Abstract

In this article, we report that usual multilayer mirror configurations to focus attosecond pulses generate geometric aberrations and can significantly stretch pulses. The numerical simulations show that the effects can be strong enough to delay some parts of the pulses of an attosecond pulse train and make them interfere with the next pulses of the train. The influence of the numerical aperture on the pulse duration is also studied, showing that such effects can occur even with very low numerical apertures.

© 2010 Optical Society of America

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    [Crossref]
  3. W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
    [Crossref]
  4. F. Quéré, C. Thaury, P. Monot, S. Dobosz, Ph. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett. 96, 125004 (2006).
    [Crossref] [PubMed]
  5. 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] [PubMed]
  6. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003).
    [Crossref] [PubMed]
  7. 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, 509–513 (2001).
    [Crossref] [PubMed]
  8. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
    [Crossref] [PubMed]
  9. A. S. Morlens, R. López-Martens, O. Boyko, P. Zeitoun, P. Balcou, K. Varjú, E. Gustafsson, T. Remetter, A. L’Huillier, S. Kazamias, J. Gautier, F. Delmotte, and M. F. Ravet, “Design and characterization of extreme-ultraviolet broadband mirrors for attosecond science,” Opt. Lett. 31, 1558–1560 (2006).
    [Crossref] [PubMed]
  10. A. Aquila, F. Salmassi, and E. Gullikson, “Metrologies for the phase characterization of attosecond extreme ultraviolet optics,” Opt. Lett. 33, 455–457 (2008).
    [Crossref] [PubMed]
  11. L. Poletto, F. Frassetto, and P. Villoresi, “Design of an extreme-ultraviolet attosecond compressor,” J. Opt. Soc. Am. B 25, B133–B136 (2008).
    [Crossref]
  12. M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. Reider, P. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (2001).
    [Crossref] [PubMed]
  13. Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119–121 (1989).
    [Crossref] [PubMed]
  14. M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
    [Crossref] [PubMed]
  15. U. Fuchs, U. D. Zeitner, and A. Tünnermann, “Ultra-short pulse propagation in complex optical systems,” Opt. Express 13, 3852–3861 (2005).
    [Crossref] [PubMed]
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  17. P. Bowlan, U. Fuchs, R. Trebino, and U. D. Zeitner, “Measuring the spatiotemporal electric field of tightly focused ultrashort pulses with sub-micron spatial resolution,” Opt. Express 16, 13663–13675 (2008).
    [Crossref] [PubMed]
  18. M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), pp. 514–515.
  19. P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
    [Crossref] [PubMed]
  20. Y. Ménesguen, S. de Rossi, E. Meltchakov, and F. Delmotte, “Aperiodic multilayer mirrors for efficient broadband reflection in the extreme ultraviolet,” Appl. Phys. A 98, 305–309 (2010).
    [Crossref]
  21. L. G. Parratt, “Surfaces studies of solids by total reflection of x-rays,” Phys. Rev. 95, 359–369 (1954).
    [Crossref]

2010 (1)

Y. Ménesguen, S. de Rossi, E. Meltchakov, and F. Delmotte, “Aperiodic multilayer mirrors for efficient broadband reflection in the extreme ultraviolet,” Appl. Phys. A 98, 305–309 (2010).
[Crossref]

2008 (5)

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

A. Aquila, F. Salmassi, and E. Gullikson, “Metrologies for the phase characterization of attosecond extreme ultraviolet optics,” Opt. Lett. 33, 455–457 (2008).
[Crossref] [PubMed]

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

P. Bowlan, U. Fuchs, R. Trebino, and U. D. Zeitner, “Measuring the spatiotemporal electric field of tightly focused ultrashort pulses with sub-micron spatial resolution,” Opt. Express 16, 13663–13675 (2008).
[Crossref] [PubMed]

2006 (3)

