Abstract

High-order harmonic generation (HHG) in laser fields of relativistic intensity is studied. It is shown that, owing to relativistic longitudinal displacement of the photoelectrons, significant HHG suppression occurs. Such suppression is greater for the low-frequency part of the HHG spectrum than for the high-frequency part. We propose to use a standing-wave pump instead of a traveling wave to overcome this effect and to enhance the efficiency of HHG. The efficiency of utilizing atoms in a standing wave decreases with growth in the pump intensity. However, in traveling-wave HHG the decrease in efficiency is still greater; therefore, using a standing wave allows one to obtain a HHG intensity that is essentially greater than in a traveling wave (for example, a gain factor of 102 can be achieved when one is pumping Ar8+ ions with a radiation of intensity 1018 W/cm2 and a wavelength of 0.3 µm).

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
    [CrossRef]
  2. Z. Chang, A. Rundquist, H.-W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
    [CrossRef]
  3. M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
    [CrossRef]
  4. N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, “Coherent soft x-ray generation by the harmonics of an ultra-high power Kr–F laser,” Phys. Rev. A 43, 1669–1672 (1991).
    [CrossRef] [PubMed]
  5. Sh. Kubodera, Yu. Nagata, Ya. Akiyama, K. Midorikawa, M. Obara, H. Tashiro, and K. Toyoda, “High order harmonics in laser-produced ions,” Phys. Rev. A 48, 4576–4582 (1993).
    [CrossRef] [PubMed]
  6. C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
    [CrossRef] [PubMed]
  7. K. Kondo, T. Tamida, Y. Nabekawa, and S. Watanabe, “High-order harmonic generation and ionization using ultrashort KrF and Ti:sapphire lasers,” Phys. Rev. A 49, 3881–3889 (1994).
    [CrossRef] [PubMed]
  8. S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
    [CrossRef]
  9. P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
    [CrossRef] [PubMed]
  10. 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, 3535–3558 (1992).
    [CrossRef] [PubMed]
  11. C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A 51, 1420–1430 (1995).
    [CrossRef] [PubMed]
  12. R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization of atoms and generation of short-wavelength radiation,” in Laser Optics ’95 and ICONO ’95: Superintense Laser Fields, A. A. Andreev and V. M. Gordienko, eds., Proc. SPIE 2770, 46–52 (1995).
    [CrossRef]
  13. R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization: electron rescattering and generation of short-wavelength radiation,” Laser Phys. 6, 79–83 (1996).
  14. R. V. Kulyagin and V. D. Taranukhin, “Generation of x-ray radiation by atoms in an ultra-high intensity laser field,” Quantum Electron. 26, 866–870 (1996).
    [CrossRef]
  15. R. V. Kulyagin and V. D. Taranukhin, “Features of high-harmonic generation by atoms at superintense and ultrashort laser pumping,” Laser Phys. 7, 623–626 (1997).
  16. V. D. Taranukhin, “Generation of coherent x-ray radiation by atoms in superstrong laser fields: fundamental restrictions, optimizations and ultimate possibilities,” in Technical Digest, XVI International Conference on Coherent and Nonlinear Optics (URSS Publishers, Moscow, 1998), p. 118.
  17. V. D. Taranukhin and N. Yu. Shubin, “Coherent x-ray generation by ions with standing wave pump radiation of relativistic intensity,” presented at the 8th Conference on Applications of High Field and Short Wavelength Sources, Potsdam, Germany (June 27–30, 1999).
  18. V. D. Taranukhin and N. Yu. Shubin, “High-order harmonic generation by multielectron atoms with laser standing wave of relativistic intensity,” in Book of Abstracts, 8th Annual International Laser Physics Workshop (Research Institute for Solid State Physics and Optics, Budapest, Hungary, 1999), pp. 103–104.
  19. V. D. Taranukhin, “Relativistic high-order harmonic generation,” Laser Phys. 10, 330–336 (2000).
  20. A. B. Kim, M. Yu. Ryabikin, and A. M. Sergeyev, “From femtosecond to attosecond pulses,”Usp. Fiz. Nauk 169, 58–66 (1999) [ Phys. Usp. 42, 56–61 (1999)].
    [CrossRef]
  21. V. D. Taranukhin and N. Yu. Shubin, “High-order harmonic generation by atoms with strong bichromatic fields,” Quantum Electron. 29, 638–643 (1999).
    [CrossRef]
  22. V. D. Taranukhin and N. Yu. Shubin, “High-order harmonic generation by atoms with strong high-frequency and low-frequency pumping,” J. Opt. Soc. Am. B 17, 1509–1516 (2000).
    [CrossRef]
  23. M. Lax, W. H. Louisell, and W. B. Knight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
    [CrossRef]
  24. J. Peatross, S. Voronov, and I. Prokopovich, “Selective zoning of high harmonic emission using counter-propagating light,” Opt. Express 1, 114–125 (1997), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  25. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
    [CrossRef] [PubMed]
  26. V. M. Vainberg, V. D. Mur, V. S. Popov, and A. V. Sergeev, “Hydrogen atom in a strong static field,” Sov. Phys. JETP 66, 258–270 (1987).
  27. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1318 (1965).
  28. A. Scrinzi, M. Geissler, and T. Brabec, “Ionization above the Coulomb barrier,” Phys. Rev. Lett. 83, 706–709 (1998).
    [CrossRef]
  29. A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms with electric AC fields,” Sov. Phys. JETP 24, 207–217 (1967).
  30. P. B. Corkum, N. H. Burnett, and M. Yu. Ivanov, “Subfemtosecond pulses,” Opt. Lett. 19, 1870–1872 (1994).
    [CrossRef] [PubMed]
  31. K. C. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3440 (1993).
    [CrossRef] [PubMed]
  32. N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418–R3421 (1995).
    [CrossRef] [PubMed]
  33. A. Lohr, W. Becker, and M. Kleber, “High-harmonic generation affected by a static electric field,” Laser Phys. 7, 615–622 (1997).
  34. D. P. Crawford and H. R. Reiss, “Stabilization in relativistic photoionization with circularly polarized light,” Phys. Rev. A 50, 1844–1850 (1994).
    [CrossRef] [PubMed]

