Abstract

High-order harmonic generation in atom clusters interacting with an intense linearly polarized laser field is studied by means of numerical simulations of the time-dependent Schrödinger equation for a two-dimensional model cluster in the single-active electron approximation. The well-known first and second cutoffs (in the atomic and molecular cases) are not clear in cluster calculations. In fact, the structure of the spectrum consists of a long plateau that extends far beyond the IP+3.17 UP limit and a collection of high-order harmonics with decreasing but significant intensities up to extremely high frequencies.

© 2001 Optical Society of America

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  1. A. McPherson, G. Gibson, H. Jara, V. Johann, T. S. Luk, I. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987).
    [CrossRef]
  2. H. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
    [CrossRef]
  3. A. L’Huillier and Ph. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70, 774–777 (1993).
    [CrossRef] [PubMed]
  4. R. Kopold, W. Becker, and M. Kebler, “Model calculations of high-harmonic generation in molecular ions,” Phys. Rev. A 58, 4022–4038 (1998).
    [CrossRef]
  5. R. Kopold and W. Becker, “High-harmonic generation in molecular ions: dipole phases and temporal aspects,” Laser Phys. 9, 398–402 (1999).
  6. S. Hüller and J. Meyer-ter-Vehn, “High-order harmonic radiation from solid layers irradiated by subpicosecond laser pulses,” Phys. Rev. A 48, 3906–3909 (1993).
    [CrossRef] [PubMed]
  7. D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
    [CrossRef] [PubMed]
  8. P. Gibbon, “High-order harmonic generation in plasmas,” IEEE J. Quantum Electron. 33, 1915–1924 (1997).
    [CrossRef]
  9. M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
    [CrossRef]
  10. A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
    [CrossRef] [PubMed]
  11. T. Ditmire, T. Donnelly, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
    [CrossRef] [PubMed]
  12. T. D. Donnelly, T. Ditmire, K. Neuman, M. D. Perry, and R. W. Falcone, “High-order harmonic generation in atom clusters,” Phys. Rev. Lett. 76, 2472–2475 (1996).
    [CrossRef] [PubMed]
  13. T. Ditmire, “Simulation of exploding clusters ionized by high-intensity femtosecond laser pulses,” Phys. Rev. A 57, R4094–R4097 (1998).
    [CrossRef]
  14. An extensive report on the laser-cluster interaction can be found in T. Ditmire, “Atomic clusters in ultrahigh intensity light fields,” Contemp. Phys. 38, 315–328 (1997).
    [CrossRef]
  15. V. Véniard, R. Taïeb, and A. Maquet, “Simple model for harmonic generation from atomic clusters,” Phys. Rev. A 60, 3952–3959 (1999).
    [CrossRef]
  16. J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535–3538 (1992).
    [CrossRef] [PubMed]
  17. K. J. Schafer, B. Yang, L. DiMauro, and K. C. Kulander, “Above thresold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
    [CrossRef] [PubMed]
  18. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
    [CrossRef] [PubMed]
  19. P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation by electron–proton recombination,” Europhys. Lett. 28, 629–633 (1994).
    [CrossRef]
  20. P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation in a partially ionized medium,” J. Opt. Soc. Am. B 13, 430–435 (1996).
    [CrossRef]
  21. R. Numico, P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation after photodissociation,” J. Phys. B 31, 4163–4172 (1998).
    [CrossRef]
  22. R. Numico, L. Roso, and L. Plaja, “Generation of trains of attosecond pulses from a photodissociated molecule,” J. Phys. B 32, 1–7 (1999).
    [CrossRef]
  23. T. Zuo, S. Chelkowski, and A. D. Bandrauk, “Harmonic generation by the H2+ molecular ion in intense laser fields,” Phys. Rev. A 48, 3837–3844 (1993).
    [CrossRef] [PubMed]
  24. A. D. Bandrauk and H. Yu, “High-order harmonic generation by one- and two-electron molecular ions with intense laser pulses,” Phys. Rev. A 59, 539–548 (1998).
    [CrossRef]
  25. J. R. Vázquez de Aldana and Luis Roso, “Nonrelativistic numerical study of atomic ionization by strong laser fields without the dipole approximation in a flat-atom model,” Phys. Rev. A 61, 043403 (2000).
    [CrossRef]
  26. K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
    [CrossRef] [PubMed]
  27. M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
    [CrossRef]

