Attosecond chirp compensation in water window by plasma dispersion

Zenghu Chang

doi:10.1364/OE.26.033238

Attosecond chirp compensation in water window by plasma dispersion

Zenghu Chang

Optics Express
Vol. 26,
Issue 25,
pp. 33238-33244
(2018)
•https://doi.org/10.1364/OE.26.033238

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Zenghu Chang, "Attosecond chirp compensation in water window by plasma dispersion," Opt. Express 26, 33238-33244 (2018)

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Table of Contents Category
- Ultrafast Optics and Attosecond/High-field Physics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: October 30, 2018
- Revised Manuscript: November 17, 2018
- Manuscript Accepted: November 17, 2018
- Published: December 5, 2018

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Open Access

Abstract

Compensating attosecond chirp (atto-chirp) of broadband high-order harmonic pulses in the water window region (282 to 533 eV) is a major challenge, due to the lack of natural materials that exhibit negative group velocity dispersion and low loss. Analysis shows that the amount of dispersion of fully ionized hydrogen plasma with suitable density-length product is sufficient to compensate the chirp of attosecond pulses with center photon energy above 300 eV. This is confirmed by numerical simulations based on the Strong Field Approximation.

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References

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P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref] [PubMed]
M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]
P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]
K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599–1602 (1993).
[Crossref] [PubMed]
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]
T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, Y. Wu, M. Chini, and Z. Chang, “Attosecond light sources in the water window,” J. Opt. 20(2), 023001 (2018).
[Crossref]
S. Kazamias and P. Balcou, “Intrinsic chirp of attosecond pulses: Single-atom model versus experiment,” Phys. Rev. A 69(6), 063416 (2004).
[Crossref]
Z. Chang, “Fundamentals of Attosecond Optics,” ISBN 9781420089370 (2011).
G. Doumy, J. Wheeler, C. Roedig, R. Chirla, P. Agostini, and L. F. DiMauro, “Attosecond synchronization of high-order harmonics from midinfrared drivers,” Phys. Rev. Lett. 102(9), 093002 (2009).
[Crossref] [PubMed]
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]
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] [PubMed]
A. Guggenmos, R. Rauhut, M. Hofstetter, S. Hertrich, B. Nickel, J. Schmidt, E. M. Gullikson, M. Seibald, W. Schnick, and U. Kleineberg, “Aperiodic CrSc multilayer mirrors for attosecond water window pulses,” Opt. Express 21(19), 21728–21740 (2013).
[Crossref] [PubMed]
L. Poletto, F. Frassetto, and P. Villoresi, “Design of an extreme-ultraviolet attosecond compressor,” J. Opt. Soc. Am. B 25(7), B133–B136 (2008).
[Crossref]
M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref] [PubMed]
M. Hoegner, https://github.com/Leberwurscht/HHGmax
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]
D. J. Spence and S. M. Hooker, “Investigation of a hydrogen plasma waveguide,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(1 Pt 2), 015401 (2001).
[PubMed]
D. Spence, A. Butler, and S. M. Hooker, “Gas-filled capillary discharge waveguides,” J. Opt. Soc. Am. B 20(1), 138–151 (2003).
[Crossref]
A. Gonsalves, F. Liu, N. Bobrova, P. Sasorov, C. Pieronek, J. Daniels, S. Antipov, J. Butler, S. Bulanov, W. Waldron, D. E. Mittelberger, and W. P. Leemans, “Demonstration of a high repetition rate capillary discharge waveguide,” J. Appl. Phys. 119(3), 033302 (2016).
[Crossref]
A. E. Dyson, C. Thornton, and S. M. Hooker, “A compact, low cost Marx bank for generating capillary discharge plasmas,” Rev. Sci. Instrum. 87(9), 093302 (2016).
[Crossref] [PubMed]
J. Breidbach and L. S. Cederbaum, “Universal attosecond response to the removal of an electron,” Phys. Rev. Lett. 94(3), 033901 (2005).
[Crossref] [PubMed]

2018 (1)

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

2016 (2)

A. Gonsalves, F. Liu, N. Bobrova, P. Sasorov, C. Pieronek, J. Daniels, S. Antipov, J. Butler, S. Bulanov, W. Waldron, D. E. Mittelberger, and W. P. Leemans, “Demonstration of a high repetition rate capillary discharge waveguide,” J. Appl. Phys. 119(3), 033302 (2016).
[Crossref]

A. E. Dyson, C. Thornton, and S. M. Hooker, “A compact, low cost Marx bank for generating capillary discharge plasmas,” Rev. Sci. Instrum. 87(9), 093302 (2016).
[Crossref] [PubMed]

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]

2013 (1)

A. Guggenmos, R. Rauhut, M. Hofstetter, S. Hertrich, B. Nickel, J. Schmidt, E. M. Gullikson, M. Seibald, W. Schnick, and U. Kleineberg, “Aperiodic CrSc multilayer mirrors for attosecond water window pulses,” Opt. Express 21(19), 21728–21740 (2013).
[Crossref] [PubMed]

2012 (1)

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).