2000

1999

A. B. Kim, M. Yu. Ryabikin, and A. M. Sergeyev, “From femtosecond to attosecond pulses,”Usp. Fiz. Nauk 169, 58–66 (1999) [ Phys. Usp. 42, 56–61 (1999)].
[CrossRef]

V. D. Taranukhin and N. Yu. Shubin, “High-order harmonic generation by atoms with strong bichromatic fields,” Quantum Electron. 29, 638–643 (1999).
[CrossRef]

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

1998

A. Scrinzi, M. Geissler, and T. Brabec, “Ionization above the Coulomb barrier,” Phys. Rev. Lett. 83, 706–709 (1998).
[CrossRef]

1997

J. Peatross, S. Voronov, and I. Prokopovich, “Selective zoning of high harmonic emission using counter-propagating light,” Opt. Express 1, 114–125 (1997), http://www.opticsexpress.org.
[CrossRef] [PubMed]

A. Lohr, W. Becker, and M. Kleber, “High-harmonic generation affected by a static electric field,” Laser Phys. 7, 615–622 (1997).

Z. Chang, A. Rundquist, H.-W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

R. V. Kulyagin and V. D. Taranukhin, “Features of high-harmonic generation by atoms at superintense and ultrashort laser pumping,” Laser Phys. 7, 623–626 (1997).

1996

R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization: electron rescattering and generation of short-wavelength radiation,” Laser Phys. 6, 79–83 (1996).

R. V. Kulyagin and V. D. Taranukhin, “Generation of x-ray radiation by atoms in an ultra-high intensity laser field,” Quantum Electron. 26, 866–870 (1996).
[CrossRef]

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

1995

C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A 51, 1420–1430 (1995).
[CrossRef] [PubMed]

R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization of atoms and generation of short-wavelength radiation,” in Laser Optics ’95 and ICONO ’95: Superintense Laser Fields, A. A. Andreev and V. M. Gordienko, eds., Proc. SPIE 2770, 46–52 (1995).
[CrossRef]

N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418–R3421 (1995).
[CrossRef] [PubMed]

1994

D. P. Crawford and H. R. Reiss, “Stabilization in relativistic photoionization with circularly polarized light,” Phys. Rev. A 50, 1844–1850 (1994).
[CrossRef] [PubMed]