2000 (1)

J. R. Vázquez de Aldana and Luis Roso, “Nonrelativistic numerical study of atomic ionization by strong laser fields without the dipole approximation in a flat-atom model,” Phys. Rev. A 61, 043403 (2000).
[CrossRef]

1999 (3)

R. Numico, L. Roso, and L. Plaja, “Generation of trains of attosecond pulses from a photodissociated molecule,” J. Phys. B 32, 1–7 (1999).
[CrossRef]

R. Kopold and W. Becker, “High-harmonic generation in molecular ions: dipole phases and temporal aspects,” Laser Phys. 9, 398–402 (1999).

V. Véniard, R. Taïeb, and A. Maquet, “Simple model for harmonic generation from atomic clusters,” Phys. Rev. A 60, 3952–3959 (1999).
[CrossRef]

1998 (5)

T. Ditmire, “Simulation of exploding clusters ionized by high-intensity femtosecond laser pulses,” Phys. Rev. A 57, R4094–R4097 (1998).
[CrossRef]

R. Kopold, W. Becker, and M. Kebler, “Model calculations of high-harmonic generation in molecular ions,” Phys. Rev. A 58, 4022–4038 (1998).
[CrossRef]

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

R. Numico, P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation after photodissociation,” J. Phys. B 31, 4163–4172 (1998).
[CrossRef]

A. D. Bandrauk and H. Yu, “High-order harmonic generation by one- and two-electron molecular ions with intense laser pulses,” Phys. Rev. A 59, 539–548 (1998).
[CrossRef]

1997 (3)

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

An extensive report on the laser-cluster interaction can be found in T. Ditmire, “Atomic clusters in ultrahigh intensity light fields,” Contemp. Phys. 38, 315–328 (1997).
[CrossRef]

P. Gibbon, “High-order harmonic generation in plasmas,” IEEE J. Quantum Electron. 33, 1915–1924 (1997).
[CrossRef]

1996 (2)

P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation in a partially ionized medium,” J. Opt. Soc. Am. B 13, 430–435 (1996).
[CrossRef]

T. D. Donnelly, T. Ditmire, K. Neuman, M. D. Perry, and R. W. Falcone, “High-order harmonic generation in atom clusters,” Phys. Rev. Lett. 76, 2472–2475 (1996).
[CrossRef] [PubMed]

1995 (2)

T. Ditmire, T. Donnelly, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
[CrossRef] [PubMed]

1994 (2)

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
[CrossRef] [PubMed]

P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation by electron–proton recombination,” Europhys. Lett. 28, 629–633 (1994).
[CrossRef]

1993 (5)

T. Zuo, S. Chelkowski, and A. D. Bandrauk, “Harmonic generation by the H2+ molecular ion in intense laser fields,” Phys. Rev. A 48, 3837–3844 (1993).
[CrossRef] [PubMed]

S. Hüller and J. Meyer-ter-Vehn, “High-order harmonic radiation from solid layers irradiated by subpicosecond laser pulses,” Phys. Rev. A 48, 3906–3909 (1993).
[CrossRef] [PubMed]

A. L’Huillier and Ph. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70, 774–777 (1993).
[CrossRef] [PubMed]

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

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

1992 (2)

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535–3538 (1992).
[CrossRef] [PubMed]

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

1988 (1)

H. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, 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)

Agostini, P.

D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
[CrossRef] [PubMed]

Andiel, U.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Antonetti, A.

D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
[CrossRef] [PubMed]

Balcou, Ph.

A. L’Huillier and Ph. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70, 774–777 (1993).
[CrossRef] [PubMed]

Bandrauk, A. D.

A. D. Bandrauk and H. Yu, “High-order harmonic generation by one- and two-electron molecular ions with intense laser pulses,” Phys. Rev. A 59, 539–548 (1998).
[CrossRef]

T. Zuo, S. Chelkowski, and A. D. Bandrauk, “Harmonic generation by the H2+ molecular ion in intense laser fields,” Phys. Rev. A 48, 3837–3844 (1993).
[CrossRef] [PubMed]

Becker, W.

