Abstract

We have experimentally investigated the use of diffraction-free beams to generate low-order harmonics in gas jets. Bessel–Gauss beams have been generated from a Ti:sapphire, 100-fs laser by use of annular apertures and then by focusing of the ring-type–produced radiation. The conversion efficiencies for these beams for the third- and fifth-order harmonic generation in xenon have been measured and compared with those of pure Gaussian beams of the same energy content. We have thus found that, by matching the gas medium length to the range of the Bessel–Gauss beams, conversion efficiencies considerably higher than those of Gaussian beams can be obtained. The experimental results have also been discussed and interpreted in terms of a simple numerical model that emphasizes the effects of phase matching in the two different geometries.

© 2000 Optical Society of America

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  1. C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
    [CrossRef]
  2. A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
    [CrossRef] [PubMed]
  3. A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculation of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
    [CrossRef]
  4. P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74, 3776–3779 (1995).
    [CrossRef] [PubMed]
  5. C. Altucci, T. Starczewski, E. Mevel, C.-G. Wahlström, B. Carré, and A. L’Huillier, J. Opt. Soc. Am. B 13, 148–156 (1996).
    [CrossRef]
  6. C. Delfin, C. de Lisio, C. Altucci, F. De Filippo, M. B. Gaarde, A. L’Huillier, and C.-G. Wahlström, “Influence of the medium length on high-order harmonic generation,” J. Phys. B: At. Mol. Opt. Physics (to be published).
  7. J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984).
  8. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  9. J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  10. V. E. Peet and R. V. Tsubin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
    [CrossRef]
  11. B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
    [CrossRef] [PubMed]
  12. S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995).
    [CrossRef] [PubMed]
  13. S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54, 2314–2325 (1996).
    [CrossRef] [PubMed]
  14. T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401–1404 (1993).
    [CrossRef] [PubMed]
  15. V. E. Peet, “Resonantly enhanced multiphoton ionization of xenon in Bessel beams,” Phys. Rev. A 53, 3679–3682 (1996).
    [CrossRef] [PubMed]
  16. C. F. R. Caron and R. M. Potvliege, “Phase matching and harmonic generation in Bessel–Gauss beams,” J. Opt. Soc. Am. B 15, 1096–1106 (1998).
    [CrossRef]
  17. C. F. R. Caron and R. M. Potvliege, “Optimum conical angle of a Bessel-Gauss beam for low-order harmonic generation in gases,” J. Opt. Soc. Am. B 16, 1377–1384 (1999).
    [CrossRef]
  18. F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
    [CrossRef]
  19. R. M. Herman and T. A. Wiggins, “High-efficiency diffractionless beams of constant size and intensity,” Appl. Opt. 33, 7297–7306 (1994).
    [CrossRef] [PubMed]
  20. R. M. Herman and T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [CrossRef]
  21. S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212–2215 (1989).
    [CrossRef] [PubMed]
  22. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
    [CrossRef]
  23. J. Zhou, J. Peatross, M. M. Murnane, and H. C. Kapteyn, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
    [CrossRef] [PubMed]
  24. A. Collins Stuart, Jr., “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. A 60, 1168–1177 (1970).
    [CrossRef]
  25. M. Santarsiero, “Propagation of generalized Bessel–Gauss beams through ABCD optical systems,” Opt. Commun. 132, 1–7 (1996).
    [CrossRef]
  26. A. L’Huillier, L.-A. Lompré, G. Mainfray, and C. Manus, “High-order harmonic generation in rare gases,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, New York, 1992), p. 139.
  27. C. Altucci, C. Beneduce, R. Bruzzese, C. De Lisio, G. S. Sorrentino, T. Starczewski, and F. Vigilante, “Characterization of pulsed gas sources for intense laser field–atom interaction experiments,” J. Phys. D 29, 68–75 (1996).
    [CrossRef]
  28. G. Naletto, L. Placentino, and G. Tondello, “Fluorescence of metachrome in the far end vacuum ultraviolet spectral region,” in X-Ray and Ultraviolet Sensors and Applications, R. B. Hoover and M. B. Williams, eds., Proc. SPIE 2519, 31–34 (1995).
  29. C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

1999 (1)

1998 (2)

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

C. F. R. Caron and R. M. Potvliege, “Phase matching and harmonic generation in Bessel–Gauss beams,” J. Opt. Soc. Am. B 15, 1096–1106 (1998).
[CrossRef]

1997 (3)