P. B. Corkum, N. H. Burnett, and M. Yu. Ivanov, “Subfemtosecond pulses,” Opt. Lett. 19, 1870–1872 (1994).
[CrossRef] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

K. Kondo, T. Tamida, Y. Nabekawa, and S. Watanabe, “High-order harmonic generation and ionization using ultrashort KrF and Ti:sapphire lasers,” Phys. Rev. A 49, 3881–3889 (1994).
[CrossRef] [PubMed]

1993

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

Sh. Kubodera, Yu. Nagata, Ya. Akiyama, K. Midorikawa, M. Obara, H. Tashiro, and K. Toyoda, “High order harmonics in laser-produced ions,” Phys. Rev. A 48, 4576–4582 (1993).
[CrossRef] [PubMed]

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
[CrossRef] [PubMed]

K. C. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3440 (1993).
[CrossRef] [PubMed]

1992

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, 3535–3558 (1992).
[CrossRef] [PubMed]

1991

N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, “Coherent soft x-ray generation by the harmonics of an ultra-high power Kr–F laser,” Phys. Rev. A 43, 1669–1672 (1991).
[CrossRef] [PubMed]

1987

V. M. Vainberg, V. D. Mur, V. S. Popov, and A. V. Sergeev, “Hydrogen atom in a strong static field,” Sov. Phys. JETP 66, 258–270 (1987).

1975

M. Lax, W. H. Louisell, and W. B. Knight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

1967

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms with electric AC fields,” Sov. Phys. JETP 24, 207–217 (1967).

1965

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1318 (1965).

Adachi, T.

N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, “Coherent soft x-ray generation by the harmonics of an ultra-high power Kr–F laser,” Phys. Rev. A 43, 1669–1672 (1991).
[CrossRef] [PubMed]

Agostini, P.

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Akiyama, Ya.

Sh. Kubodera, Yu. Nagata, Ya. Akiyama, K. Midorikawa, M. Obara, H. Tashiro, and K. Toyoda, “High order harmonics in laser-produced ions,” Phys. Rev. A 48, 4576–4582 (1993).
[CrossRef] [PubMed]

Balcou, Ph.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
[CrossRef] [PubMed]

Becker, W.

A. Lohr, W. Becker, and M. Kleber, “High-harmonic generation affected by a static electric field,” Laser Phys. 7, 615–622 (1997).

Blyth, W. J.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

Brabec, T.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

A. Scrinzi, M. Geissler, and T. Brabec, “Ionization above the Coulomb barrier,” Phys. Rev. Lett. 83, 706–709 (1998).
[CrossRef]

Breger, P.

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Budil, K. C.

K. C. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3440 (1993).
[CrossRef] [PubMed]

Burnett, K.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

Burnett, N. H.

N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418–R3421 (1995).
[CrossRef] [PubMed]

P. B. Corkum, N. H. Burnett, and M. Yu. Ivanov, “Subfemtosecond pulses,” Opt. Lett. 19, 1870–1872 (1994).
[CrossRef] [PubMed]

Chang, Z.

Z. Chang, A. Rundquist, H.-W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Cheng, Z.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

Constant, E.

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Corkum, P. B.

N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418–R3421 (1995).
[CrossRef] [PubMed]

P. B. Corkum, N. H. Burnett, and M. Yu. Ivanov, “Subfemtosecond pulses,” Opt. Lett. 19, 1870–1872 (1994).
[CrossRef] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

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

Crawford, D. P.

D. P. Crawford and H. R. Reiss, “Stabilization in relativistic photoionization with circularly polarized light,” Phys. Rev. A 50, 1844–1850 (1994).
[CrossRef] [PubMed]

Ditmire, T.

K. C. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3440 (1993).
[CrossRef] [PubMed]

Dorrer, Ch.

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Garzella, D.

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Geissler, M.

A. Scrinzi, M. Geissler, and T. Brabec, “Ionization above the Coulomb barrier,” Phys. Rev. Lett. 83, 706–709 (1998).
[CrossRef]

Hata, K.

N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, “Coherent soft x-ray generation by the harmonics of an ultra-high power Kr–F laser,” Phys. Rev. A 43, 1669–1672 (1991).
[CrossRef] [PubMed]

Hentschel, M.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

Ivanov, M. Yu.