R. Kopold and W. Becker, “High-harmonic generation in molecular ions: dipole phases and temporal aspects,” Laser Phys. 9, 398–402 (1999).

R. Kopold, W. Becker, and M. Kebler, “Model calculations of high-harmonic generation in molecular ions,” Phys. Rev. A 58, 4022–4038 (1998).
[CrossRef]

Borisov, A. B.

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
[CrossRef] [PubMed]

Boyer, K.

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
[CrossRef] [PubMed]

A. McPherson, G. Gibson, H. Jara, V. Johann, T. S. Luk, I. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987).
[CrossRef]

Burnett, K.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

Chambers, D. M.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Chelkowski, S.

T. Zuo, S. Chelkowski, and A. D. Bandrauk, “Harmonic generation by the H2+ molecular ion in intense laser fields,” Phys. Rev. A 48, 3837–3844 (1993).
[CrossRef] [PubMed]

Chen, X.

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
[CrossRef] [PubMed]

Cooper, J.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

Corkum, P. B.

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

Dangor, A. E.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

de Aldana, J. R. Vázquez

J. R. Vázquez de Aldana and Luis Roso, “Nonrelativistic numerical study of atomic ionization by strong laser fields without the dipole approximation in a flat-atom model,” Phys. Rev. A 61, 043403 (2000).
[CrossRef]

DiMauro, L.

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

Ditmire, T.

T. Ditmire, “Simulation of exploding clusters ionized by high-intensity femtosecond laser pulses,” Phys. Rev. A 57, R4094–R4097 (1998).
[CrossRef]

An extensive report on the laser-cluster interaction can be found in T. Ditmire, “Atomic clusters in ultrahigh intensity light fields,” Contemp. Phys. 38, 315–328 (1997).
[CrossRef]

T. D. Donnelly, T. Ditmire, K. Neuman, M. D. Perry, and R. W. Falcone, “High-order harmonic generation in atom clusters,” Phys. Rev. Lett. 76, 2472–2475 (1996).
[CrossRef] [PubMed]

T. Ditmire, T. Donnelly, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

Donnelly, T.

T. Ditmire, T. Donnelly, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

Donnelly, T. D.

T. D. Donnelly, T. Ditmire, K. Neuman, M. D. Perry, and R. W. Falcone, “High-order harmonic generation in atom clusters,” Phys. Rev. Lett. 76, 2472–2475 (1996).
[CrossRef] [PubMed]

Eidmann, K.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Engers, T.

D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
[CrossRef] [PubMed]

Falcone, R. W.

T. D. Donnelly, T. Ditmire, K. Neuman, M. D. Perry, and R. W. Falcone, “High-order harmonic generation in atom clusters,” Phys. Rev. Lett. 76, 2472–2475 (1996).
[CrossRef] [PubMed]

T. Ditmire, T. Donnelly, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

Ferray, H.

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

Gahn, C.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Gibbon, P.

P. Gibbon, “High-order harmonic generation in plasmas,” IEEE J. Quantum Electron. 33, 1915–1924 (1997).
[CrossRef]

Gibson, G.

Grillon, G.

D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
[CrossRef] [PubMed]

Hüller, S.

S. Hüller and J. Meyer-ter-Vehn, “High-order harmonic radiation from solid layers irradiated by subpicosecond laser pulses,” Phys. Rev. A 48, 3906–3909 (1993).
[CrossRef] [PubMed]

Jara, H.

Jenke, G.

D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
[CrossRef] [PubMed]

Johann, V.

Kebler, M.

R. Kopold, W. Becker, and M. Kebler, “Model calculations of high-harmonic generation in molecular ions,” Phys. Rev. A 58, 4022–4038 (1998).
[CrossRef]

Keitel, C. H.

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

Knight, P. L.

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

Kopold, R.

R. Kopold and W. Becker, “High-harmonic generation in molecular ions: dipole phases and temporal aspects,” Laser Phys. 9, 398–402 (1999).

R. Kopold, W. Becker, and M. Kebler, “Model calculations of high-harmonic generation in molecular ions,” Phys. Rev. A 58, 4022–4038 (1998).
[CrossRef]

Krause, J. L.

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535–3538 (1992).
[CrossRef] [PubMed]

Kulander, K. C.

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

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535–3538 (1992).
[CrossRef] [PubMed]

L’Huillier, A.

