Abstract

We report experiments on ultrashort pulses that maintain their strong lateral and longitudinal localization in a bulk linear highly dispersive medium. The diameter of the central peak and the temporal width of the field autocorrelation function of the pulses were 20 µm and 210  fs, respectively, and the spatiotemporal structure was preserved in the course of 7-cm propagation in the sample. The pulses were obtained with a computer hologram designed for generating the Bessel beam and can be applied in femtosecond laser optics.

© 1997 Optical Society of America

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Corrections

Heiki Sõnajalg, Margus Rätsep, and Peeter Saari, "Demonstration of the Bessel-X pulse propagating with strong lateral and longitudinal localization in a dispersive medium: errata," Opt. Lett. 22, 745-745 (1997)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-22-10-745

References

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984).
  2. J. N. Brittingham, J. Appl. Phys. 54, 1179 (1983).
    [Crossref]
  3. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [Crossref] [PubMed]
  4. I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, J. Math. Phys. 30, 1254 (1989).
    [Crossref]
  5. P. L. Overfelt, Phys. Rev. A 44, 3941 (1991).
    [Crossref] [PubMed]
  6. J. Lu and J. F. Greenleaf, IEEE Trans. Ultrasonics Ferroelectron. Freq. Control 39, 19 (1992).
    [Crossref]
  7. P. Saari, in Ultrafast Processes in Spectroscopy, O. Svelto, S. De Silvestri, and G. Denardo, eds. (Plenum, New York, 1996), pp. 151–156.
    [Crossref]
  8. J. Durnin, J. J. Miceli, and J. H. Eberly, Opt. Lett. 13, 79 (1988).
    [Crossref]
  9. J. Rosen, B. Salik, A. Yariv, and H.-K. Liu, Opt. Lett. 20, 423 (1995).
    [Crossref] [PubMed]
  10. D. Eliyahu, R. A. Salvatore, J. Rosen, A. Yariv, and J.-J. Drolet, Opt. Lett. 20, 1412 (1995).
    [Crossref] [PubMed]
  11. H. Sõnajalg and P. Saari, Opt. Lett. 21, 1162 (1996).
    [Crossref]
  12. R. P. MacDonald, J. Chrostowski, S. A. Boothroyd, and B. A. Syrett, Appl. Opt. 32, 6470 (1993).
    [Crossref] [PubMed]
  13. V. P. Koronkevich, I. A. Mikhaltsova, E. G. Churin, and Yu. I. Yurlov, Appl. Opt. 34, 5761 (1995).
    [Crossref] [PubMed]
  14. J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), Chap.  3.
  15. A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
    [Crossref]
  16. The result is similar to the one given by Eqs.  (6)–(8) of Ref.  11, where one should take M=1 and replace the term k-k0/kf in Eq.  (8) with 1/f+δ-k0/kf.
  17. A. T. Friberg, J. Opt. Soc. Am. A 13, 743 (1996).
    [Crossref]

1996 (2)

1995 (3)

1993 (1)

1992 (1)

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrasonics Ferroelectron. Freq. Control 39, 19 (1992).
[Crossref]

1991 (1)

P. L. Overfelt, Phys. Rev. A 44, 3941 (1991).
[Crossref] [PubMed]

1989 (2)

I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, J. Math. Phys. 30, 1254 (1989).
[Crossref]

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[Crossref]

1988 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

1983 (1)

J. N. Brittingham, J. Appl. Phys. 54, 1179 (1983).
[Crossref]

Besieris, I. M.

I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, J. Math. Phys. 30, 1254 (1989).
[Crossref]

Boothroyd, S. A.

Brittingham, J. N.

J. N. Brittingham, J. Appl. Phys. 54, 1179 (1983).
[Crossref]

Chrostowski, J.

Churin, E. G.

Débarre, A.

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[Crossref]

Drolet, J.-J.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Opt. Lett. 13, 79 (1988).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Opt. Lett. 13, 79 (1988).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

Eliyahu, D.

