Abstract

In the race toward attosecond pulses, for which high-order harmonics generated in rare gases are the best candidates, both the harmonic spectral range and the spectral phase have to be controlled. We demonstrate that multilayer extreme-ultraviolet chirped mirrors can be numerically optimized and designed to compensate for the intrinsic harmonic chirp that was recently discovered and that is responsible for temporal broadening of pulses. A simulation shows that an optimized mirror is capable of compressing the duration from 260to90as. This new technique is an interesting solution because of its ability to cover a wider spectral range than other technical devices that have already been proposed to overcome the chirp of high harmonics.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  7. A. Wonisch, Th. Westerwalbesloh, W. Hachmann, N. Kabachnik, U. Kleineberg, and U. Heinzmann, Thin Solid Films 464–465, 473 (2004).
    [CrossRef]
  8. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huiller, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
    [CrossRef] [PubMed]
  9. http://www-cxro.lbl.gov/optica?constants/asf.html.
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    [CrossRef] [PubMed]
  12. http://cletus.phys.columbia.edu/?windt/idl/imd/index.html.

2004 (3)

S. Kazamias and P. Balcou, Phys. Rev. A 69, 063416 (2004).
[CrossRef]

A. Wonisch, Th. Westerwalbesloh, W. Hachmann, N. Kabachnik, U. Kleineberg, and U. Heinzmann, Thin Solid Films 464–465, 473 (2004).
[CrossRef]

K. T. Kim, C. M. Kim, M. G. Baik, G. Umesh, and C. H. Nam, Phys. Rev. A 69, 051805(R) (2004).
[CrossRef]

2003 (1)

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

2002 (1)

I. L. Beigman, A. S. Pirozhkov, and E. N. Ragozin, J. Opt. A, Pure Appl. Opt. 4, 433 (2002).
[CrossRef]

2001 (1)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

1996 (1)

P. Antoine, A. L’Huiller, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
[CrossRef] [PubMed]

1994 (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huiller, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

1992 (1)

G. Casella and E. L. George, Am. Stat. 46, 167 (1992).

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Agostini, P.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Antoine, P.

P. Antoine, A. L’Huiller, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
[CrossRef] [PubMed]

Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Baik, M. G.

K. T. Kim, C. M. Kim, M. G. Baik, G. Umesh, and C. H. Nam, Phys. Rev. A 69, 051805(R) (2004).
[CrossRef]

Balcou, P.

S. Kazamias and P. Balcou, Phys. Rev. A 69, 063416 (2004).
[CrossRef]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huiller, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

Beigman, I. L.

I. L. Beigman, A. S. Pirozhkov, and E. N. Ragozin, J. Opt. A, Pure Appl. Opt. 4, 433 (2002).
[CrossRef]

Breger, P.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Carré, B.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

Casella, G.

G. Casella and E. L. George, Am. Stat. 46, 167 (1992).

Corkum, P. B.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huiller, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

de Bohan, A.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

Franzinski, L. J.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

George, E. L.

G. Casella and E. L. George, Am. Stat. 46, 167 (1992).

Hachmann, W.

A. Wonisch, Th. Westerwalbesloh, W. Hachmann, N. Kabachnik, U. Kleineberg, and U. Heinzmann, Thin Solid Films 464–465, 473 (2004).
[CrossRef]

Heinzmann, U.

A. Wonisch, Th. Westerwalbesloh, W. Hachmann, N. Kabachnik, U. Kleineberg, and U. Heinzmann, Thin Solid Films 464–465, 473 (2004).
[CrossRef]

Ivanov, M. Y.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huiller, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

Kabachnik, N.

A. Wonisch, Th. Westerwalbesloh, W. Hachmann, N. Kabachnik, U. Kleineberg, and U. Heinzmann, Thin Solid Films 464–465, 473 (2004).
[CrossRef]

Kazamias, S.

S. Kazamias and P. Balcou, Phys. Rev. A 69, 063416 (2004).
[CrossRef]

Kim, C. M.

K. T. Kim, C. M. Kim, M. G. Baik, G. Umesh, and C. H. Nam, Phys. Rev. A 69, 051805(R) (2004).
[CrossRef]

Kim, K. T.

K. T. Kim, C. M. Kim, M. G. Baik, G. Umesh, and C. H. Nam, Phys. Rev. A 69, 051805(R) (2004).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Kleineberg, U.

