Abstract

Numerical analysis of the self-focusing of femtosecond optical pulses reveals that the usually invoked slowly varying envelope approximation breaks down long before the temporal structure reaches the time scale of an optical cycle. This breakdown leads to a dramatic departure from the recently predicted symmetric development of the self-focusing pulse. By properly including the linear space–time focusing properties of short pulses, it is found that the trailing half of the self-focusing pulse is greatly enhanced and culminates in the formation of a trailing shock edge.

© 1992 Optical Society of America

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References

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  1. Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975);J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
    [CrossRef]
  2. V. N. Lugovi, A. M. Prokhorov, JETP Lett. 7, 117 (1968);M. M. T. Loy, Y. R. Shen, Phys. Rev. Lett. 22, 994 (1969).
    [CrossRef]
  3. J. H. Glownia, G. Arjavalingam, P. P. Sorokin, J. E. Rothenberg, Opt. Lett. 11, 79 (1986);J. H. Glownia, J. Misewich, P. P. Sorokin, J. Opt. Soc. Am. B 3, 1573 (1986).
    [CrossRef] [PubMed]
  4. P. B. Corkum, C. Rolland, T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1986);P. B. Corkum, C. Rolland, IEEE J. Quantum Electron. 25, 2634 (1989);D. Strickland, P. B. Corkum, Proc. Soc. Photo-Opt. Instrum. Eng. 1413, 54 (1991).
    [CrossRef] [PubMed]
  5. D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, J. G. Fujimoto, Opt. Lett. 17, 511 (1992).
    [CrossRef] [PubMed]
  6. P. Chernev, V. Petrov, Opt. Lett. 17, 172 (1992).
    [CrossRef] [PubMed]
  7. J. E. Rothenberg, Opt. Lett. 17, 583 (1992).
    [CrossRef] [PubMed]
  8. V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1976);S. N. Vlasov, L. V. Piskunova, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).
  9. Y. Silberberg, Opt. Lett. 15, 1282 (1990).
    [CrossRef] [PubMed]
  10. N. N. Akhmediev, V. I. Korneev, R. F. Nabiev, Opt. Lett. 17, 393 (1990).
    [CrossRef]
  11. Z. Bor, Opt. Lett. 14, 119 (1989).
    [CrossRef] [PubMed]
  12. F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
    [CrossRef]
  13. M. D. Feit, J. A. Fleck, J. Opt. Soc. Am. B 5, 633 (1988).
    [CrossRef]
  14. G. Yang, Y. R. Shen, Opt. Lett. 9, 510 (1984).
    [CrossRef] [PubMed]
  15. A. Dalgarno, A. E. Kingston, Proc. R. Soc. London Ser. A 259, 424 (1961).
  16. I. H. Malitson, J. Opt. Soc. Am. 55, 1205 (1965).
    [CrossRef]
  17. W. J. Tomlinson, R. H. Stolen, A. M. Johnson, Opt. Lett. 10, 457 (1985);J. E. Rothenberg, D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
    [CrossRef] [PubMed]

1992 (3)

1990 (2)

1989 (1)

1988 (1)

1986 (2)

P. B. Corkum, C. Rolland, T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1986);P. B. Corkum, C. Rolland, IEEE J. Quantum Electron. 25, 2634 (1989);D. Strickland, P. B. Corkum, Proc. Soc. Photo-Opt. Instrum. Eng. 1413, 54 (1991).
[CrossRef] [PubMed]

J. H. Glownia, G. Arjavalingam, P. P. Sorokin, J. E. Rothenberg, Opt. Lett. 11, 79 (1986);J. H. Glownia, J. Misewich, P. P. Sorokin, J. Opt. Soc. Am. B 3, 1573 (1986).
[CrossRef] [PubMed]

1985 (1)

1984 (1)

1976 (1)

V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1976);S. N. Vlasov, L. V. Piskunova, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

1975 (1)

Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975);J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

1968 (1)

V. N. Lugovi, A. M. Prokhorov, JETP Lett. 7, 117 (1968);M. M. T. Loy, Y. R. Shen, Phys. Rev. Lett. 22, 994 (1969).
[CrossRef]

1967 (1)

F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

1965 (1)

1961 (1)

A. Dalgarno, A. E. Kingston, Proc. R. Soc. London Ser. A 259, 424 (1961).

Acioli, L. H.

Akhmediev, N. N.

Arjavalingam, G.

Bor, Z.

Chernev, P.

Corkum, P. B.

P. B. Corkum, C. Rolland, T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1986);P. B. Corkum, C. Rolland, IEEE J. Quantum Electron. 25, 2634 (1989);D. Strickland, P. B. Corkum, Proc. Soc. Photo-Opt. Instrum. Eng. 1413, 54 (1991).
[CrossRef] [PubMed]

Dalgarno, A.

A. Dalgarno, A. E. Kingston, Proc. R. Soc. London Ser. A 259, 424 (1961).

DeMartini, F.

F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Feit, M. D.

Fleck, J. A.

Fujimoto, J. G.