P. B. Corkum, N. H. Burnett, and M. Yu. Ivanov, “Subfemtosecond pulses,” Opt. Lett. 19, 1870–1872 (1994).
[CrossRef] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Kálmán, P.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

Kan, C.

N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418–R3421 (1995).
[CrossRef] [PubMed]

Kapteyn, H. C.

Z. Chang, A. Rundquist, H.-W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Keitel, C. H.

C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A 51, 1420–1430 (1995).
[CrossRef] [PubMed]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1318 (1965).

Key, M. H.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

Kim, A. B.

A. B. Kim, M. Yu. Ryabikin, and A. M. Sergeyev, “From femtosecond to attosecond pulses,”Usp. Fiz. Nauk 169, 58–66 (1999) [ Phys. Usp. 42, 56–61 (1999)].
[CrossRef]

Kleber, M.

A. Lohr, W. Becker, and M. Kleber, “High-harmonic generation affected by a static electric field,” Laser Phys. 7, 615–622 (1997).

Knight, P. L.

C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A 51, 1420–1430 (1995).
[CrossRef] [PubMed]

Knight, W. B.

M. Lax, W. H. Louisell, and W. B. Knight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Kondo, K.

K. Kondo, T. Tamida, Y. Nabekawa, and S. Watanabe, “High-order harmonic generation and ionization using ultrashort KrF and Ti:sapphire lasers,” Phys. Rev. A 49, 3881–3889 (1994).
[CrossRef] [PubMed]

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, 3535–3558 (1992).
[CrossRef] [PubMed]

Krausz, F.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

Kubodera, Sh.

Sh. Kubodera, Yu. Nagata, Ya. Akiyama, K. Midorikawa, M. Obara, H. Tashiro, and K. Toyoda, “High order harmonics in laser-produced ions,” Phys. Rev. A 48, 4576–4582 (1993).
[CrossRef] [PubMed]

Kulander, K. C.

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, 3535–3558 (1992).
[CrossRef] [PubMed]

Kulyagin, R. V.

R. V. Kulyagin and V. D. Taranukhin, “Features of high-harmonic generation by atoms at superintense and ultrashort laser pumping,” Laser Phys. 7, 623–626 (1997).

R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization: electron rescattering and generation of short-wavelength radiation,” Laser Phys. 6, 79–83 (1996).

R. V. Kulyagin and V. D. Taranukhin, “Generation of x-ray radiation by atoms in an ultra-high intensity laser field,” Quantum Electron. 26, 866–870 (1996).
[CrossRef]

R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization of atoms and generation of short-wavelength radiation,” in Laser Optics ’95 and ICONO ’95: Superintense Laser Fields, A. A. Andreev and V. M. Gordienko, eds., Proc. SPIE 2770, 46–52 (1995).
[CrossRef]

L’Huillier, A.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

K. C. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3440 (1993).
[CrossRef] [PubMed]

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
[CrossRef] [PubMed]

Larsson, J.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
[CrossRef] [PubMed]

Lax, M.

M. Lax, W. H. Louisell, and W. B. Knight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Le Blanc, C.

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Lewenstein, M.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Lohr, A.

A. Lohr, W. Becker, and M. Kleber, “High-harmonic generation affected by a static electric field,” Laser Phys. 7, 615–622 (1997).

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. Knight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Mével, E.

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Midorikawa, K.

Sh. Kubodera, Yu. Nagata, Ya. Akiyama, K. Midorikawa, M. Obara, H. Tashiro, and K. Toyoda, “High order harmonics in laser-produced ions,” Phys. Rev. A 48, 4576–4582 (1993).
[CrossRef] [PubMed]

Mur, V. D.

V. M. Vainberg, V. D. Mur, V. S. Popov, and A. V. Sergeev, “Hydrogen atom in a strong static field,” Sov. Phys. JETP 66, 258–270 (1987).

Murnane, M. M.

Z. Chang, A. Rundquist, H.-W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Nabekawa, Y.

K. Kondo, T. Tamida, Y. Nabekawa, and S. Watanabe, “High-order harmonic generation and ionization using ultrashort KrF and Ti:sapphire lasers,” Phys. Rev. A 49, 3881–3889 (1994).
[CrossRef] [PubMed]

Nagata, Yu.