2009 (1)

G. Doumy, J. Wheeler, C. Roedig, R. Chirla, P. Agostini, and L. F. DiMauro, “Attosecond synchronization of high-order harmonics from midinfrared drivers,” Phys. Rev. Lett. 102(9), 093002 (2009).
[Crossref] [PubMed]

2008 (1)

L. Poletto, F. Frassetto, and P. Villoresi, “Design of an extreme-ultraviolet attosecond compressor,” J. Opt. Soc. Am. B 25(7), B133–B136 (2008).
[Crossref]

2005 (1)

J. Breidbach and L. S. Cederbaum, “Universal attosecond response to the removal of an electron,” Phys. Rev. Lett. 94(3), 033901 (2005).
[Crossref] [PubMed]

2004 (2)

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]

S. Kazamias and P. Balcou, “Intrinsic chirp of attosecond pulses: Single-atom model versus experiment,” Phys. Rev. A 69(6), 063416 (2004).
[Crossref]

2003 (1)

D. Spence, A. Butler, and S. M. Hooker, “Gas-filled capillary discharge waveguides,” J. Opt. Soc. Am. B 20(1), 138–151 (2003).
[Crossref]

2001 (4)

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. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292(5522), 1689–1692 (2001).
[Crossref] [PubMed]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

D. J. Spence and S. M. Hooker, “Investigation of a hydrogen plasma waveguide,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(1 Pt 2), 015401 (2001).
[PubMed]

1994 (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref] [PubMed]

1993 (2)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599–1602 (1993).
[Crossref] [PubMed]

Agostini, P.

Alisauskas, S.

Andriukaitis, G.

Antipov, S.

Arpin, P.

Augé, F.

Baik, M.-G.

Balciunas, T.

Balcou, P.

S. Kazamias and P. Balcou, “Intrinsic chirp of attosecond pulses: Single-atom model versus experiment,” Phys. Rev. A 69(6), 063416 (2004).
[Crossref]

Baltuska, A.

Becker, A.

Bobrova, N.

Brabec, T.

Breger, P.

Breidbach, J.

J. Breidbach and L. S. Cederbaum, “Universal attosecond response to the removal of an electron,” Phys. Rev. Lett. 94(3), 033901 (2005).
[Crossref] [PubMed]

Brown, S.

Bulanov, S.

Butler, A.

D. Spence, A. Butler, and S. M. Hooker, “Gas-filled capillary discharge waveguides,” J. Opt. Soc. Am. B 20(1), 138–151 (2003).
[Crossref]

Butler, J.

Cederbaum, L. S.

J. Breidbach and L. S. Cederbaum, “Universal attosecond response to the removal of an electron,” Phys. Rev. Lett. 94(3), 033901 (2005).
[Crossref] [PubMed]

Chang, Z.

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]

Chen, M.-C.

Cheng, Y.

Chew, A.

Chini, M.

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]

Chirla, R.

Corkum, P.

Corkum, P. B.

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

Cunningham, E.

Daniels, J.

DiMauro, L. F.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599–1602 (1993).
[Crossref] [PubMed]

Doumy, G.

Drescher, M.

Dyson, A. E.

A. E. Dyson, C. Thornton, and S. M. Hooker, “A compact, low cost Marx bank for generating capillary discharge plasmas,” Rev. Sci. Instrum. 87(9), 093302 (2016).
[Crossref] [PubMed]

Frassetto, F.

L. Poletto, F. Frassetto, and P. Villoresi, “Design of an extreme-ultraviolet attosecond compressor,” J. Opt. Soc. Am. B 25(7), B133–B136 (2008).
[Crossref]

Gaeta, A.

Gonsalves, A.

Guggenmos, A.

Gullikson, E. M.

Heinzmann, U.

Hentschel, M.

Hernandez-Garcia, C.

Hertrich, S.

Hofstetter, M.

Hooker, S. M.

A. E. Dyson, C. Thornton, and S. M. Hooker, “A compact, low cost Marx bank for generating capillary discharge plasmas,” Rev. Sci. Instrum. 87(9), 093302 (2016).
[Crossref] [PubMed]

D. Spence, A. Butler, and S. M. Hooker, “Gas-filled capillary discharge waveguides,” J. Opt. Soc. Am. B 20(1), 138–151 (2003).
[Crossref]

D. J. Spence and S. M. Hooker, “Investigation of a hydrogen plasma waveguide,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(1 Pt 2), 015401 (2001).
[PubMed]

Hu, S.

Ivanov, M. Y.

Jaron-Becker, A.

Kapteyn, H. C.

Kazamias, S.

S. Kazamias and P. Balcou, “Intrinsic chirp of attosecond pulses: Single-atom model versus experiment,” Phys. Rev. A 69(6), 063416 (2004).
[Crossref]

Kienberger, R.

Kim, C. M.

Kim, K. T.

Kleineberg, U.

Krausz, F.

Kulander, K. C.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599–1602 (1993).
[Crossref] [PubMed]

L’Huillier, A.

Leemans, W. P.

Lewenstein, M.

Li, J.

Liu, F.

Milosevic, N.

