Abstract

A novel single-shot second-order autocorrelation scheme for extreme-ultraviolet radiation (XUV) is proposed. It is based on an ion-imaging technique, which provides spatial information of ionization products in the focal volume of the XUV beam. Using simple analytical and detailed numerical modeling, an evaluation toward selecting an optimum configuration has been performed. The implementation of the concept to characterize attosecond pulses is discussed, and the proposed setups are assessed.

© 2014 Optical Society of America

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  1. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
    [CrossRef]
  2. A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
    [CrossRef]
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    [CrossRef]
  6. H. G. Muller, “Reconstruction of attosecond harmonic beating by interference of two-photon transitions,” Appl. Phys. B 74, s17–s21 (2002).
    [CrossRef]
  7. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, R. Taeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003).
    [CrossRef]
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    [CrossRef]
  9. M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
    [CrossRef]
  10. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
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    [CrossRef]
  12. J. Gagnon, E. Goulielmakis, and V. S. Yakovlev, “The accurate FROG characterization of attosecond pulses from streaking measurements,” Appl. Phys. B 92, 25–32 (2008).
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    [CrossRef]
  15. Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Conclusive evidence of an attosecond pulse train observed with the mode-resolved autocorrelation technique,” Phys. Rev. Lett. 96, 083901 (2006).
    [CrossRef]
  16. Y. Nomura, R. Hörlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, “Attosecond phase-locking of harmonics emitted from laser-produced plasmas,” Nat. Phys. 5, 124–128 (2008).
    [CrossRef]
  17. Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train in the single-cycle regime,” Phys. Rev. Lett. 97, 153904 (2006).
    [CrossRef]
  18. P. Heissler, P. Tzallas, J. M. Mikhailova, K. Khrennikov, L. Waldecker, F. Krausz, S. Karsch, D. Charalambidis, and G. D. Tsakiris, “Two-photon above-threshold ionization using extreme-ultraviolet harmonic emission from relativistic laser–plasma interaction,” New J. Phys. 14, 043025 (2012).
    [CrossRef]
  19. P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781–784 (2011).
    [CrossRef]
  20. K. Midorikawa, Y. Nabekawa, and A. Suda, “XUV multiphoton processes with intense high-order harmonics,” Prog. Quantum Electron. 32, 43–88 (2008).
    [CrossRef]
  21. P. A. Carpeggiani, P. Tzallas, A. Palacios, D. Gray, F. Martín, and D. Charalambidis, “Disclosing intrinsic molecular dynamics on the 1-fs scale through extreme-ultraviolet pump-probe measurements,” Phys. Rev. A 89, 023420 (2014).
  22. I. Grguras, A. R. Maier, C. Behrens, T. Mazza, T. J. Kelly, P. Radcliffe, S. Dusterer, A. K. Kazansky, N. M. Kabachnik, Th. Tschentscher, J. T. Costello, M. Meyer, M. C. Hoffmann, H. Schlarb, and A. L. Cavalieri, “Ultrafast x-ray pulse characterization at free-electron lasers,” Nat. Photonics 6, 852–857 (2012).
    [CrossRef]
  23. Y. Mairesse, O. Gobert, P. Breger, H. Merdji, P. Meynadier, P. Monchicourt, M. Perdrix, P. Salières, and B. Carré, “High harmonic XUV spectral phase interferometry for direct electric-field reconstruction,” Phys. Rev. Lett. 94, 173903 (2005).
    [CrossRef]
  24. E. Cormier, I. A. Walmsley, E. M. Kosik, A. S. Wyatt, L. Corner, and L. F. DiMauro, “Self-referencing, spectrally, or spatially encoded spectral interferometry for the complete characterization of attosecond electromagnetic pulses,” Phys. Rev. Lett. 94, 033905 (2005).
    [CrossRef]
  25. J. Janszky, G. Corradi, and R. N. Gyuzalian, “On a possibility of analysing the temporal characteristics of short light pulses,” Opt. Commun. 23, 293–298 (1977).
    [CrossRef]
  26. F. Salin, P. Georges, G. Roger, and A. Brun, “Single-shot measurement of a 52-fs pulse,” Appl. Opt. 26, 4528–4531 (1987).
    [CrossRef]
  27. P. Simon, H. Gerhardt, and S. Szatmari, “A single-shot autocorrelator for UV femtosecond pulses,” Meas. Sci. Technol. 1, 637–639 (1990).
    [CrossRef]
  28. A. Brun, P. Georges, G. Le Saux, and F. Salin, “Single-shot characterization of ultrashort light pulses,” J. Phys. D 24, 1225–1233 (1991).
    [CrossRef]
  29. L. A. A. Nikolopoulos, E. P. Benis, P. Tzallas, D. Charalambidis, K. Witte, and G. D. Tsakiris, “Second order autocorrelation of an XUV attosecond pulse train,” Phys. Rev. Lett. 94, 113905 (2005).
    [CrossRef]
  30. M. Schultze, B. Bergues, H. Schröder, F. Krausz, and K. L. Kompa, “Spatially resolved measurement of ionization yields in the focus of an intense laser pulse,” New J. Phys. 13, 033001 (2011).
    [CrossRef]
  31. P. Heissler, R. Hörlein, J. M. Mikhailova, L. Waldecker, P. Tzallas, A. Buck, K. Schmid, C. M. S. Sears, F. Krausz, L. Veisz, M. Zepf, and G. D. Tsakiris, “Few-cycle driven relativistically oscillating plasma mirrors: a source of intense isolated attosecond pulses,” Phys. Rev. Lett. 108, 235003 (2012).
    [CrossRef]
  32. M. Born and E. Wolf, Principles of Optics (Pergamon, 1985).
  33. N. A. Papadogiannis, L. A. A. Nikolopoulos, D. Charalambidis, G. D. Tsakiris, P. Tzallas, and K. Witte, “On the feasibility of performing non-linear autocorrelation with attosecond pulse trains,” Appl. Phys. B 76, 721–727 (2003).
    [CrossRef]
  34. A. Saenz and P. Lambropoulos, “Theoretical two- three- and four-photon ionization cross sections of helium in the XUV range,” J. Phys. B 32, 5629–5637 (1999).
    [CrossRef]