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

V. E. Peet and R. V. Tsubin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[CrossRef]

1996 (6)

C. Altucci, T. Starczewski, E. Mevel, C.-G. Wahlström, B. Carré, and A. L’Huillier, J. Opt. Soc. Am. B 13, 148–156 (1996).
[CrossRef]

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54, 2314–2325 (1996).
[CrossRef] [PubMed]

V. E. Peet, “Resonantly enhanced multiphoton ionization of xenon in Bessel beams,” Phys. Rev. A 53, 3679–3682 (1996).
[CrossRef] [PubMed]

J. Zhou, J. Peatross, M. M. Murnane, and H. C. Kapteyn, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

M. Santarsiero, “Propagation of generalized Bessel–Gauss beams through ABCD optical systems,” Opt. Commun. 132, 1–7 (1996).
[CrossRef]

C. Altucci, C. Beneduce, R. Bruzzese, C. De Lisio, G. S. Sorrentino, T. Starczewski, and F. Vigilante, “Characterization of pulsed gas sources for intense laser field–atom interaction experiments,” J. Phys. D 29, 68–75 (1996).
[CrossRef]

1995 (2)

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995).
[CrossRef] [PubMed]

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

1994 (1)

1993 (3)

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401–1404 (1993).
[CrossRef] [PubMed]

B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
[CrossRef] [PubMed]

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

1992 (1)

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculation of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[CrossRef]

1991 (1)

1989 (1)

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212–2215 (1989).
[CrossRef] [PubMed]

1987 (3)

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

1970 (1)

A. Collins Stuart, Jr., “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. A 60, 1168–1177 (1970).
[CrossRef]

Altucci, C.

C. Altucci, C. Beneduce, R. Bruzzese, C. De Lisio, G. S. Sorrentino, T. Starczewski, and F. Vigilante, “Characterization of pulsed gas sources for intense laser field–atom interaction experiments,” J. Phys. D 29, 68–75 (1996).
[CrossRef]

C. Altucci, T. Starczewski, E. Mevel, C.-G. Wahlström, B. Carré, and A. L’Huillier, J. Opt. Soc. Am. B 13, 148–156 (1996).
[CrossRef]

Augst, S.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212–2215 (1989).
[CrossRef] [PubMed]

Backus, S.

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Balcou, P.

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculation of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[CrossRef]

Beneduce, C.

C. Altucci, C. Beneduce, R. Bruzzese, C. De Lisio, G. S. Sorrentino, T. Starczewski, and F. Vigilante, “Characterization of pulsed gas sources for intense laser field–atom interaction experiments,” J. Phys. D 29, 68–75 (1996).
[CrossRef]

Boyd, R. W.

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54, 2314–2325 (1996).
[CrossRef] [PubMed]

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995).
[CrossRef] [PubMed]

Bruzzese, R.

C. Altucci, C. Beneduce, R. Bruzzese, C. De Lisio, G. S. Sorrentino, T. Starczewski, and F. Vigilante, “Characterization of pulsed gas sources for intense laser field–atom interaction experiments,” J. Phys. D 29, 68–75 (1996).
[CrossRef]

Burnett, N. H.

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Candel, S.

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculation of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[CrossRef]

Caron, C. F. R.

Carré, B.

Chang, Z.

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Chin, S. L.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212–2215 (1989).
[CrossRef] [PubMed]

Christov, I. P.

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

De Lisio, C.

C. Altucci, C. Beneduce, R. Bruzzese, C. De Lisio, G. S. Sorrentino, T. Starczewski, and F. Vigilante, “Characterization of pulsed gas sources for intense laser field–atom interaction experiments,” J. Phys. D 29, 68–75 (1996).
[CrossRef]

Durfee III, C. G.

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Durnin, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

Eberly, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212–2215 (1989).
[CrossRef] [PubMed]

Glushko, B.

B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
[CrossRef] [PubMed]

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Herman, R. M.

Herminghaus, S.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401–1404 (1993).
[CrossRef] [PubMed]

Herne, C.

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Huang, H.

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54, 2314–2325 (1996).
[CrossRef] [PubMed]

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995).
[CrossRef] [PubMed]

Kan, C.

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Kapteyn, H. C.

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

J. Zhou, J. Peatross, M. M. Murnane, and H. C. Kapteyn, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Koppitsch, R.

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Krausz, F.

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Kryzhanovsky, B.

B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
[CrossRef] [PubMed]

Kulander, K. C.