A. L’Huillier and Ph. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70, 774–777 (1993).
[CrossRef] [PubMed]

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

Li, X. F.

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

Lompré, L. A.

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

Luk, T. S.

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
[CrossRef] [PubMed]

A. McPherson, G. Gibson, H. Jara, V. Johann, T. S. Luk, I. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987).
[CrossRef]

Machacek, A.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Mainfray, G.

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

Manus, C.

H. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, 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.

V. Véniard, R. Taïeb, and A. Maquet, “Simple model for harmonic generation from atomic clusters,” Phys. Rev. A 60, 3952–3959 (1999).
[CrossRef]

McIntyre, I.

McPherson, A.

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
[CrossRef] [PubMed]

A. McPherson, G. Gibson, H. Jara, V. Johann, T. S. Luk, I. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987).
[CrossRef]

Meyer-ter-Vehn, J.

S. Hüller and J. Meyer-ter-Vehn, “High-order harmonic radiation from solid layers irradiated by subpicosecond laser pulses,” Phys. Rev. A 48, 3906–3909 (1993).
[CrossRef] [PubMed]

Moreno, P.

R. Numico, P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation after photodissociation,” J. Phys. B 31, 4163–4172 (1998).
[CrossRef]

P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation in a partially ionized medium,” J. Opt. Soc. Am. B 13, 430–435 (1996).
[CrossRef]

P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation by electron–proton recombination,” Europhys. Lett. 28, 629–633 (1994).
[CrossRef]

Mysyrowicz, A.

D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
[CrossRef] [PubMed]

Neuman, K.

T. D. Donnelly, T. Ditmire, K. Neuman, M. D. Perry, and R. W. Falcone, “High-order harmonic generation in atom clusters,” Phys. Rev. Lett. 76, 2472–2475 (1996).
[CrossRef] [PubMed]

Nibbering, E.

D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
[CrossRef] [PubMed]

Norreys, P. A.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Numico, R.

R. Numico, L. Roso, and L. Plaja, “Generation of trains of attosecond pulses from a photodissociated molecule,” J. Phys. B 32, 1–7 (1999).
[CrossRef]

R. Numico, P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation after photodissociation,” J. Phys. B 31, 4163–4172 (1998).
[CrossRef]

Perry, M. D.

T. D. Donnelly, T. Ditmire, K. Neuman, M. D. Perry, and R. W. Falcone, “High-order harmonic generation in atom clusters,” Phys. Rev. Lett. 76, 2472–2475 (1996).
[CrossRef] [PubMed]

T. Ditmire, T. Donnelly, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

Plaja, L.

R. Numico, L. Roso, and L. Plaja, “Generation of trains of attosecond pulses from a photodissociated molecule,” J. Phys. B 32, 1–7 (1999).
[CrossRef]

R. Numico, P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation after photodissociation,” J. Phys. B 31, 4163–4172 (1998).
[CrossRef]

P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation in a partially ionized medium,” J. Opt. Soc. Am. B 13, 430–435 (1996).
[CrossRef]

P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation by electron–proton recombination,” Europhys. Lett. 28, 629–633 (1994).
[CrossRef]

Pretzler, G.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Protopapas, M.

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

Reed, V. C.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

Rhodes, C. K.

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
[CrossRef] [PubMed]

A. McPherson, G. Gibson, H. Jara, V. Johann, T. S. Luk, I. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987).
[CrossRef]

Roso, L.

R. Numico, L. Roso, and L. Plaja, “Generation of trains of attosecond pulses from a photodissociated molecule,” J. Phys. B 32, 1–7 (1999).
[CrossRef]

R. Numico, P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation after photodissociation,” J. Phys. B 31, 4163–4172 (1998).
[CrossRef]

P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation in a partially ionized medium,” J. Opt. Soc. Am. B 13, 430–435 (1996).
[CrossRef]

P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation by electron–proton recombination,” Europhys. Lett. 28, 629–633 (1994).
[CrossRef]

Roso, Luis

J. R. Vázquez de Aldana and Luis Roso, “Nonrelativistic numerical study of atomic ionization by strong laser fields without the dipole approximation in a flat-atom model,” Phys. Rev. A 61, 043403 (2000).
[CrossRef]

Schafer, K. J.

