Abstract

Attosecond experiments involving focusing of attosecond light pulses can suffer from a spread of the attosecond radiation both in space and time due to optical aberrations. We present a detailed numerical study of the distortions induced in the most common focusing geometries that make use of parabolic, spherical, toroidal and ellipsoidal mirrors. We deduce the consequences on the pulse duration and possible issues that could arise in applications of attosecond pulses. This should serve as a guideline for setting up attosecond focusing optics.

© 2013 OSA

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References

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2012 (1)

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Y. Ivanov, O. Smirnova, and N. Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature (London) 485, 343–346 (2012).
[Crossref]

2011 (1)

2010 (4)

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]

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[Crossref] [PubMed]

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12, 093001 (2010).
[Crossref]

C. Bourassin-Bouchet, S. de Rossi, F. Delmotte, and P. Chavel, “Spatiotemporal distortions of attosecond pulses,” J. Opt. Soc. Am. A 27, 1395–1403 (2010).
[Crossref]

2009 (1)

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
[Crossref] [PubMed]

2008 (1)

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]

2007 (1)

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
[Crossref]

2006 (1)

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

2005 (1)

2004 (2)

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432, 867–871 (2004).
[Crossref]

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature (London) 432, 605–608 (2004).
[Crossref]

2003 (1)

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, 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 (2)

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 (London) 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] [PubMed]

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]

1992 (1)

1989 (1)

Agostini, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, 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]

Akturk, S.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12, 093001 (2010).
[Crossref]

Altucci, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

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]

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]

Avaldi, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Azzeer, A. M.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[Crossref] [PubMed]

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]

Baltuska, A.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
[Crossref]

Benedetti, E.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Billon, M.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
[Crossref] [PubMed]

Blümel, L.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
[Crossref]

Bor, Z.

Born, M.

M. Born and E. Wolf, Principles of Optics7th ed. (Pergamon, London, 1999).

Bourassin-Bouchet, C.

Bourhis, E.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
[Crossref] [PubMed]

Bowlan, P.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12, 093001 (2010).
[Crossref]

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 (London) 414, 509–513 (2001).
[Crossref]

Breger, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, 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]

Bruner, B. D.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Y. Ivanov, O. Smirnova, and N. Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature (London) 485, 343–346 (2012).
[Crossref]

Bucksbaum, P. H.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
[Crossref] [PubMed]

Burgdörfer, J.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[Crossref] [PubMed]

Calegari, F.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Carré, B.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
[Crossref] [PubMed]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, 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]

Caumes, J-P.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
[Crossref] [PubMed]

Cavalieri, A. L.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[Crossref] [PubMed]

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
[Crossref]

Chavel, P.

Corkum, P.

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 (London) 414, 509–513 (2001).
[Crossref]

Corkum, P. B.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432, 867–871 (2004).
[Crossref]

Dagan, M.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Y. Ivanov, O. Smirnova, and N. Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature (London) 485, 343–346 (2012).
[Crossref]

de Bohan, A.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, 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).
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de Rossi, S.

De Silvestri, S.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314, 443–446 (2006).
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Delmotte, F.

Dinu, L. C.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, 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).
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Drescher, M.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
[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 (London) 414, 509–513 (2001).
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Dudovich, N.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Y. Ivanov, O. Smirnova, and N. Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature (London) 485, 343–346 (2012).
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Echenique, P. M.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
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Ernstorfer, R.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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Fajardo, M.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
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Feist, J.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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Fieß, M.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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Flammini, R.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314, 443–446 (2006).
[Crossref] [PubMed]

Frasinski, L. J.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, 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).
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Fuchs, U.

Gagnon, J.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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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]

Garzella, D.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
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Gauthier, D.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
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Gautier, J.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
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Géléoc, M.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
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Gierak, J.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
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Gobert, O.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
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Goulielmakis, E.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[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).
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Gu, X.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12, 093001 (2010).
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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).
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Hajdu, J.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
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Heinzmann, U.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
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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 (London) 414, 509–513 (2001).
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Hendel, S.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
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Hentschel, M.

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 (London) 414, 509–513 (2001).
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Hergott, J-F.

A. Ravasio, D. Gauthier, F. R. N. C. Maia, M. Billon, J-P. Caumes, D. Garzella, M. Géléoc, O. Gobert, J-F. Hergott, A-M. Pena, H. Perez, B. Carré, E. Bourhis, J. Gierak, A. Madouri, D. Mailly, B. Schiedt, M. Fajardo, J. Gautier, P. Zeitoun, P. H. Bucksbaum, J. Hajdu, and H. Merdji, “Single-Shot Diffractive Imaging with a Table-Top Femtosecond Soft X-Ray Laser-Harmonics Source,” Phys. Rev. Lett. 103, 028104 (2009).
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Hofstetter, M.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[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).
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Holzwarth, R.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
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Horvath, B.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
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Itatani, J.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432, 867–871 (2004).
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Ivanov, M. Y.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Y. Ivanov, O. Smirnova, and N. Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature (London) 485, 343–346 (2012).
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Kanai, T.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature (London) 432, 605–608 (2004).
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Karpowicz, N.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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Kempe, M.

Kieffer, J. C.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432, 867–871 (2004).
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Kienberger, R.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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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. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
[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 (London) 414, 509–513 (2001).
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Kleineberg, U.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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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. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
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Komninos, Y.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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Korbman, M.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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Kosuge, A.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature (London) 432, 605–608 (2004).
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Kovac?ev, M.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, 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).
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Krausz, F.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[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]

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltŭska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
[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 (London) 414, 509–513 (2001).
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L’Huillier, A.

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

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432, 867–871 (2004).
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Lewenstein, M.