A. Wonisch, Th. Westerwalbesloh, W. Hachmann, N. Kabachnik, U. Kleineberg, and U. Heinzmann, Thin Solid Films 464–465, 473 (2004).
[CrossRef]

Kovacev, M.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

L’Huiller, A.

P. Antoine, A. L’Huiller, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
[CrossRef] [PubMed]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huiller, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

Lewenstein, M.

P. Antoine, A. L’Huiller, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
[CrossRef] [PubMed]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huiller, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

Mairesse, Y.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

Merdji, H.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

Monchicourt, P.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

Muller, H. G.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Nam, C. H.

K. T. Kim, C. M. Kim, M. G. Baik, G. Umesh, and C. H. Nam, Phys. Rev. A 69, 051805(R) (2004).
[CrossRef]

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Pirozhkov, A. S.

I. L. Beigman, A. S. Pirozhkov, and E. N. Ragozin, J. Opt. A, Pure Appl. Opt. 4, 433 (2002).
[CrossRef]

Ragozin, E. N.

I. L. Beigman, A. S. Pirozhkov, and E. N. Ragozin, J. Opt. A, Pure Appl. Opt. 4, 433 (2002).
[CrossRef]

Salières, P.

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Umesh, G.

K. T. Kim, C. M. Kim, M. G. Baik, G. Umesh, and C. H. Nam, Phys. Rev. A 69, 051805(R) (2004).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Westerwalbesloh, Th.

A. Wonisch, Th. Westerwalbesloh, W. Hachmann, N. Kabachnik, U. Kleineberg, and U. Heinzmann, Thin Solid Films 464–465, 473 (2004).
[CrossRef]

Wonisch, A.

A. Wonisch, Th. Westerwalbesloh, W. Hachmann, N. Kabachnik, U. Kleineberg, and U. Heinzmann, Thin Solid Films 464–465, 473 (2004).
[CrossRef]

Am. Stat. (1)

G. Casella and E. L. George, Am. Stat. 46, 167 (1992).

J. Opt. A, Pure Appl. Opt. (1)

I. L. Beigman, A. S. Pirozhkov, and E. N. Ragozin, J. Opt. A, Pure Appl. Opt. 4, 433 (2002).
[CrossRef]

Phys. Rev. A (3)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huiller, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

S. Kazamias and P. Balcou, Phys. Rev. A 69, 063416 (2004).
[CrossRef]

K. T. Kim, C. M. Kim, M. G. Baik, G. Umesh, and C. H. Nam, Phys. Rev. A 69, 051805(R) (2004).
[CrossRef]

Phys. Rev. Lett. (1)

P. Antoine, A. L’Huiller, and M. Lewenstein, Phys. Rev. Lett. 77, 1234 (1996).
[CrossRef] [PubMed]

Science (3)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Y. Mairesse, A. de Bohan, L. J. Franzinski, H. Merdji, P. Monchicourt, P. Breger, M. Kovacev, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003).
[CrossRef] [PubMed]

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Thin Solid Films (1)

A. Wonisch, Th. Westerwalbesloh, W. Hachmann, N. Kabachnik, U. Kleineberg, and U. Heinzmann, Thin Solid Films 464–465, 473 (2004).
[CrossRef]

Other (2)

http://www-cxro.lbl.gov/optica?constants/asf.html.

http://cletus.phys.columbia.edu/?windt/idl/imd/index.html.

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Figures (4)

Fig. 1
Fig. 1

(a) Recombination time and (b) chirp versus harmonic order assuming neon as the generating gas and an IR laser intensity of 7.5 × 10 14 W cm 2 (solid curves) and 5 × 10 14 W cm 2 (dashed curves).

Fig. 2
Fig. 2

Designed chirped mirror consisting of alternating Si (light gray) and Mo (dark gray) deposited on a Si O 2 substrate.

Fig. 3
Fig. 3

Reflectivity (dashed curve) and phase (solid curve) at normal incidence for the chirped mirror represented in Fig. 2.

Fig. 4
Fig. 4

Attosecond pulse before (gray line) and after compression by the chirped mirror (black line). Each pulse has been artificially centered in time for better comparison. The pulse repetition rate is 1.33 fs in both cases.

Equations (1)

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x ( t , t ) = e E 0 m ω 2 [ cos ( ω t ) cos ( ω t ) ] + e E 0 m ω sin ( ω t ) ( t t ) .

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