Sh. Kubodera, Yu. Nagata, Ya. Akiyama, K. Midorikawa, M. Obara, H. Tashiro, and K. Toyoda, “High order harmonics in laser-produced ions,” Phys. Rev. A 48, 4576–4582 (1993).
[CrossRef] [PubMed]

Nakai, M.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

Neely, D.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

Nodomi, R.

N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, “Coherent soft x-ray generation by the harmonics of an ultra-high power Kr–F laser,” Phys. Rev. A 43, 1669–1672 (1991).
[CrossRef] [PubMed]

Obara, M.

Sh. Kubodera, Yu. Nagata, Ya. Akiyama, K. Midorikawa, M. Obara, H. Tashiro, and K. Toyoda, “High order harmonics in laser-produced ions,” Phys. Rev. A 48, 4576–4582 (1993).
[CrossRef] [PubMed]

Offenberger, A. A.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

Peatross, J.

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms with electric AC fields,” Sov. Phys. JETP 24, 207–217 (1967).

Perry, M. D.

K. C. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3440 (1993).
[CrossRef] [PubMed]

Persson, A.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
[CrossRef] [PubMed]

Popov, V. S.

V. M. Vainberg, V. D. Mur, V. S. Popov, and A. V. Sergeev, “Hydrogen atom in a strong static field,” Sov. Phys. JETP 66, 258–270 (1987).

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms with electric AC fields,” Sov. Phys. JETP 24, 207–217 (1967).

Preston, S. G.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

Prokopovich, I.

Reiss, H. R.

D. P. Crawford and H. R. Reiss, “Stabilization in relativistic photoionization with circularly polarized light,” Phys. Rev. A 50, 1844–1850 (1994).
[CrossRef] [PubMed]

Rundquist, A.

Z. Chang, A. Rundquist, H.-W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Ryabikin, M. Yu.

A. B. Kim, M. Yu. Ryabikin, and A. M. Sergeyev, “From femtosecond to attosecond pulses,”Usp. Fiz. Nauk 169, 58–66 (1999) [ Phys. Usp. 42, 56–61 (1999)].
[CrossRef]

Salieres, P.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
[CrossRef] [PubMed]

K. C. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3440 (1993).
[CrossRef] [PubMed]

Salin, F.

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Sanpera, A.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

Sarukura, N.

N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, “Coherent soft x-ray generation by the harmonics of an ultra-high power Kr–F laser,” Phys. Rev. A 43, 1669–1672 (1991).
[CrossRef] [PubMed]

Schafer, K. J.

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, 3535–3558 (1992).
[CrossRef] [PubMed]

Schnürer, M.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

Scrinzi, A.

A. Scrinzi, M. Geissler, and T. Brabec, “Ionization above the Coulomb barrier,” Phys. Rev. Lett. 83, 706–709 (1998).
[CrossRef]

Sergeev, A. V.

V. M. Vainberg, V. D. Mur, V. S. Popov, and A. V. Sergeev, “Hydrogen atom in a strong static field,” Sov. Phys. JETP 66, 258–270 (1987).

Sergeyev, A. M.

A. B. Kim, M. Yu. Ryabikin, and A. M. Sergeyev, “From femtosecond to attosecond pulses,”Usp. Fiz. Nauk 169, 58–66 (1999) [ Phys. Usp. 42, 56–61 (1999)].
[CrossRef]

Shubin, N. Yu.

V. D. Taranukhin and N. Yu. Shubin, “High-order harmonic generation by atoms with strong high-frequency and low-frequency pumping,” J. Opt. Soc. Am. B 17, 1509–1516 (2000).
[CrossRef]

V. D. Taranukhin and N. Yu. Shubin, “High-order harmonic generation by atoms with strong bichromatic fields,” Quantum Electron. 29, 638–643 (1999).
[CrossRef]

R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization: electron rescattering and generation of short-wavelength radiation,” Laser Phys. 6, 79–83 (1996).

R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization of atoms and generation of short-wavelength radiation,” in Laser Optics ’95 and ICONO ’95: Superintense Laser Fields, A. A. Andreev and V. M. Gordienko, eds., Proc. SPIE 2770, 46–52 (1995).
[CrossRef]

Smith, C. G.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

Starczewski, T.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
[CrossRef] [PubMed]

Svanberg, S.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
[CrossRef] [PubMed]

Tamida, T.