A. S. Morlens, R. López-Martens, O. Boyko, P. Zeitoun, P. Balcou, K. Varjú, E. Gustafsson, T. Remetter, A. L’Huillier, S. Kazamias, J. Gautier, F. Delmotte, and M. F. Ravet, “Design and characterization of extreme-ultraviolet broadband mirrors for attosecond science,” Opt. Lett. 31, 1558–1560 (2006).
[Crossref] [PubMed]

F. Quéré, C. Thaury, P. Monot, S. Dobosz, Ph. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett. 96, 125004 (2006).
[Crossref] [PubMed]

Z. L. Horvàth, A. P. Kovács, and Z. Bor, “Distortion of ultrashort pulses caused by aberrations” in International Conference on Ultrafast Phenomena (UP), 2006 OSA Technical Digest Series (Optical Society of America, 2006), paper ThD16.

2005 (1)

2003 (1)

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

2001 (3)

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, 509–513 (2001).
[Crossref] [PubMed]

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] [PubMed]

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

1999 (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), pp. 514–515.

1995 (1)

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
[Crossref] [PubMed]

1993 (1)

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[Crossref] [PubMed]

1989 (1)

1988 (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

1987 (1)

1954 (1)

L. G. Parratt, “Surfaces studies of solids by total reflection of x-rays,” Phys. Rev. 95, 359–369 (1954).
[Crossref]

Agostini, P.

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

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] [PubMed]

Aquila, A.

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Audebert, P.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, Ph. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett. 96, 125004 (2006).
[Crossref] [PubMed]

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] [PubMed]

Balcou, P.

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] [PubMed]

Bor, Z.

Z. L. Horvàth, A. P. Kovács, and Z. Bor, “Distortion of ultrashort pulses caused by aberrations” in International Conference on Ultrafast Phenomena (UP), 2006 OSA Technical Digest Series (Optical Society of America, 2006), paper ThD16.

Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119–121 (1989).
[Crossref] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), pp. 514–515.

Boutu, W.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

Bowlan, P.

Boyer, K.

Boyko, O.

Brabec, T.

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, 509–513 (2001).
[Crossref] [PubMed]

Breger, P.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

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

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] [PubMed]

Caillat, J.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

Carré, B.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

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

Corkum, P.

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, 509–513 (2001).
[Crossref] [PubMed]

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

de Bohan, A.

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

de Rossi, S.

Y. Ménesguen, S. de Rossi, E. Meltchakov, and F. Delmotte, “Aperiodic multilayer mirrors for efficient broadband reflection in the extreme ultraviolet,” Appl. Phys. A 98, 305–309 (2010).
[Crossref]

Delmotte, F.

Dinu, L. C.

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

Dobosz, S.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, Ph. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett. 96, 125004 (2006).
[Crossref] [PubMed]

Drescher, M.

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, 509–513 (2001).
[Crossref] [PubMed]

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

Ferray, M.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Frasinski, L. J.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

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

Frassetto, F.

Fuchs, U.

Gagnon, J.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Gautier, J.

Geindre, J. -P.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, Ph. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett. 96, 125004 (2006).
[Crossref] [PubMed]

Gibson, G.

Goulielmakis, E.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Gullikson, E.

Gullikson, E. M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Gustafsson, E.

Haessler, S.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

Heinzmann, U.

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, 509–513 (2001).
[Crossref] [PubMed]

Hentschel, M.

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, 509–513 (2001).
[Crossref] [PubMed]

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

Hofstetter, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Horvàth, Z. L.

Z. L. Horvàth, A. P. Kovács, and Z. Bor, “Distortion of ultrashort pulses caused by aberrations” in International Conference on Ultrafast Phenomena (UP), 2006 OSA Technical Digest Series (Optical Society of America, 2006), paper ThD16.

Jara, H.

Johann, U.

Kazamias, S.

Kempe, M.

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[Crossref] [PubMed]

Kienberger, R.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. Reider, P. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291, 1923–1927 (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, 509–513 (2001).
[Crossref] [PubMed]

Kleineberg, U.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Kovacev, M.

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

Kovács, A. P.