Friberg, A. T.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), Chap.  3.

Greenleaf, J. F.

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrasonics Ferroelectron. Freq. Control 39, 19 (1992).
[Crossref]

Keller, J.-C.

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[Crossref]

Koronkevich, V. P.

Le Gouët, J.-L.

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[Crossref]

Liu, H.-K.

Lu, J.

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrasonics Ferroelectron. Freq. Control 39, 19 (1992).
[Crossref]

MacDonald, R. P.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Opt. Lett. 13, 79 (1988).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

Mikhaltsova, I. A.

Overfelt, P. L.

P. L. Overfelt, Phys. Rev. A 44, 3941 (1991).
[Crossref] [PubMed]

Richard, A.

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[Crossref]

Rosen, J.

Saari, P.

H. Sõnajalg and P. Saari, Opt. Lett. 21, 1162 (1996).
[Crossref]

P. Saari, in Ultrafast Processes in Spectroscopy, O. Svelto, S. De Silvestri, and G. Denardo, eds. (Plenum, New York, 1996), pp. 151–156.
[Crossref]

Salik, B.

Salvatore, R. A.

Shaarawi, A. M.

I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, J. Math. Phys. 30, 1254 (1989).
[Crossref]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984).

Sõnajalg, H.

Syrett, B. A.

Tchénio, P.

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[Crossref]

Yariv, A.

Yurlov, Yu. I.

Ziolkowski, R. W.

I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, J. Math. Phys. 30, 1254 (1989).
[Crossref]

Appl. Opt. (2)

IEEE Trans. Ultrasonics Ferroelectron. Freq. Control (1)

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrasonics Ferroelectron. Freq. Control 39, 19 (1992).
[Crossref]

J. Appl. Phys. (1)

J. N. Brittingham, J. Appl. Phys. 54, 1179 (1983).
[Crossref]

J. Math. Phys. (1)

I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, J. Math. Phys. 30, 1254 (1989).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[Crossref]

Opt. Lett. (4)

Phys. Rev. A (1)

P. L. Overfelt, Phys. Rev. A 44, 3941 (1991).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

Other (4)

The result is similar to the one given by Eqs.  (6)–(8) of Ref.  11, where one should take M=1 and replace the term k-k0/kf in Eq.  (8) with 1/f+δ-k0/kf.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984).

P. Saari, in Ultrafast Processes in Spectroscopy, O. Svelto, S. De Silvestri, and G. Denardo, eds. (Plenum, New York, 1996), pp. 151–156.
[Crossref]

J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), Chap.  3.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for generating the Bessel-X pulse and recording the cross-correlation function of the on-axis field at the front and the rear plane of the optical sample. The Bessel-X pulse propagates in the gray region. BS’s, beam splitters; L’s, lenses.

Fig. 2
Fig. 2

Cross-correlation function of the on-axis field at the front and the rear planes of the sample recorded with two different positions of the point source, δ=3 cm (squares) and δ=12 cm (diamonds), and fitted with Gaussians of 254 and 208  fs FWHM, respectively.

Fig. 3
Fig. 3

(a) Calculated (solid curve) and measured (squares) width of the cross-correlation function, τc, at different positions of the point source. Experimental data are fitted with a polynomial (dashed curve). For comparison the width of the autocorrelation function (210  fs FWHM) is shown (dotted line). (b) Calculated width of the cross-correlation function of the Bessel-X pulse (solid line) and a plane-wave pulse (dashed curve), at the different propagation depths z in the glassy sample. The optimum configuration δ=12.7 cm, l=60 cm is assumed for the Bessel-X pulse.

Equations (4)

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Nρ=1λ0ρf2+ρ2+1λ0 sin Θ.
kθv=2πNρ-kρ/f+δ,
θv=Θ1-δflf+δ+ωω0-1lf+δ+1,
Θ=2n0n13lf+δ2+4lf+δ+1+2δflf+δlf+δ+11/21-δflf+δ2·

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