K. Kondo, T. Tamida, Y. Nabekawa, and S. Watanabe, “High-order harmonic generation and ionization using ultrashort KrF and Ti:sapphire lasers,” Phys. Rev. A 49, 3881–3889 (1994).
[CrossRef] [PubMed]

Taranukhin, V. D.

V. D. Taranukhin and N. Yu. Shubin, “High-order harmonic generation by atoms with strong high-frequency and low-frequency pumping,” J. Opt. Soc. Am. B 17, 1509–1516 (2000).
[CrossRef]

V. D. Taranukhin, “Relativistic high-order harmonic generation,” Laser Phys. 10, 330–336 (2000).

V. D. Taranukhin and N. Yu. Shubin, “High-order harmonic generation by atoms with strong bichromatic fields,” Quantum Electron. 29, 638–643 (1999).
[CrossRef]

R. V. Kulyagin and V. D. Taranukhin, “Features of high-harmonic generation by atoms at superintense and ultrashort laser pumping,” Laser Phys. 7, 623–626 (1997).

R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization: electron rescattering and generation of short-wavelength radiation,” Laser Phys. 6, 79–83 (1996).

R. V. Kulyagin and V. D. Taranukhin, “Generation of x-ray radiation by atoms in an ultra-high intensity laser field,” Quantum Electron. 26, 866–870 (1996).
[CrossRef]

R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization of atoms and generation of short-wavelength radiation,” in Laser Optics ’95 and ICONO ’95: Superintense Laser Fields, A. A. Andreev and V. M. Gordienko, eds., Proc. SPIE 2770, 46–52 (1995).
[CrossRef]

Tashiro, H.

Sh. Kubodera, Yu. Nagata, Ya. Akiyama, K. Midorikawa, M. Obara, H. Tashiro, and K. Toyoda, “High order harmonics in laser-produced ions,” Phys. Rev. A 48, 4576–4582 (1993).
[CrossRef] [PubMed]

Tempea, G.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

Terent’ev, M. V.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms with electric AC fields,” Sov. Phys. JETP 24, 207–217 (1967).

Toyoda, K.

Sh. Kubodera, Yu. Nagata, Ya. Akiyama, K. Midorikawa, M. Obara, H. Tashiro, and K. Toyoda, “High order harmonics in laser-produced ions,” Phys. Rev. A 48, 4576–4582 (1993).
[CrossRef] [PubMed]

Vainberg, V. M.

V. M. Vainberg, V. D. Mur, V. S. Popov, and A. V. Sergeev, “Hydrogen atom in a strong static field,” Sov. Phys. JETP 66, 258–270 (1987).

Voronov, S.

Wahlstrom, C. G.

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
[CrossRef] [PubMed]

Wang, H.-W.

Z. Chang, A. Rundquist, H.-W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Wark, J. S.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

Watanabe, M.

N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, “Coherent soft x-ray generation by the harmonics of an ultra-high power Kr–F laser,” Phys. Rev. A 43, 1669–1672 (1991).
[CrossRef] [PubMed]

Watanabe, S.

K. Kondo, T. Tamida, Y. Nabekawa, and S. Watanabe, “High-order harmonic generation and ionization using ultrashort KrF and Ti:sapphire lasers,” Phys. Rev. A 49, 3881–3889 (1994).
[CrossRef] [PubMed]

N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, “Coherent soft x-ray generation by the harmonics of an ultra-high power Kr–F laser,” Phys. Rev. A 43, 1669–1672 (1991).
[CrossRef] [PubMed]

Zepf, M.

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Laser Phys.

A. Lohr, W. Becker, and M. Kleber, “High-harmonic generation affected by a static electric field,” Laser Phys. 7, 615–622 (1997).

R. V. Kulyagin and V. D. Taranukhin, “Features of high-harmonic generation by atoms at superintense and ultrashort laser pumping,” Laser Phys. 7, 623–626 (1997).

R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization: electron rescattering and generation of short-wavelength radiation,” Laser Phys. 6, 79–83 (1996).

V. D. Taranukhin, “Relativistic high-order harmonic generation,” Laser Phys. 10, 330–336 (2000).

Opt. Express

Opt. Lett.