Mittelberger, D. E.

Mucke, O. D.

Muller, H. G.

Mullot, G.

Murnane, M. M.

Nam, C. H.

Nickel, B.

Paul, P. M.

Pieronek, C.

Plaja, L.

Poletto, L.

L. Poletto, F. Frassetto, and P. Villoresi, “Design of an extreme-ultraviolet attosecond compressor,” J. Opt. Soc. Am. B 25(7), B133–B136 (2008).
[Crossref]

Popmintchev, D.

Popmintchev, T.

Pugzlys, A.

Rauhut, R.

Reider, G. A.

Ren, X.

Roedig, C.

Sasorov, P.

Schafer, K. J.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599–1602 (1993).
[Crossref] [PubMed]

Schmidt, J.

Schnick, W.

Schrauth, S. E.

Seibald, M.

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]

Shim, B.

Spence, D.

D. Spence, A. Butler, and S. M. Hooker, “Gas-filled capillary discharge waveguides,” J. Opt. Soc. Am. B 20(1), 138–151 (2003).
[Crossref]

Spence, D. J.

D. J. Spence and S. M. Hooker, “Investigation of a hydrogen plasma waveguide,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(1 Pt 2), 015401 (2001).
[PubMed]

Spielmann, C.

Thornton, C.

A. E. Dyson, C. Thornton, and S. M. Hooker, “A compact, low cost Marx bank for generating capillary discharge plasmas,” Rev. Sci. Instrum. 87(9), 093302 (2016).
[Crossref] [PubMed]

Toma, E. S.

Umesh, G.

Villoresi, P.

L. Poletto, F. Frassetto, and P. Villoresi, “Design of an extreme-ultraviolet attosecond compressor,” J. Opt. Soc. Am. B 25(7), B133–B136 (2008).
[Crossref]

Waldron, W.

Wang, Y.

Wheeler, J.

Wu, Y.

Yang, B.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599–1602 (1993).
[Crossref] [PubMed]

Yin, Y.

Zhao, K.

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]

J. Appl. Phys. (1)

J. Opt. (1)

J. Opt. Soc. Am. B (2)

D. Spence, A. Butler, and S. M. Hooker, “Gas-filled capillary discharge waveguides,” J. Opt. Soc. Am. B 20(1), 138–151 (2003).
[Crossref]

L. Poletto, F. Frassetto, and P. Villoresi, “Design of an extreme-ultraviolet attosecond compressor,” J. Opt. Soc. Am. B 25(7), B133–B136 (2008).
[Crossref]

Nat. Commun. (1)

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]

Nature (1)

Opt. Express (1)

Phys. Rev. A (4)

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]

S. Kazamias and P. Balcou, “Intrinsic chirp of attosecond pulses: Single-atom model versus experiment,” Phys. Rev. A 69(6), 063416 (2004).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

D. J. Spence and S. M. Hooker, “Investigation of a hydrogen plasma waveguide,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(1 Pt 2), 015401 (2001).
[PubMed]

Phys. Rev. Lett. (4)

J. Breidbach and L. S. Cederbaum, “Universal attosecond response to the removal of an electron,” Phys. Rev. Lett. 94(3), 033901 (2005).
[Crossref] [PubMed]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70(11), 1599–1602 (1993).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

A. E. Dyson, C. Thornton, and S. M. Hooker, “A compact, low cost Marx bank for generating capillary discharge plasmas,” Rev. Sci. Instrum. 87(9), 093302 (2016).
[Crossref] [PubMed]

Science (2)

Other (2)

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

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

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Fig. 1 (a) Driving laser field. (b) Power spectrum of the X-ray pulse. (c) Phases of X-rays with and without chirp compensation by plasma dispersion.

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Fig. 2 Electric fields of the X-ray pulses. (a) Without chirp compensation. (b) With chirp compensation. (c) Transform-limited. The pulse durations,

τ_{p}

, are the FWHM of the intensity profiles.

Download Full Size | PPT Slide | PDF

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ℏ ω_{c} = I_{p} + 3 \times 10^{- 13} I_{0} λ_{0}^{2},

C h i r p = 1.63 \times 10^{18} \frac{1}{I_{0} λ_{0}} .

n (ω_{x}) = \sqrt{1 - \frac{ω_{p}^{2}}{ω_{x}^{2}}},

ω_{p} = \sqrt{\frac{e^{2} N_{e}}{ε_{0} m_{e}}},

n (ω_{x}) \approx 1 - \frac{1}{2} \frac{ω_{p}^{2}}{ω_{x}^{2}} .

v_{g} (ω_{x}) = \frac{d ω_{k}}{d k_{x}} = n (ω_{x}) c,

G V D (ω_{x}) \approx - \frac{ω_{p}^{2}}{c ω_{x}^{3}} = - \frac{e^{2}}{ε_{0} m_{e} c} \frac{N_{e}}{ω_{x}^{3}},

G D D (ℏ ω_{x}) = - \frac{e^{2} ℏ^{3}}{ε_{0} m_{e} c} \frac{N_{e} L_{p}}{{(ℏ ω_{x})}^{3}} .