2014 (1)

P. A. Carpeggiani, P. Tzallas, A. Palacios, D. Gray, F. Martín, and D. Charalambidis, “Disclosing intrinsic molecular dynamics on the 1-fs scale through extreme-ultraviolet pump-probe measurements,” Phys. Rev. A 89, 023420 (2014).

2012 (3)

I. Grguras, A. R. Maier, C. Behrens, T. Mazza, T. J. Kelly, P. Radcliffe, S. Dusterer, A. K. Kazansky, N. M. Kabachnik, Th. Tschentscher, J. T. Costello, M. Meyer, M. C. Hoffmann, H. Schlarb, and A. L. Cavalieri, “Ultrafast x-ray pulse characterization at free-electron lasers,” Nat. Photonics 6, 852–857 (2012).
[CrossRef]

P. Heissler, P. Tzallas, J. M. Mikhailova, K. Khrennikov, L. Waldecker, F. Krausz, S. Karsch, D. Charalambidis, and G. D. Tsakiris, “Two-photon above-threshold ionization using extreme-ultraviolet harmonic emission from relativistic laser–plasma interaction,” New J. Phys. 14, 043025 (2012).
[CrossRef]

P. Heissler, R. Hörlein, J. M. Mikhailova, L. Waldecker, P. Tzallas, A. Buck, K. Schmid, C. M. S. Sears, F. Krausz, L. Veisz, M. Zepf, and G. D. Tsakiris, “Few-cycle driven relativistically oscillating plasma mirrors: a source of intense isolated attosecond pulses,” Phys. Rev. Lett. 108, 235003 (2012).
[CrossRef]

2011 (2)

M. Schultze, B. Bergues, H. Schröder, F. Krausz, and K. L. Kompa, “Spatially resolved measurement of ionization yields in the focus of an intense laser pulse,” New J. Phys. 13, 033001 (2011).
[CrossRef]

