j = 1 J F j ω 0 j 2 ω 0 j 2 ω x 2 + i γ j ω x ,
n ( ω x ) = 1 ω p 2 ω x 2 ,
ω p = e 2 N e ε 0 m e ,
n ( ω x ) 1 1 2 ω p 2 ω x 2 .
G D D ( ω x ) = e 2 3 ε 0 m e c N e L ( ω x ) 3

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