Phys. Rev. A

K. C. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3440 (1993).
[CrossRef] [PubMed]

N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418–R3421 (1995).
[CrossRef] [PubMed]

D. P. Crawford and H. R. Reiss, “Stabilization in relativistic photoionization with circularly polarized light,” Phys. Rev. A 50, 1844–1850 (1994).
[CrossRef] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

M. Lax, W. H. Louisell, and W. B. Knight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, “Coherent soft x-ray generation by the harmonics of an ultra-high power Kr–F laser,” Phys. Rev. A 43, 1669–1672 (1991).
[CrossRef] [PubMed]

Sh. Kubodera, Yu. Nagata, Ya. Akiyama, K. Midorikawa, M. Obara, H. Tashiro, and K. Toyoda, “High order harmonics in laser-produced ions,” Phys. Rev. A 48, 4576–4582 (1993).
[CrossRef] [PubMed]

C. G. Wahlstrom, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salieres, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709–4720 (1993).
[CrossRef] [PubMed]

K. Kondo, T. Tamida, Y. Nabekawa, and S. Watanabe, “High-order harmonic generation and ionization using ultrashort KrF and Ti:sapphire lasers,” Phys. Rev. A 49, 3881–3889 (1994).
[CrossRef] [PubMed]

S. G. Preston, A. Sanpera, M. Zepf, W. J. Blyth, C. G. Smith, J. S. Wark, M. H. Key, K. Burnett, M. Nakai, D. Neely, and A. A. Offenberger, “High-order harmonics of a 248.6 nm KrF laser from helium and neon ions,” Phys. Rev. A 53, R31–R34 (1996).
[CrossRef]

C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A 51, 1420–1430 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett.

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Z. Chang, A. Rundquist, H.-W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (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, 3535–3558 (1992).
[CrossRef] [PubMed]

A. Scrinzi, M. Geissler, and T. Brabec, “Ionization above the Coulomb barrier,” Phys. Rev. Lett. 83, 706–709 (1998).
[CrossRef]

Phys. Usp.

A. B. Kim, M. Yu. Ryabikin, and A. M. Sergeyev, “From femtosecond to attosecond pulses,”Usp. Fiz. Nauk 169, 58–66 (1999) [ Phys. Usp. 42, 56–61 (1999)].
[CrossRef]

Proc. SPIE

R. V. Kulyagin, N. Yu. Shubin, and V. D. Taranukhin, “Tunnel above-threshold ionization of atoms and generation of short-wavelength radiation,” in Laser Optics ’95 and ICONO ’95: Superintense Laser Fields, A. A. Andreev and V. M. Gordienko, eds., Proc. SPIE 2770, 46–52 (1995).
[CrossRef]

Quantum Electron.

V. D. Taranukhin and N. Yu. Shubin, “High-order harmonic generation by atoms with strong bichromatic fields,” Quantum Electron. 29, 638–643 (1999).
[CrossRef]

R. V. Kulyagin and V. D. Taranukhin, “Generation of x-ray radiation by atoms in an ultra-high intensity laser field,” Quantum Electron. 26, 866–870 (1996).
[CrossRef]

Sov. Phys. JETP

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms with electric AC fields,” Sov. Phys. JETP 24, 207–217 (1967).

V. M. Vainberg, V. D. Mur, V. S. Popov, and A. V. Sergeev, “Hydrogen atom in a strong static field,” Sov. Phys. JETP 66, 258–270 (1987).

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1318 (1965).

Other

V. D. Taranukhin, “Generation of coherent x-ray radiation by atoms in superstrong laser fields: fundamental restrictions, optimizations and ultimate possibilities,” in Technical Digest, XVI International Conference on Coherent and Nonlinear Optics (URSS Publishers, Moscow, 1998), p. 118.

V. D. Taranukhin and N. Yu. Shubin, “Coherent x-ray generation by ions with standing wave pump radiation of relativistic intensity,” presented at the 8th Conference on Applications of High Field and Short Wavelength Sources, Potsdam, Germany (June 27–30, 1999).

V. D. Taranukhin and N. Yu. Shubin, “High-order harmonic generation by multielectron atoms with laser standing wave of relativistic intensity,” in Book of Abstracts, 8th Annual International Laser Physics Workshop (Research Institute for Solid State Physics and Optics, Budapest, Hungary, 1999), pp. 103–104.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Dependencies on ionization time t0 of the electron’s time evolution in the continuum τ=tr-t0 [calculated from Eq. (8); τ is normalized with respect to the pump’s optical period T]; the average velocity of the electron’s longitudinal motion vz¯=zr/τ in a traveling wave (normalized with respect to z0/T); the velocity of the spread in the photoelectron wave packet Vsp [normalized with respect to F01/2(2Ip)-1/4]; and photoelectron kinetic energy Er (normalized with respect to 3.17 Uq). Calculations were made in the framework of the semiclassical model with relativistic effects taken into account in the first approximation of parameter v/c.