P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781–784 (2011).
[CrossRef]

2009 (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009.
[CrossRef]

2008 (3)

J. Gagnon, E. Goulielmakis, and V. S. Yakovlev, “The accurate FROG characterization of attosecond pulses from streaking measurements,” Appl. Phys. B 92, 25–32 (2008).
[CrossRef]

Y. Nomura, R. Hörlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, “Attosecond phase-locking of harmonics emitted from laser-produced plasmas,” Nat. Phys. 5, 124–128 (2008).
[CrossRef]

K. Midorikawa, Y. Nabekawa, and A. Suda, “XUV multiphoton processes with intense high-order harmonics,” Prog. Quantum Electron. 32, 43–88 (2008).
[CrossRef]

2006 (2)

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train in the single-cycle regime,” Phys. Rev. Lett. 97, 153904 (2006).
[CrossRef]

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Conclusive evidence of an attosecond pulse train observed with the mode-resolved autocorrelation technique,” Phys. Rev. Lett. 96, 083901 (2006).
[CrossRef]

2005 (4)

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

Y. Mairesse, O. Gobert, P. Breger, H. Merdji, P. Meynadier, P. Monchicourt, M. Perdrix, P. Salières, and B. Carré, “High harmonic XUV spectral phase interferometry for direct electric-field reconstruction,” Phys. Rev. Lett. 94, 173903 (2005).
[CrossRef]

E. Cormier, I. A. Walmsley, E. M. Kosik, A. S. Wyatt, L. Corner, and L. F. DiMauro, “Self-referencing, spectrally, or spatially encoded spectral interferometry for the complete characterization of attosecond electromagnetic pulses,” Phys. Rev. Lett. 94, 033905 (2005).
[CrossRef]

L. A. A. Nikolopoulos, E. P. Benis, P. Tzallas, D. Charalambidis, K. Witte, and G. D. Tsakiris, “Second order autocorrelation of an XUV attosecond pulse train,” Phys. Rev. Lett. 94, 113905 (2005).
[CrossRef]

2004 (2)

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

2003 (4)

P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, “Direct observation of attosecond light bunching,” Nature 426, 267–271 (2003).
[CrossRef]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, R. Taeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

N. A. Papadogiannis, L. A. A. Nikolopoulos, D. Charalambidis, G. D. Tsakiris, P. Tzallas, and K. Witte, “On the feasibility of performing non-linear autocorrelation with attosecond pulse trains,” Appl. Phys. B 76, 721–727 (2003).
[CrossRef]

2002 (1)

H. G. Muller, “Reconstruction of attosecond harmonic beating by interference of two-photon transitions,” Appl. Phys. B 74, s17–s21 (2002).
[CrossRef]

2001 (3)

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
[CrossRef]

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

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

1999 (1)

A. Saenz and P. Lambropoulos, “Theoretical two- three- and four-photon ionization cross sections of helium in the XUV range,” J. Phys. B 32, 5629–5637 (1999).
[CrossRef]

1998 (1)

1991 (1)

A. Brun, P. Georges, G. Le Saux, and F. Salin, “Single-shot characterization of ultrashort light pulses,” J. Phys. D 24, 1225–1233 (1991).
[CrossRef]

1990 (1)

P. Simon, H. Gerhardt, and S. Szatmari, “A single-shot autocorrelator for UV femtosecond pulses,” Meas. Sci. Technol. 1, 637–639 (1990).
[CrossRef]

1987 (1)

1977 (1)

J. Janszky, G. Corradi, and R. N. Gyuzalian, “On a possibility of analysing the temporal characteristics of short light pulses,” Opt. Commun. 23, 293–298 (1977).
[CrossRef]

Agostini, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, R. Taeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

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

Augé, F.

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

Balcou, Ph.

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

Baltuska, A.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

Bammer, F.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Behrens, C.