Z. L. Horvàth, A. P. Kovács, and Z. Bor, “Distortion of ultrashort pulses caused by aberrations” in International Conference on Ultrafast Phenomena (UP), 2006 OSA Technical Digest Series (Optical Society of America, 2006), paper ThD16.

Krausz, F.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[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, 509–513 (2001).
[Crossref] [PubMed]

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

L’Huillier, A.

A. S. Morlens, R. López-Martens, O. Boyko, P. Zeitoun, P. Balcou, K. Varjú, E. Gustafsson, T. Remetter, A. L’Huillier, S. Kazamias, J. Gautier, F. Delmotte, and M. F. Ravet, “Design and characterization of extreme-ultraviolet broadband mirrors for attosecond science,” Opt. Lett. 31, 1558–1560 (2006).
[Crossref] [PubMed]

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
[Crossref] [PubMed]

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Lewenstein, M.

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
[Crossref] [PubMed]

Li, X. F.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Lompre, L. A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

López-Martens, R.

Luk, T. S.

Mainfray, G.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Mairesse, Y.

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

Manus, C.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Maquet, A.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

Martin, Ph.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, Ph. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett. 96, 125004 (2006).
[Crossref] [PubMed]

McIntyre, I. A.

McPherson, A.

Meltchakov, E.

Y. Ménesguen, S. de Rossi, E. Meltchakov, and F. Delmotte, “Aperiodic multilayer mirrors for efficient broadband reflection in the extreme ultraviolet,” Appl. Phys. A 98, 305–309 (2010).
[Crossref]

Ménesguen, Y.

Y. Ménesguen, S. de Rossi, E. Meltchakov, and F. Delmotte, “Aperiodic multilayer mirrors for efficient broadband reflection in the extreme ultraviolet,” Appl. Phys. A 98, 305–309 (2010).
[Crossref]

Merdji, H.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

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

Milosevic, N.

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, 509–513 (2001).
[Crossref] [PubMed]

Monchicourt, P.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

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

Monot, P.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, Ph. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett. 96, 125004 (2006).
[Crossref] [PubMed]

Morlens, A. S.

Muller, H. G.

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

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] [PubMed]

Mullot, G.

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] [PubMed]

Parratt, L. G.

L. G. Parratt, “Surfaces studies of solids by total reflection of x-rays,” Phys. Rev. 95, 359–369 (1954).
[Crossref]

Paul, P. M.

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] [PubMed]

Poletto, L.

Quéré, F.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, Ph. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett. 96, 125004 (2006).
[Crossref] [PubMed]

Ravet, M. F.

Reider, G.

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

Reider, G. A.

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, 509–513 (2001).
[Crossref] [PubMed]

Remetter, T.

Rhodes, C. K.

Rudolph, W.

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[Crossref] [PubMed]

Salières, P.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

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

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
[Crossref] [PubMed]

Salmassi, F.

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Spielmann, C.

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, 509–513 (2001).
[Crossref] [PubMed]

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

Stankiewicz, M.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

Taieb, R.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

Taïeb, R.

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

Tempea, G.

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

Thaury, C.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, Ph. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett. 96, 125004 (2006).
[Crossref] [PubMed]

Toma, E. S.

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] [PubMed]

Trebino, R.

Tünnermann, A.

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Varjú, K.

Villoresi, P.

Waters, G.

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), pp. 514–515.

Yakovlev, V. S.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Zeitner, U. D.

Zeitoun, P.