Fig. 2
Fig. 2

Maximum generated frequency Ω versus pump intensity I at pump wavelength λ=308 nm. Circles, traveling wave; solid curve, standing wave, za=0 (the straight-line dependence corresponds to the nonrelativistic formula Ω0=Ip+3.17Uq); triangles, standing wave, za=0.025λ; squares, standing wave, za=0.05λ. Calculations were made in the framework of the semiclassical model for an Ar8+ ion (ionization potential Ip=15.5 atomic units).

Fig. 3
Fig. 3

Ratio ηt(topt) of cutoff harmonic intensities (with frequency 3.17Uq+Ip) of the traveling wave and the standing wave at za=0 as a function of pump intensity I. Solid curve, semiclassical analysis; triangles, model quantum-mechanical calculation.

Fig. 4
Fig. 4

High-order harmonic spectra (quantum-mechanical calculations) generated by an Ar8+ ion with a pump of intensity I=8×1017 W/cm2 and wavelength λ=308 nm: 1, traveling wave; 2, standing wave, za=0; 3, standing wave, za=0, with only the contribution of electrons with t0>topt taken into account.

Fig. 5
Fig. 5

High-order harmonic spectra (quantum-mechanical calculations) generated by an Ar8+ ion with pump intensity I=1018 W/cm2 and wavelength λ=308 nm: 1, traveling wave; 2, standing wave, za=0; 3, standing wave, za=0.0125λ; 4, standing wave, za=0.025λ; 5, standing wave, total spectrum (normalized with respect to a single atom) generated by atoms with za in the range 0<za<λ/4.

Equations (28)

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

i|Ψ˙(r, t)=[H0+H1(t)]|Ψ(r, t),
H1=ic A+12c2 A2,
F=-1c At,B=×A
D(t)=a*(t)0t dt0b[a(t0)]1|r|fr(r-rc, t, t0)×exp(-i t0t E(p0)dt+ip0r),
VspF1/2(2Ip)-1/4
dpdt=-F-1c(v×B)-Z rr3,
r(t0)=r0,v(t0)=v0,
x(t)=x0[cos(ωt)-cos(ωt0)+ω(t-t0)sin(ωt0)],
vx(t)=ωx0[sin(ωt0-sin(ωt)],
t0=1ω arctan 1-cos(ωτ)ωτ-sin(ωτ).
f(t0,t)=-sin(2ωt)/8+sin(ωt0)[cos(ωt)-cos(ωt0)]
+ω(t-t0)[sin2(ωt0)+cos(2ωt0)/4]
+sin(2ωt0)/8,
vz=ωz0[-cos(2ωt)/4-sin(ωt0)sin(ωt)+1/4
+sin2(ωt0)/2].
zr(t0)>Vspτ(t0),
dvzdt=F122ωc sin(4πz/λ)[sin2(ωt)-sin(ωt)sin(ωt0)],
z(t0)=za,vz(t0)=0.
z=z0g(t0, t)sin(4πza/λ)/2+za,
g(t0, t)={-1/2+ω(t-t0)[ω(t-t0)-sin(2ωt0)]/4+sin(ωt0)sin(ωt)+[cos(2ωt)+3 cos(2ωt0)]/8},
vz=ωz0 sin(4πza/λ)/2{ω(t-t0/2)-[sin(2ωt)+sin(2ωt0)]/4+sin(ωt0)cos(ωt)}.
sin|4πza/λ|<fr(t0)/gr(t0),
INexp{-2[zr(t0)/Vspτ(t0)]2}.
ηt(t0)exp[-2af2(t0)],
ηs(t0, za)exp[-ag2(t0)sin2(4πza/λ)],
ηs,t(t1)ηs,t(topt)α.
ξ=4λ 0l dza exp-12ag2(t0)sin2(2kza),
ξ=(2/π)1/2 erf(21/2πlag/λ)/ag,

Metrics