I. Grguras, A. R. Maier, C. Behrens, T. Mazza, T. J. Kelly, P. Radcliffe, S. Dusterer, A. K. Kazansky, N. M. Kabachnik, Th. Tschentscher, J. T. Costello, M. Meyer, M. C. Hoffmann, H. Schlarb, and A. L. Cavalieri, “Ultrafast x-ray pulse characterization at free-electron lasers,” Nat. Photonics 6, 852–857 (2012).
[CrossRef]

Benis, E. P.

L. A. A. Nikolopoulos, E. P. Benis, P. Tzallas, D. Charalambidis, K. Witte, and G. D. Tsakiris, “Second order autocorrelation of an XUV attosecond pulse train,” Phys. Rev. Lett. 94, 113905 (2005).
[CrossRef]

Bergues, B.

M. Schultze, B. Bergues, H. Schröder, F. Krausz, and K. L. Kompa, “Spatially resolved measurement of ionization yields in the focus of an intense laser pulse,” New J. Phys. 13, 033001 (2011).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1985).

Brabec, T.

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

Breger, P.

Y. Mairesse, O. Gobert, P. Breger, H. Merdji, P. Meynadier, P. Monchicourt, M. Perdrix, P. Salières, and B. Carré, “High harmonic XUV spectral phase interferometry for direct electric-field reconstruction,” Phys. Rev. Lett. 94, 173903 (2005).
[CrossRef]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, R. Taeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

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

Brun, A.

A. Brun, P. Georges, G. Le Saux, and F. Salin, “Single-shot characterization of ultrashort light pulses,” J. Phys. D 24, 1225–1233 (1991).
[CrossRef]

F. Salin, P. Georges, G. Roger, and A. Brun, “Single-shot measurement of a 52-fs pulse,” Appl. Opt. 26, 4528–4531 (1987).
[CrossRef]

Buck, A.

P. Heissler, R. Hörlein, J. M. Mikhailova, L. Waldecker, P. Tzallas, A. Buck, K. Schmid, C. M. S. Sears, F. Krausz, L. Veisz, M. Zepf, and G. D. Tsakiris, “Few-cycle driven relativistically oscillating plasma mirrors: a source of intense isolated attosecond pulses,” Phys. Rev. Lett. 108, 235003 (2012).
[CrossRef]

Carpeggiani, P. A.

P. A. Carpeggiani, P. Tzallas, A. Palacios, D. Gray, F. Martín, and D. Charalambidis, “Disclosing intrinsic molecular dynamics on the 1-fs scale through extreme-ultraviolet pump-probe measurements,” Phys. Rev. A 89, 023420 (2014).

Carré, B.

Y. Mairesse, O. Gobert, P. Breger, H. Merdji, P. Meynadier, P. Monchicourt, M. Perdrix, P. Salières, and B. Carré, “High harmonic XUV spectral phase interferometry for direct electric-field reconstruction,” Phys. Rev. Lett. 94, 173903 (2005).
[CrossRef]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, R. Taeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

Cavalieri, A. L.

I. Grguras, A. R. Maier, C. Behrens, T. Mazza, T. J. Kelly, P. Radcliffe, S. Dusterer, A. K. Kazansky, N. M. Kabachnik, Th. Tschentscher, J. T. Costello, M. Meyer, M. C. Hoffmann, H. Schlarb, and A. L. Cavalieri, “Ultrafast x-ray pulse characterization at free-electron lasers,” Nat. Photonics 6, 852–857 (2012).
[CrossRef]

Charalambidis, D.

P. A. Carpeggiani, P. Tzallas, A. Palacios, D. Gray, F. Martín, and D. Charalambidis, “Disclosing intrinsic molecular dynamics on the 1-fs scale through extreme-ultraviolet pump-probe measurements,” Phys. Rev. A 89, 023420 (2014).