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

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535–3538 (1992).
[CrossRef] [PubMed]

Shiryaev, O. B.

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
[CrossRef] [PubMed]

Taïeb, R.

V. Véniard, R. Taïeb, and A. Maquet, “Simple model for harmonic generation from atomic clusters,” Phys. Rev. A 60, 3952–3959 (1999).
[CrossRef]

Thompson, B. D.

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
[CrossRef] [PubMed]

Tsakiris, G. D.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Véniard, V.

V. Véniard, R. Taïeb, and A. Maquet, “Simple model for harmonic generation from atomic clusters,” Phys. Rev. A 60, 3952–3959 (1999).
[CrossRef]

von der Linde, D.

D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
[CrossRef] [PubMed]

Wark, J. S.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Watts, I.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Witte, K.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Yang, B.

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

Yu, H.

A. D. Bandrauk and H. Yu, “High-order harmonic generation by one- and two-electron molecular ions with intense laser pulses,” Phys. Rev. A 59, 539–548 (1998).
[CrossRef]

Zepf, M.

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Zuo, T.

T. Zuo, S. Chelkowski, and A. D. Bandrauk, “Harmonic generation by the H2+ molecular ion in intense laser fields,” Phys. Rev. A 48, 3837–3844 (1993).
[CrossRef] [PubMed]

Contemp. Phys. (1)

An extensive report on the laser-cluster interaction can be found in T. Ditmire, “Atomic clusters in ultrahigh intensity light fields,” Contemp. Phys. 38, 315–328 (1997).
[CrossRef]

Europhys. Lett. (1)

P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation by electron–proton recombination,” Europhys. Lett. 28, 629–633 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Gibbon, “High-order harmonic generation in plasmas,” IEEE J. Quantum Electron. 33, 1915–1924 (1997).
[CrossRef]

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

J. Phys. B (3)

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

R. Numico, P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation after photodissociation,” J. Phys. B 31, 4163–4172 (1998).
[CrossRef]

R. Numico, L. Roso, and L. Plaja, “Generation of trains of attosecond pulses from a photodissociated molecule,” J. Phys. B 32, 1–7 (1999).
[CrossRef]

Laser Phys. (1)

R. Kopold and W. Becker, “High-harmonic generation in molecular ions: dipole phases and temporal aspects,” Laser Phys. 9, 398–402 (1999).

Phys. Rev. A (9)

S. Hüller and J. Meyer-ter-Vehn, “High-order harmonic radiation from solid layers irradiated by subpicosecond laser pulses,” Phys. Rev. A 48, 3906–3909 (1993).
[CrossRef] [PubMed]

D. von der Linde, T. Engers, G. Jenke, P. Agostini, G. Grillon, E. Nibbering, A. Mysyrowicz, and A. Antonetti, “Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses,” Phys. Rev. A 52, R25–R27 (1995).
[CrossRef] [PubMed]

T. Zuo, S. Chelkowski, and A. D. Bandrauk, “Harmonic generation by the H2+ molecular ion in intense laser fields,” Phys. Rev. A 48, 3837–3844 (1993).
[CrossRef] [PubMed]

A. D. Bandrauk and H. Yu, “High-order harmonic generation by one- and two-electron molecular ions with intense laser pulses,” Phys. Rev. A 59, 539–548 (1998).
[CrossRef]

J. R. Vázquez de Aldana and Luis Roso, “Nonrelativistic numerical study of atomic ionization by strong laser fields without the dipole approximation in a flat-atom model,” Phys. Rev. A 61, 043403 (2000).
[CrossRef]

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

R. Kopold, W. Becker, and M. Kebler, “Model calculations of high-harmonic generation in molecular ions,” Phys. Rev. A 58, 4022–4038 (1998).
[CrossRef]

T. Ditmire, “Simulation of exploding clusters ionized by high-intensity femtosecond laser pulses,” Phys. Rev. A 57, R4094–R4097 (1998).
[CrossRef]

V. Véniard, R. Taïeb, and A. Maquet, “Simple model for harmonic generation from atomic clusters,” Phys. Rev. A 60, 3952–3959 (1999).
[CrossRef]

Phys. Rev. E (1)

