Abstract

We present what is to our knowledge the first three-dimensional model of a femtosecond pulse propagating in a Ti:sapphire laser crystal, which includes dispersion, self-focusing, and finite response time of the medium and does not assume the slowly varying envelope approximation. The combined action of material dispersion and phase modulation leads to a dramatic space–time focusing on the pulse. Dispersion prevents catastrophic self-focusing and self-steepening of the pulse, even though the peak power of the pulse is much greater than the critical power for self-focusing filamentation. Extrapolation of these results to shorter-pulse durations shows that this space–time focusing mechanism can operate even for pulses with durations close to the response time of the Kerr nonlinearity.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. G. Lariontsev, V. N. Serkin, Sov. J. Quantum Electron. 5, 796 (1976).
    [CrossRef]
  2. M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
    [CrossRef]
  3. D. E. Spence, P. N. Kean, W. Sibbett, Opt. Lett. 16, 42 (1991).
    [CrossRef] [PubMed]
  4. M. T. Asaki, C. P. Huang, D. Garvey, J. Zhou, H. C. Kapteyn, M. M. Murnane, Opt. Lett. 18, 977 (1993).
    [CrossRef] [PubMed]
  5. P. Curley, C. Spielmann, T. Brabec, F. Krausz, E. Wintner, A. Schmidt, Opt. Lett. 18, 54 (1993).
    [CrossRef] [PubMed]
  6. J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, I. Christov, Opt. Lett. 19, 1149 (1994).
    [PubMed]
  7. M. Piché, F. Salin, Opt. Lett. 18, 1041 (1993).
    [CrossRef] [PubMed]
  8. F. Salin, P. Grangier, P. Georges, A. Brun, Opt. Lett. 15, 1374 (1990).
    [CrossRef] [PubMed]
  9. J. Herrmann, J. Opt. Soc. Am. B 11, 498 (1994).
    [CrossRef]
  10. D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, J. G. Fujimoto, Opt. Lett. 17, 1 (1992).
    [CrossRef]
  11. F. Salin, J. Squire, M. Piché, Opt. Lett. 16, 1674 (1991).
    [CrossRef] [PubMed]
  12. H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
    [CrossRef]
  13. K. H. Lin, W. F. Hsieh, J. Opt. Soc. Am. B 11, 737 (1994).
    [CrossRef]
  14. R. W. Ziolkowski, J. B. Judkins, J. Opt. Soc. Am. B 10, 186 (1993).
    [CrossRef]
  15. D. Strickland, P. B. Corkum, J. Opt. Soc. Am. B 11, 492 (1994).
    [CrossRef]
  16. I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. P. Zhou, C.-P. Huang, Opt. Lett. 19, 1465 (1994).
    [CrossRef] [PubMed]
  17. F. D. Martini, C. H. Townes, T. K. Guftason, P. L. Kelly, Phys. Rev. 164, 312 (1967).
    [CrossRef]
  18. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), p. 44.
  19. I. P. Christov, Opt. Commun. 53, 364 (1985).
    [CrossRef]
  20. J. E. Rothenberg, Opt. Lett. 17, 1340 (1992).
    [CrossRef] [PubMed]
  21. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1991), p. 319.

1994 (5)

1993 (4)

1992 (3)

1991 (2)

1990 (1)

1987 (1)

M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
[CrossRef]

1985 (1)

I. P. Christov, Opt. Commun. 53, 364 (1985).
[CrossRef]

1976 (1)

E. G. Lariontsev, V. N. Serkin, Sov. J. Quantum Electron. 5, 796 (1976).
[CrossRef]

1967 (1)

F. D. Martini, C. H. Townes, T. K. Guftason, P. L. Kelly, Phys. Rev. 164, 312 (1967).
[CrossRef]

Acioli, L. H.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), p. 44.

Asaki, M. T.

Brabec, T.

Brun, A.

Christov, I.

Christov, I. P.

Corkum, P. B.

Curley, P.

Diodati, F. P.

M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
[CrossRef]

Fujimoto, J. G.