P. Heissler, P. Tzallas, J. M. Mikhailova, K. Khrennikov, L. Waldecker, F. Krausz, S. Karsch, D. Charalambidis, and G. D. Tsakiris, “Two-photon above-threshold ionization using extreme-ultraviolet harmonic emission from relativistic laser–plasma interaction,” New J. Phys. 14, 043025 (2012).
[CrossRef]

P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781–784 (2011).
[CrossRef]

Y. Nomura, R. Hörlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, “Attosecond phase-locking of harmonics emitted from laser-produced plasmas,” Nat. Phys. 5, 124–128 (2008).
[CrossRef]

L. A. A. Nikolopoulos, E. P. Benis, P. Tzallas, D. Charalambidis, K. Witte, and G. D. Tsakiris, “Second order autocorrelation of an XUV attosecond pulse train,” Phys. Rev. Lett. 94, 113905 (2005).
[CrossRef]

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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

Veisz, L.

P. Heissler, R. Hörlein, J. M. Mikhailova, L. Waldecker, P. Tzallas, A. Buck, K. Schmid, C. M. S. Sears, F. Krausz, L. Veisz, M. Zepf, and G. D. Tsakiris, “Few-cycle driven relativistically oscillating plasma mirrors: a source of intense isolated attosecond pulses,” Phys. Rev. Lett. 108, 235003 (2012).
[CrossRef]

Y. Nomura, R. Hörlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, “Attosecond phase-locking of harmonics emitted from laser-produced plasmas,” Nat. Phys. 5, 124–128 (2008).
[CrossRef]

Waldecker, L.

P. Heissler, P. Tzallas, J. M. Mikhailova, K. Khrennikov, L. Waldecker, F. Krausz, S. Karsch, D. Charalambidis, and G. D. Tsakiris, “Two-photon above-threshold ionization using extreme-ultraviolet harmonic emission from relativistic laser–plasma interaction,” New J. Phys. 14, 043025 (2012).
[CrossRef]

P. Heissler, R. Hörlein, J. M. Mikhailova, L. Waldecker, P. Tzallas, A. Buck, K. Schmid, C. M. S. Sears, F. Krausz, L. Veisz, M. Zepf, and G. D. Tsakiris, “Few-cycle driven relativistically oscillating plasma mirrors: a source of intense isolated attosecond pulses,” Phys. Rev. Lett. 108, 235003 (2012).
[CrossRef]

Walmsley, I. A.

E. Cormier, I. A. Walmsley, E. M. Kosik, A. S. Wyatt, L. Corner, and L. F. DiMauro, “Self-referencing, spectrally, or spatially encoded spectral interferometry for the complete characterization of attosecond electromagnetic pulses,” Phys. Rev. Lett. 94, 033905 (2005).
[CrossRef]

Watanabe, S.

Westerwalbesloh, Th.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Witte, K.

L. A. A. Nikolopoulos, E. P. Benis, P. Tzallas, D. Charalambidis, K. Witte, and G. D. Tsakiris, “Second order autocorrelation of an XUV attosecond pulse train,” Phys. Rev. Lett. 94, 113905 (2005).
[CrossRef]

N. A. Papadogiannis, L. A. A. Nikolopoulos, D. Charalambidis, G. D. Tsakiris, P. Tzallas, and K. Witte, “On the feasibility of performing non-linear autocorrelation with attosecond pulse trains,” Appl. Phys. B 76, 721–727 (2003).
[CrossRef]

P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, “Direct observation of attosecond light bunching,” Nature 426, 267–271 (2003).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1985).

Wyatt, A. S.

E. Cormier, I. A. Walmsley, E. M. Kosik, A. S. Wyatt, L. Corner, and L. F. DiMauro, “Self-referencing, spectrally, or spatially encoded spectral interferometry for the complete characterization of attosecond electromagnetic pulses,” Phys. Rev. Lett. 94, 033905 (2005).
[CrossRef]

Yakovlev, V.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

Yakovlev, V. S.

J. Gagnon, E. Goulielmakis, and V. S. Yakovlev, “The accurate FROG characterization of attosecond pulses from streaking measurements,” Appl. Phys. B 92, 25–32 (2008).
[CrossRef]

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

Yamanouchi, K.