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculation of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[CrossRef]

L’Huillier, A.

C. Altucci, T. Starczewski, E. Mevel, C.-G. Wahlström, B. Carré, and A. L’Huillier, J. Opt. Soc. Am. B 13, 148–156 (1996).
[CrossRef]

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

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculation of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[CrossRef]

Larsson, J.

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

Lewenstein, M.

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

Lezner, M.

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Mevel, E.

Meyerhofer, D. D.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212–2215 (1989).
[CrossRef] [PubMed]

Miceli, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Murnane, M. M.

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

J. Zhou, J. Peatross, M. M. Murnane, and H. C. Kapteyn, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Peatross, J.

J. Zhou, J. Peatross, M. M. Murnane, and H. C. Kapteyn, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Peet, V. E.

V. E. Peet and R. V. Tsubin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[CrossRef]

V. E. Peet, “Resonantly enhanced multiphoton ionization of xenon in Bessel beams,” Phys. Rev. A 53, 3679–3682 (1996).
[CrossRef] [PubMed]

Persson, A.

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

Potvliege, R. M.

Rundquist, A.

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Salières, P.

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

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

Santarsiero, M.

M. Santarsiero, “Propagation of generalized Bessel–Gauss beams through ABCD optical systems,” Opt. Commun. 132, 1–7 (1996).
[CrossRef]

Sarkisyan, D.

B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
[CrossRef] [PubMed]

Sartania, S.

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Schafer, K. J.

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculation of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[CrossRef]

Schnürer, M.

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Sorrentino, G. S.

C. Altucci, C. Beneduce, R. Bruzzese, C. De Lisio, G. S. Sorrentino, T. Starczewski, and F. Vigilante, “Characterization of pulsed gas sources for intense laser field–atom interaction experiments,” J. Phys. D 29, 68–75 (1996).
[CrossRef]

Spielmann, C.

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Starczewski, T.

C. Altucci, C. Beneduce, R. Bruzzese, C. De Lisio, G. S. Sorrentino, T. Starczewski, and F. Vigilante, “Characterization of pulsed gas sources for intense laser field–atom interaction experiments,” J. Phys. D 29, 68–75 (1996).
[CrossRef]

C. Altucci, T. Starczewski, E. Mevel, C.-G. Wahlström, B. Carré, and A. L’Huillier, J. Opt. Soc. Am. B 13, 148–156 (1996).
[CrossRef]

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

Strickland, D.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212–2215 (1989).
[CrossRef] [PubMed]

Stuart Jr., A. Collins

A. Collins Stuart, Jr., “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. A 60, 1168–1177 (1970).
[CrossRef]

Svanberg, S.

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

Tewari, S. P.

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54, 2314–2325 (1996).
[CrossRef] [PubMed]

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995).
[CrossRef] [PubMed]

Tsubin, R. V.

V. E. Peet and R. V. Tsubin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[CrossRef]

Vigilante, F.

C. Altucci, C. Beneduce, R. Bruzzese, C. De Lisio, G. S. Sorrentino, T. Starczewski, and F. Vigilante, “Characterization of pulsed gas sources for intense laser field–atom interaction experiments,” J. Phys. D 29, 68–75 (1996).
[CrossRef]

Wahlström, C.-G.

C. Altucci, T. Starczewski, E. Mevel, C.-G. Wahlström, B. Carré, and A. L’Huillier, J. Opt. Soc. Am. B 13, 148–156 (1996).
[CrossRef]

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

Wiggins, T. A.

Wobrauschek, P.

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Wulle, T.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401–1404 (1993).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, J. Peatross, M. M. Murnane, and H. C. Kapteyn, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (3)

J. Phys. D (1)

C. Altucci, C. Beneduce, R. Bruzzese, C. De Lisio, G. S. Sorrentino, T. Starczewski, and F. Vigilante, “Characterization of pulsed gas sources for intense laser field–atom interaction experiments,” J. Phys. D 29, 68–75 (1996).
[CrossRef]

Opt. Commun. (2)

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

M. Santarsiero, “Propagation of generalized Bessel–Gauss beams through ABCD optical systems,” Opt. Commun. 132, 1–7 (1996).
[CrossRef]

Phys. Rev. A (6)

V. E. Peet, “Resonantly enhanced multiphoton ionization of xenon in Bessel beams,” Phys. Rev. A 53, 3679–3682 (1996).
[CrossRef] [PubMed]

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, P. 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]