D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, J. G. Fujimoto, Opt. Lett. 17, 1 (1992).
[CrossRef]

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

Garvey, D.

Georges, P.

Grangier, P.

Guftason, T. K.

F. D. Martini, C. H. Townes, T. K. Guftason, P. L. Kelly, Phys. Rev. 164, 312 (1967).
[CrossRef]

Haus, H. A.

D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, J. G. Fujimoto, Opt. Lett. 17, 1 (1992).
[CrossRef]

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

Herrmann, J.

Hsieh, W. F.

Huang, C. P.

Huang, C.-P.

Huang, D.

Ippen, E. P.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

Judkins, J. B.

Kapteyn, H. C.

Kean, P. N.

Kelly, P. L.

F. D. Martini, C. H. Townes, T. K. Guftason, P. L. Kelly, Phys. Rev. 164, 312 (1967).
[CrossRef]

Krausz, F.

Lariontsev, E. G.

E. G. Lariontsev, V. N. Serkin, Sov. J. Quantum Electron. 5, 796 (1976).
[CrossRef]

Lin, K. H.

Marconi, M. C.

M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
[CrossRef]

Martinez, O. E.

M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
[CrossRef]

Martini, F. D.

F. D. Martini, C. H. Townes, T. K. Guftason, P. L. Kelly, Phys. Rev. 164, 312 (1967).
[CrossRef]

Murnane, M. M.

Piché, M.

Rothenberg, J. E.

Salin, F.

Schmidt, A.

Serkin, V. N.

E. G. Lariontsev, V. N. Serkin, Sov. J. Quantum Electron. 5, 796 (1976).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1991), p. 319.

Sibbett, W.

Spence, D. E.

Spielmann, C.

Squire, J.

Strickland, D.

Taft, G.

Townes, C. H.

F. D. Martini, C. H. Townes, T. K. Guftason, P. L. Kelly, Phys. Rev. 164, 312 (1967).
[CrossRef]

Ulman, M.

Wintner, E.

Zhou, J.

Zhou, J. P.

Ziolkowski, R. W.

IEEE J. Quantum Electron. (1)

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (2)

M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
[CrossRef]

I. P. Christov, Opt. Commun. 53, 364 (1985).
[CrossRef]

Opt. Lett. (10)

Phys. Rev. (1)

F. D. Martini, C. H. Townes, T. K. Guftason, P. L. Kelly, Phys. Rev. 164, 312 (1967).
[CrossRef]

Sov. J. Quantum Electron. (1)

E. G. Lariontsev, V. N. Serkin, Sov. J. Quantum Electron. 5, 796 (1976).
[CrossRef]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), p. 44.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1991), p. 319.

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 (3)

Fig. 1
Fig. 1

Topography of the space–time evolution of a weak femtosecond pulse in a Ti:sapphire crystal of length l = 2.3 mm: (a) first pass, the spatial interval between patterns is l/4 mm; (b) second pass, the spatial interval is l/3 mm. The vertical axis represents radial distance.

Fig. 2
Fig. 2

Space–time self-focusing of intense femtosecond pulse in Ti:sapphire crystal: (a) first pass, (b) second pass.

Fig. 3
Fig. 3

Dependence of the peak intensity of the pulse on the propagation distance within the crystal. Solid curve, 9 fs, optimal focus; short-dashed curve, 9 fs, shifted focus; long-dashed curve, 9 fs, τr = 5 fs; dotted curve, 5 fs, optimal focus, τr = 2 fs.

Equations (3)

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

E i + 2 ( r t , z , t ) = N i + 1 [ n 2 ( t ) , z ] E i ( k t , ω ) P ( k t , ω ) × exp [ i ( k t · r t - ω t ) ] d k t d ω ,
N i + 1 [ n 2 ( t ) , z ] = exp [ i k 0 n 2 ( t ) z - 2 c n 2 ( t ) t z ] ,
n 2 ( t ) = n 2 ( 0 ) τ r - t E i + 1 2 exp [ ( t - t ) / τ r ] d t ,

Metrics