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Conclusive evidence of an attosecond pulse train observed with the mode-resolved autocorrelation technique,” Phys. Rev. Lett. 96, 083901 (2006).
[CrossRef]

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train in the single-cycle regime,” Phys. Rev. Lett. 97, 153904 (2006).
[CrossRef]

Yudin, G. L.

F. Quéré, J. Itatani, G. L. Yudin, and P. B. Corkum, “Temporal characterization of attosecond pulses,” in Ultrafast Optics IV, F. Krausz, G. Korn, P. Corkum, and I. A. Walmsley, eds. Vol. 95 of Springer Series in Optical Sciences (Springer, 2004), pp. 259–270.

Zepf, M.

P. Heissler, R. Hörlein, J. M. Mikhailova, L. Waldecker, P. Tzallas, A. Buck, K. Schmid, C. M. S. Sears, F. Krausz, L. Veisz, M. Zepf, and G. D. Tsakiris, “Few-cycle driven relativistically oscillating plasma mirrors: a source of intense isolated attosecond pulses,” Phys. Rev. Lett. 108, 235003 (2012).
[CrossRef]

Y. Nomura, R. Hörlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, “Attosecond phase-locking of harmonics emitted from laser-produced plasmas,” Nat. Phys. 5, 124–128 (2008).
[CrossRef]

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N. A. Papadogiannis, L. A. A. Nikolopoulos, D. Charalambidis, G. D. Tsakiris, P. Tzallas, and K. Witte, “On the feasibility of performing non-linear autocorrelation with attosecond pulse trains,” Appl. Phys. B 76, 721–727 (2003).
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P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781–784 (2011).
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Y. Nomura, R. Hörlein, P. Tzallas, B. Dromey, S. Rykovanov, Zs. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, and G. D. Tsakiris, “Attosecond phase-locking of harmonics emitted from laser-produced plasmas,” Nat. Phys. 5, 124–128 (2008).
[CrossRef]

Nature (4)

P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, “Direct observation of attosecond light bunching,” Nature 426, 267–271 (2003).
[CrossRef]

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[CrossRef]

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
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A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

New J. Phys. (2)

P. Heissler, P. Tzallas, J. M. Mikhailova, K. Khrennikov, L. Waldecker, F. Krausz, S. Karsch, D. Charalambidis, and G. D. Tsakiris, “Two-photon above-threshold ionization using extreme-ultraviolet harmonic emission from relativistic laser–plasma interaction,” New J. Phys. 14, 043025 (2012).
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Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train in the single-cycle regime,” Phys. Rev. Lett. 97, 153904 (2006).
[CrossRef]

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Conclusive evidence of an attosecond pulse train observed with the mode-resolved autocorrelation technique,” Phys. Rev. Lett. 96, 083901 (2006).
[CrossRef]

L. A. A. Nikolopoulos, E. P. Benis, P. Tzallas, D. Charalambidis, K. Witte, and G. D. Tsakiris, “Second order autocorrelation of an XUV attosecond pulse train,” Phys. Rev. Lett. 94, 113905 (2005).
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Y. Mairesse, O. Gobert, P. Breger, H. Merdji, P. Meynadier, P. Monchicourt, M. Perdrix, P. Salières, and B. Carré, “High harmonic XUV spectral phase interferometry for direct electric-field reconstruction,” Phys. Rev. Lett. 94, 173903 (2005).
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E. Cormier, I. A. Walmsley, E. M. Kosik, A. S. Wyatt, L. Corner, and L. F. DiMauro, “Self-referencing, spectrally, or spatially encoded spectral interferometry for the complete characterization of attosecond electromagnetic pulses,” Phys. Rev. Lett. 94, 033905 (2005).
[CrossRef]

P. Heissler, R. Hörlein, J. M. Mikhailova, L. Waldecker, P. Tzallas, A. Buck, K. Schmid, C. M. S. Sears, F. Krausz, L. Veisz, M. Zepf, and G. D. Tsakiris, “Few-cycle driven relativistically oscillating plasma mirrors: a source of intense isolated attosecond pulses,” Phys. Rev. Lett. 108, 235003 (2012).
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E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[CrossRef]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
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Other (2)

F. Quéré, J. Itatani, G. L. Yudin, and P. B. Corkum, “Temporal characterization of attosecond pulses,” in Ultrafast Optics IV, F. Krausz, G. Korn, P. Corkum, and I. A. Walmsley, eds. Vol. 95 of Springer Series in Optical Sciences (Springer, 2004), pp. 259–270.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1985).