Glownia, J. H.

Gustafson, T. K.

F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Haus, H. A.

Huang, D.

Johnson, A. M.

Kelley, P. L.

F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Kingston, A. E.

A. Dalgarno, A. E. Kingston, Proc. R. Soc. London Ser. A 259, 424 (1961).

Korneev, V. I.

Lugovi, V. N.

V. N. Lugovi, A. M. Prokhorov, JETP Lett. 7, 117 (1968);M. M. T. Loy, Y. R. Shen, Phys. Rev. Lett. 22, 994 (1969).
[CrossRef]

Malitson, I. H.

Nabiev, R. F.

Petrov, V.

Prokhorov, A. M.

V. N. Lugovi, A. M. Prokhorov, JETP Lett. 7, 117 (1968);M. M. T. Loy, Y. R. Shen, Phys. Rev. Lett. 22, 994 (1969).
[CrossRef]

Rolland, C.

P. B. Corkum, C. Rolland, T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1986);P. B. Corkum, C. Rolland, IEEE J. Quantum Electron. 25, 2634 (1989);D. Strickland, P. B. Corkum, Proc. Soc. Photo-Opt. Instrum. Eng. 1413, 54 (1991).
[CrossRef] [PubMed]

Rothenberg, J. E.

Shen, Y. R.

G. Yang, Y. R. Shen, Opt. Lett. 9, 510 (1984).
[CrossRef] [PubMed]

Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975);J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Silberberg, Y.

Sorokin, P. P.

Srinivasan-Rao, T.

P. B. Corkum, C. Rolland, T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1986);P. B. Corkum, C. Rolland, IEEE J. Quantum Electron. 25, 2634 (1989);D. Strickland, P. B. Corkum, Proc. Soc. Photo-Opt. Instrum. Eng. 1413, 54 (1991).
[CrossRef] [PubMed]

Stolen, R. H.

Synakh, V. S.

V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1976);S. N. Vlasov, L. V. Piskunova, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

Tomlinson, W. J.

Townes, C. H.

F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Ulman, M.

Yang, G.

Zakharov, V. E.

V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1976);S. N. Vlasov, L. V. Piskunova, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

J. Opt. Soc. Am. (1)

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

JETP Lett. (1)

V. N. Lugovi, A. M. Prokhorov, JETP Lett. 7, 117 (1968);M. M. T. Loy, Y. R. Shen, Phys. Rev. Lett. 22, 994 (1969).
[CrossRef]

Opt. Lett. (9)

Phys. Rev. (1)

F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Phys. Rev. Lett. (1)

P. B. Corkum, C. Rolland, T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1986);P. B. Corkum, C. Rolland, IEEE J. Quantum Electron. 25, 2634 (1989);D. Strickland, P. B. Corkum, Proc. Soc. Photo-Opt. Instrum. Eng. 1413, 54 (1991).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A (1)

A. Dalgarno, A. E. Kingston, Proc. R. Soc. London Ser. A 259, 424 (1961).

Prog. Quantum Electron. (1)

Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975);J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1976);S. N. Vlasov, L. V. Piskunova, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

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Figures (3)

Fig. 1
Fig. 1

Intensity on axis versus time of a self-focusing pulse in a normally dispersive medium at the propagation distances indicated, calculated with the use of the NLSE [Eq. (1)]. The peak intensities relative to the input are (a) 30, (b) 62, (c) 97, (d) 150, (e) 320, and (f) 600.

Fig. 2
Fig. 2

Same as in Fig. 1, except calculated in a non-SVEA by including space–time focusing based on Eq. (3). The peak intensities relative to the input are (a) 29, (b) 61, (c) 140, (d) 270, (e) 540, and (f) 990.

Fig. 3
Fig. 3

Intensity on axis versus time in an anomalously dispersive medium calculated by including space–time focusing in a non-SVEA based on Eq. (3) (solid curves), at the propagation distances indicated, and by the NLSE [Eq. (1), dashed curves] for which the propagation distances are less by 1.0 mm. The respective peak intensities relative to the input for the non-SVEA and the NLSE calculations are (a) 9, 7; (b) 20, 15; (c) 55, 35; (d) 150, 80; (e) 330, 170; and (f) 640, 740.

Equations (5)

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E z + i [ k ( 2 ) / 2 ] 2 E t 2 i 2 k 0 ( 2 E x 2 + 2 E y 2 ) = i n 2 ( ω 0 / c ) | E | 2 E ,
E ˜ z = i [ k ( 2 ) Ω 2 2 k x 2 + k y 2 2 k 0 ] E ˜ i γ E ˜ ,
k z = [ k ( Ω ) 2 k x 2 k y 2 ] 1 / 2 [ k ( Ω ) 2 k T 2 ] 1 / 2 ,
k z k 0 + Ω / v g + k ( 2 ) Ω 2 / 2 k T 2 / 2 k ( Ω ) .
k z k 0 Ω / v g k ( 2 ) Ω 2 2 k T 2 2 k 0 ( 1 Ω k 0 v g ) .

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