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
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Appl. Phys. A (1)

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J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432, 867–871 (2004).
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Figures (12)

Fig. 1
Fig. 1

Description of the geometric approach (a) Geometrical rays are reflected off a grazing incidence toroidal mirror and recombine in the focal point. (b) 2D spot diagram, calculated in a plane perpendicular to the optical axis. (c) Corresponding 3D spot diagram. (d) 3D spot diagram seen from above along with the surface of the mirror. The colormap represents the relative delay between the rays.

Fig. 2
Fig. 2

(a) Principle of the simulation of the gaussian source with the ray-tracing. (b) Resulting spectrally integrated gaussian flux distribution on the mirror surface. (c) 3D spot diagram obtained if taking into account the flux distribution on the mirror. (d) Spatio-temporal intensity distribution obtained by the diffractive approach. The projections on the (x,t) and (y,t) sides of the box stand for two slices of the 3D pulse located on the dashed lines. The projection on the (x,y) side corresponds to the temporally integrated pulse, that is the image that should be obtained if using a CCD sensor. (e) The spatially integrated pulse IG (t) associated to the spatio-temporal pulse is depicted above the box along with its global duration ΔtG and the decomposition of the latter into the four durations.

Fig. 3
Fig. 3

Spatio-temporal evolution of an attosecond pulse focused by a parabola. Central panel: description of the two focusing geometries. (a) (resp. (b)) Evolution of the (x,y,t) intensity distribution of the attosecond pulse along the z axis near the paraxial focus when considering a 0° (resp. 1°) field angle.

Fig. 4
Fig. 4

Evolution of the angle of incidence of the rays (main pannel) and of the polychromatic flux (smaller panel), at the surface of (a) a focusing multilayer mirror for a 1° field angle, and of (d) a toroidal mirror in a 2f – 2f geometry for a grazing angle of 11.5°. (b) Reflectivity and phase of the broadband multilayer mirror described in Ref. [21] for an angle of incidence of 0° and 5°. (c) Reflectivity and phase of a platinum mirror for an angle of incidence of 78.5°, that is a grazing angle of 11.5°, and of 45°.

Fig. 5
Fig. 5

Detailed evolution of a pulse focused by a parabola in the case (a) (resp. (b)) of 0° (resp. 1°) field angle. Upper panel: studied focusing geometry. Left panel: 3D spot diagram. Right panel: evolution of the modulus of the electric field in the y = 0 plane, shaded in grey on the 3D spot diagrams.

Fig. 6
Fig. 6

Spatio-temporal evolution of an attosecond pulse focused by a spherical mirror. Central panel: description of the two focusing geometries. (a) (resp. (b)) Evolution of the (x,y,t) intensity distribution of the attosecond pulse along the z axis near the paraxial focus when considering a 0° (resp. 1°) field angle.

Fig. 7
Fig. 7

Detailed evolution of a pulse focused by a spherical mirror. Upper panel: studied focusing geometry. Central panel (resp. lower panel): evolution of the modulus of the electric field in the y = 0 plane (resp. of the corresponding 3D spot diagram), 150 μm before the paraxial focus (a–c) and at the focus (b–d) when considering a 0° (a–b) and 1° field angle (c–d). The shaded plane on the 3D spot diagrams indicates the y = 0 plane.

Fig. 8
Fig. 8

Spatio-temporal evolution of an attosecond pulse focused by a toroidal mirror. Central panel: description of the three focusing geometries. (a–c) Evolution of the (x,y,z,t) intensity distribution of the attosecond pulse near the paraxial focus when considering (a) a magnification of 1 (2f – 2f geometry), (b) a magnification of 0.5, and (c) a 2f – 2f geometry with an error of 0.1° on the grazing angle.

Fig. 9
Fig. 9

Diffractive and geometric structures of pulses focused by toroidal and ellipsoidal mirrors in a 2f – 2f geometry. Upper panels: description of the focusing geometry. (a–b) Evolution of the 3D spot diagrams (left) and of the modulus of the electric field in the y = 0 plane (right) at the paraxial focus, in the case of (a) an ellipsoidal and (b) toroidal mirror. The shaded plane on the 3D spot diagrams at the paraxial focus indicates the y = 0 plane. (c) 3D spot diagram at the paraxial focus of the toroidal mirror if considering the rays reflected off the full surface of the mirror.

Fig. 10
Fig. 10

Detailed evolution of a pulse focused by a toroidal mirror in the case of (a) a 0.5 magnifying power and (b) an error of 0.1° on the grazing angle with a magnification of 1. Upper panel: studied focusing geometry. Left panel: 3D spot diagram. Right panel: evolution of the modulus of the electric field in the y = 0 plane, shaded in grey on the 3D spot diagrams.

Fig. 11
Fig. 11

Summary of the aberrations introduced by the four studied mirrors. The colormap indicates the dominant aberration for a given position of the focal point.

Fig. 12
Fig. 12

Decomposition of the global duration of three pulses focused by (a) an ellipsoidal mirror in a 2f – 2f geometry, (b) a spherical mirror with a zero field angle, and (c) a toroidal mirror with a magnification of 0.5. (a–c) central panel: instantaneous frequency of the pulse in the y = 0 plane. Lateral panels: local spectra and local group delays at three positions. Upper panel: spatially integrated pulse IG (t) and its RMS global duration ΔtG, along with its decomposition. IG (t) and ΔtG are estimated by integrating the full 3D pulse, even though only the pulse in the plane y = 0 is plotted.

Equations (2)

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E ( x , y , ω ) f ( ω ) g ( x , y ) = | f ( ω ) | | g ( x , y ) | exp [ i Ψ ( x , y ) + i Φ ( ω ) ] .
Δ t G 2 = Δ t F T G 2 + τ S P 2 + τ A C 2 + τ P C 2

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