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Figures (11)

Fig. 1.
Fig. 1.

Concept of the proposed SSAC scheme. In the upper-right inset, a schematic of the proposed setup is shown. The imaging ion-microscope provides an image of the ionization products around the common focal spots of the intersecting XUV beams. In the lower-left inset, the analogy to single-shot AC using fs-laser pulses and crystals is indicated. Provided that a two-photon ionization occurs, the fringe pattern shown schematically is the second-order AC trace to be analyzed.

Fig. 2.
Fig. 2.

Geometry considered in the model calculation.

Fig. 3.
Fig. 3.

Plot of the expression in Eqs. (6) and (8) for a group of equal amplitude odd harmonics between q=101111 and for f=5cm, d=0.3cm, and λ=800nm.

Fig. 4.
Fig. 4.

Plot of the expression in Eqs. (10) and (11) for q=915 and equal amplitudes. The geometry parameters are the same as in Fig. 3.

Fig. 5.
Fig. 5.

Second-order AC pattern due to the interference of the harmonic radiation emanating from two aperture of 100 μm in diameter. Upper panels: The profile of the converging XUV beam and the mask imposed to it. Lower panels: The second-order AC pattern in the two planes around the XUV focus as obtained from the numerical evaluation of Eq. (17). The geometry parameters and the harmonic selection are the same as in Fig. 4 (q=915 and equal amplitudes).

Fig. 6.
Fig. 6.

Second-order AC pattern due to the interference of the harmonic radiation emanating from two slits of 100 μm wide and 5 mm long. Upper panels: The profile of the converging XUV beam and the mask imposed to it. Lower panels: The second-order AC pattern in the two planes around the XUV focus as obtained from the numerical evaluation of Eq. (17). The geometry parameters and the harmonic selection are the same as in Fig. 4. (q=915 and equal amplitudes).

Fig. 7.
Fig. 7.

Schematic diagrams of two possible setups for a cross-beam arrangement. (a) Setup for low-order harmonics (long wavelength XUV emission) and (b) for higher-order harmonics (short wavelength XUV emission). (c) Reflectivity of Si as a function of angle of incidence ψ for parallel (solid line) and perpendicular (dashed line) polarization and for the indicated harmonic orders q.

Fig. 8.
Fig. 8.

Numerical calculation of the cross-beam arrangement using a wavefront beam splitter. The upper panel shows the illumination geometry and the interference pattern for the H9 harmonic at the focus. The FWHM extent of the focal spot in the two directions is also indicated. The lower panel shows the second-order signal due to two-photon ionization by the harmonic group of H9–H15. The pattern in the yz plane is what an ion microscope with enough resolution would record.

Fig. 9.
Fig. 9.

Numerical calculation of the cross-beam arrangement using a wavefront beam splitter for the indicated combinations of focal lengths f and angles of intersection θ. The upper panel shows the first-order AC trace while the lower the second-order. The apparent signal assuming a spatial resolution of Δs=2μm is shown as a gray shaded area.

Fig. 10.
Fig. 10.

Analysis of the 2D image of the beam-splitter case described in Section 4.D for an instrument resolution of Δs=2μm. The image has been smoothed to a degree corresponding to the finite instrument resolution and scaled to actual proportions. The line-outs along the axis of propagation of one of the beams and transverse to the z axis are shown by the red yellow-filled line.

Fig. 11.
Fig. 11.