Appl. Phys. A (1)

Y. Ménesguen, S. de Rossi, E. Meltchakov, and F. Delmotte, “Aperiodic multilayer mirrors for efficient broadband reflection in the extreme ultraviolet,” Appl. Phys. A 98, 305–309 (2010).
[Crossref]

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

J. Phys. B (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

Nat. Phys. (1)

W. Boutu, S. Haessler, H. Merdji, P. Breger, G. Waters, M. Stankiewicz, L. J. Frasinski, R. Taieb, J. Caillat, A. Maquet, P. Monchicourt, B. Carré, and P. Salières, “Coherent control of attosecond emission from aligned molecules,” Nat. Phys. 4, 545–549 (2008).
[Crossref]

Nature (1)

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, 509–513 (2001).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. (1)

L. G. Parratt, “Surfaces studies of solids by total reflection of x-rays,” Phys. Rev. 95, 359–369 (1954).
[Crossref]

Phys. Rev. A (1)

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

F. Quéré, C. Thaury, P. Monot, S. Dobosz, Ph. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett. 96, 125004 (2006).
[Crossref] [PubMed]

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
[Crossref] [PubMed]

Science (4)

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] [PubMed]

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

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

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

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), pp. 514–515.

Z. L. Horvàth, A. P. Kovács, and Z. Bor, “Distortion of ultrashort pulses caused by aberrations” in International Conference on Ultrafast Phenomena (UP), 2006 OSA Technical Digest Series (Optical Society of America, 2006), paper ThD16.

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Figures (11)

Fig. 1
Fig. 1

Reflection of the EUV beam on a mirror. The ray-tracing software allows us to geometrically describe the attosecond pulse in the integration plane.

Fig. 2
Fig. 2

Spectral amplitude (a) of a single attosecond pulse and (b) of an attosecond pulse train. The reflectivity spectrum of the mirror is shown in dashed line.

Fig. 3
Fig. 3

Radial intensity distribution of (a) a single attosecond pulse and (b) an attosecond pulse train focused by an on-axis parabolic mirror.

Fig. 4
Fig. 4

Radial intensity distribution of a single attosecond pulse focused by an on-axis parabolic mirror 25 μ m after the paraxial focus.

Fig. 5
Fig. 5

Radial intensity distribution nearby the paraxial focus when using an on-axis spherical mirror. We consider (a) a single attosecond pulse and (b) an attosecond pulse train.

Fig. 6
Fig. 6

Intensity distribution in two orthogonal planes when studying either (a) a single attosecond pulse or (b) an attosecond pulse train after their reflection on a 1° field angle parabolic mirror. The bold lateral lines on each image indicate the position of the corresponding orthogonal section of the pulse.

Fig. 7
Fig. 7

3D Intensity distribution (a) of a single attosecond pulse or (b) of an attosecond pulse train 75 μ m before the paraxial focus after their reflection on a 1° field angle parabolic multilayer mirror.

Fig. 8
Fig. 8

Intensity distribution in two orthogonal planes when studying either (a) a single attosecond pulse or (b) an attosecond pulse train after their reflection on a 1° field angle spherical mirror.

Fig. 9
Fig. 9

3D Intensity distribution (a) of a single attosecond pulse or (b) of an attosecond pulse train 150 μ m before the paraxial focus after its reflection on a 1° field angle parabolic multilayer mirror.

Fig. 10
Fig. 10

Modulus of the electric field in the plane of symmetry of the pulse train reflected by a 1° field angle spherical mirror.

Fig. 11
Fig. 11

Evolution of (a) the 80% energy pulse duration and (b) the FWHM with respect to the image NA. The pulse durations are normalized with respect to the initial pulse duration.

Equations (5)

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

I ( θ , z , λ ) I 0 ( λ ) w 0 2 z 2 θ 0 ( λ ) 2 exp [ θ 2 2 θ 0 ( λ ) 2 ] ,
F r ( M , λ ) = I ( S , M , λ ) Δ Ω ( M ) | r ( S , M , λ ) | 2 .
E ( P , λ ) = [ F r ( M , λ ) ] 1 / 2 exp { i ϕ source ( λ ) + i ϕ mirror ( P , λ ) + 2 i π λ [ ( S M ) + ( M P ) ] } ,
E ( P , λ ) i λ + + E ( P , λ ) exp ( 2 i π λ P P ) P P cos [ γ ( P , P ) ] d S plane ,
I ( P , t ) = | F T 1 [ E ( P , υ ) ] | 2 ,

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