M. Zepf, G. D. Tsakiris, G. Pretzler, I. Watts, D. M. Chambers, P. A. Norreys, U. Andiel, A. E. Dangor, K. Eidmann, C. Gahn, A. Machacek, J. S. Wark, and K. Witte, “Role of the plasma scale length in the harmonic generation from solid targets,” Phys. Rev. E 58, R5253–R5256 (1998).
[CrossRef]

Phys. Rev. Lett. (7)

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell and L-shell transitions,” Phys. Rev. Lett. 72, 1810–1813 (1994).
[CrossRef] [PubMed]

T. Ditmire, T. Donnelly, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

T. D. Donnelly, T. Ditmire, K. Neuman, M. D. Perry, and R. W. Falcone, “High-order harmonic generation in atom clusters,” Phys. Rev. Lett. 76, 2472–2475 (1996).
[CrossRef] [PubMed]

A. L’Huillier and Ph. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70, 774–777 (1993).
[CrossRef] [PubMed]

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535–3538 (1992).
[CrossRef] [PubMed]

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

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

Rep. Prog. Phys. (1)

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Surface plots of (a) the atomic and (b) the cluster potentials as indicated in Eqs. (1) and (2).

Fig. 2
Fig. 2

Harmonic spectra for a laser with E0=0.06 a.u. (I0=1.26×1014 W/cm2) and frequency ωL=0.057 a.u. (wavelength 800 nm). Vertical axis, log10 of the harmonic intensity with arbitrary units. Horizontal axis, harmonic order. For these parameters IP+3.17 UP24 ωL and IP+8 UP47 ωL: (a) wave function initially distributed across all the atoms in the cluster, (b) initial wave function localized at the central atom. For this simulation the cluster is oriented with δ=π/6. (c) The well-known atomic case, for comparison.

Fig. 3
Fig. 3

Harmonic spectra for a higher laser intensity. All parameters, except for those of the laser field, are equal to those in Fig. 2. Now E0=0.1 a.u. (I0=3.51×1014 W/cm2) is considered. (a) Wave function initially distributed across all the atoms in the cluster, (b) initial wave function localized at the central atom. For this simulation the cluster is oriented with δ=π/6. (c) The well-known atomic case, for comparison. For these parameters IP+3.17 UP51 ωL and IP+8 UP116 ωL.

Fig. 4
Fig. 4

Snapshots of the electron population after the third and fifth cycles of the interaction with the laser for the same parameters as in Fig. 3(b) (initially localized wave function). The cluster is oriented with δ=π/6, and the laser is linearly polarized along the vertical axis. Contour lines are set on a logarithmic scale, and distances are expressed in atomic units (a.u.)

Fig. 5
Fig. 5

Snapshots of the electron population after the third and fifth cycles of the interaction with the laser for the same parameters as in Fig. 3(a) (initially distributed wave function). The cluster is oriented with δ=π/6, and the laser is linearly polarized along the vertical axis. Contour lines are set on a logarithmic scale, and distances are expressed in atomic units (a.u.)

Fig. 6
Fig. 6

Influence of the orientation of the cluster and the laser for the same parameters as in Fig. 3 but now with δ=0. (a) Initially distributed wave function; cf. Fig. 3(a). (b) initially localized wave function; cf. Fig. 3(b). The atomic case of Fig. 3(c) is obviously independent of orientation angle δ.

Equations (12)

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

VA(x, y)=-e2(x2+y2+a2)1/2 exp-x2+y2b.
VC(x, y)=n,m VA(x-xn,m, y-yn,m)
a=d[cos(δ), sin(δ)],
b=d[cos(δ+π/3), sin(δ+π/3)],
xn,m=nd cos(δ)+md cos(δ+π/3),
yn,m=nd sin(δ)+md sin(δ+π/3).
i tΨ(x, y, t)=H(x, y, t)Ψ(x, y, t)=12m p+ec A(t)2+VC(x, y)×Ψ(x, y, t).
Φ(x, y, t=0)=ϕ0(x, y).
Φ(x, y, t=0)=1N n,m ϕ0(x-xn,m, y-yn,m).
A(t)=-c 0t E0f(t)sin(ωLt)dtey,
D(w)=12π 0T a(t)exp(-iωLt)dt,
a(t)=d2dt2r=-1mH(x, y, t).

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