Simulated ion signal for the indicated total number of ions and two different values of spatial resolution. The top row shows a line-out of the time-averaged second-order signal of the setup shown in Fig. 8 for infinite resolution (blue line) and convolved with the instrument function for finite resolution (red line) of Δs=2μm (left column) and Δs=1μm (right column). Assuming Poisson distribution for the number of ions in each bin, the statistical signal expected for the total number of ions indicated and the two resolution values are shown in the lower six panels by the green-filled points. The green dashed curve is a spline interpolation to guide the eye.

Tables (2)

Tables Icon

Table 1. Estimated Number of Ions for a Range of XUV Intensity Values and He Densities

Tables Icon

Table 2. Summary of the Performance for the Three Setups Considereda

Equations (23)

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a=λ041sinθ,
SAC(x,y,z)+|EA(tτ)+EB(t+τ)|4dt.
τas=τAC·sinθ.
Eq(y,z,t)=Eq[ej(lqy+kqzωqt)+ej(lqy+kqzωqt)]=Eq[ej(kqzωqt)(e+jlqy+ejlqy)]=2Eqcos(lqy)ej(kqzωqt),
Itot(y,z,t)=qEq(y,z,t)×pEp*(y,z,t)=q2Eqcos(lqy)ej(kqzωqt)×p2Epcos(lpy)ej(kpzωpt)=4q,pEqEpcos(lqy)cos(lpy)ej[(kqkp)z(ωqωp)t].
I^tot(y)=4qEq2cos2(lqy)=4qEq2cos2(qπ2ya).
Itot2(y,z,t)=[q2Eqcos(lqy)ej(kqzωqt)×p2Epcos(lpy)ej(kpzωpt)]2=24[q,pEqEpcos(lqy)cos(lpy)ej[(kqkp)z(ωqωp)t]]2=24q,p,n,mEqEpEnEmcos(lqy)cos(lpy)cos(lny)cos(lmy)×ej[(kqkp+knkm)z(ωqωp+ωnωm)t].
I^tot2(y)=24q,p,n,mRq,p,n,mEqEpEnEmcos(lqy)cos(lpy)cos(lny)cos(lmy)=24q,p,n,mRq,p,n,mEqEpEnEmcos(qπ2ya)cos(pπ2ya)cos(nπ2ya)cos(mπ2ya)whereRq,p,n,m=1forq+pnm=0andRq,p,n,m=0otherwise.
I(y)=[2J1(v)v]2,
I^tot(y)=4q[Eq2J1(vq)vqcos(uq)]2,
I^tot2(y)=28q,p,n,mRq,p,n,mEqEpEnEm×J1(vq)vqcos(uq)J1(vp)vpcos(up)J1(vn)vncos(un)J1(vm)vmcos(um)whereRq,p,n,m=1forq+pnm=0andRq,p,n,m=0otherwise.
Utot(P)Wej[k0(sf)]sdS,
Utot(P,t)WM(Q)qej[kq(sf)ωqt]dS,
Utot(P,t)qUqejωqtwhereUq=WM(Q)ej[kq(sf)]dS.
Itot(x,y,z,t)qUqejωqt×pUp*e+jωptq,pUqUp*ej[(ωqωp)t].
I^tot(x,y,z)qUqUq*.
Itot2(x,y,z,t)[q,pUqUp*ej[(ωqωp)t]]2and thus toI^tot2(x,y,z)q,p,n,mRq,p,n,m[UqUpUn*Um*],whereRq,p,n,m=1forq+pnm=0andRq,p,n,m=0otherwise.
Papt=I(d/2,f)πD24=2PXUVπwb2exp(d22wb2)πD24.
Imean=2PaptπRAiry2.
Pslit2PXUVπwb2exp(d22wb2)lylx/2+lx/2exp(2x2wb2)dx2PXUVπwb2exp(d22wb2)lyπ2wb.
Imean=2PslitLxLy.
Imean=PXUVLxLy.
Nions=Nas×σHe(2)×+VρHe(IXUV(r⃗,t)ωXUV)2dtdV=Nas×σHe(2)×ρHe×[IpeakωXUV]2+e2t2τas2dtVF(r⃗)2dV=Nas×σHe(2)×ρHe×[IpeakωXUV]2π2×τas×FV.

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