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculation of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[CrossRef]

V. E. Peet and R. V. Tsubin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[CrossRef]

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995).
[CrossRef] [PubMed]

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54, 2314–2325 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (7)

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401–1404 (1993).
[CrossRef] [PubMed]

B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
[CrossRef] [PubMed]

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212–2215 (1989).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

J. Zhou, J. Peatross, M. M. Murnane, and H. C. Kapteyn, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

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

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Science (2)

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lezner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Other (4)

C. Delfin, C. de Lisio, C. Altucci, F. De Filippo, M. B. Gaarde, A. L’Huillier, and C.-G. Wahlström, “Influence of the medium length on high-order harmonic generation,” J. Phys. B: At. Mol. Opt. Physics (to be published).

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984).

G. Naletto, L. Placentino, and G. Tondello, “Fluorescence of metachrome in the far end vacuum ultraviolet spectral region,” in X-Ray and Ultraviolet Sensors and Applications, R. B. Hoover and M. B. Williams, eds., Proc. SPIE 2519, 31–34 (1995).

A. L’Huillier, L.-A. Lompré, G. Mainfray, and C. Manus, “High-order harmonic generation in rare gases,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, New York, 1992), p. 139.

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Figures (8)

Fig. 1
Fig. 1

Calculated transverse intensity profile of the electric field diffracted by an annular slit and focused successively by a 200-mm focal-length lens, for z=190 mm (dotted curve), z=200 mm (dashed curve), z=210 mm (solid curve), and for λ=800 nm. The inner and outer radii of the slit are 1 and 1.5 mm, respectively, the incoming beam diameter being 6 mm.

Fig. 2
Fig. 2

(a) Measured intensity distribution of a Bessel–Gauss beam at the focal plane. The plot refers to a He–Ne laser beam apertured by an annular slit with an inner radius of 1.5 mm and outer radius of 2 mm and then focused by a 200-mm focal-length lens. (b) One-dimensional representation of the intensity distribution along the horizontal diameter (x coordinate) at three different planes, for z=190 mm (dotted curve), z=200 mm (dashed curve), and z=210 mm (solid curve).

Fig. 3
Fig. 3

(a) Schematic layout of experimental setup. (b) Cylindrical cell used for varying the gas medium length L.

Fig. 4
Fig. 4

Normalized power spectra of (a) third and (b) fifth harmonics in xenon, obtained with a Bessel–Gauss beam of 0.16 mJ (circles) and with a pure Gaussian beam (squares) having equal energy. L, corresponding in this case to the gas jet length, is ∼0.7 mm.

Fig. 5
Fig. 5

Third-harmonic yield versus the delay time, t, between the laser pulse and the gas valve opening time, for L=10 mm in xenon. The gas inlet valve repetition rate and opening time are 10 Hz and 500 µs, respectively. The valve was operated with a backing pressure of 3 bars.

Fig. 6
Fig. 6

Ratio R between the third-harmonic intensity produced in xenon by a Bessel–Gauss beam and that produced by a Gaussian beam with the same energy content plotted versus the laser-pulse average energy at a valve backing pressure of 3 bars for (a) L=16 mm and (b) L=8 mm.

Fig. 7
Fig. 7

Ratio R versus the medium length L for the third harmonic in xenon at three different laser-pulse average energies: 160 µJ (squares), 100 µJ (circles), and 80 µJ (triangles).

Fig. 8
Fig. 8

Calculated ratio R=IH3BG/IH3G versus L/ρ for ρ=11 mm and b=2 mm in xenon, corresponding to the diffraction limit of our experimental case.

Equations (8)

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Vi(r)=E0 exp-r2wi2,
Vout(r, z)=E0 expikz+kr22z-iλz×r0r1dρρJ0kρrzexp[-ρ2F(z)],
F(z)=1wi2+ik2z1-zf.
Vout(r, z=f)
E0 expikf+kr22f-iλf×exp[-(r0+δ/2)2]f2krkr0(r/f)k(r0+δ/2)r/fdζζJ0(ζ)=E0 expikf+kr22f-(r0+δ/2)2-i2πr×(r0+δ)J1kr(r0+δ)f-r0J1krr0f,
ddz[zp+1Jp+1(z)]=zp+1Jp(z).
R=IHnBGIHnG,n=3,5,
Eq(r; L)N0Dq4π|r|q2k2-L/2L/2 exp[iqk(|r|-z)]Eq(z)dz,

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