Abstract

Under the combined effect of diffraction, anomalous dispersion, and nonlinear refraction, an optical pulse can collapse simultaneously in time and space. Such a collapse could yield short pulses with extremely large optical fields. Light bullets—pulses that propagate without change in space or time—are also possible. The condition for such a collapse and possible experiments are discussed.

© 1990 Optical Society of America

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References

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  1. For reviews of self-focusing, see S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi and E. O. Schulz-DuBois, eds. (North-Holland, Amsterdam, 1972); Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975); J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
    [Crossref]
  2. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [Crossref]
  3. P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
    [Crossref]
  4. V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  5. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  6. S. Maneuf and F. Reynaud, Opt. Commun. 66, 325 (1988); J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, Opt. Lett. 15, 471 (1990).
    [Crossref] [PubMed]
  7. The self-trapped beam power in 2d calculated here is different by 1.5% from the value given in Ref.2.
  8. V. E. Zakharov and V. S. Synakh, Sov. Phys. JETP 41, 465 (1975); V. E. Zakharov, N. E. Kosmatov, and V. F. Shvets, JETP Lett. 49, 492 (1989).
  9. V. M. Malkin, JETP Lett. 48, 653 (1988); S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).
  10. M. D. Feit and J. A. Fleck, J. Opt. Soc. Am. B 5, 633 (1988).
    [Crossref]
  11. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and A. H. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
    [Crossref]

1989 (1)

1988 (3)

S. Maneuf and F. Reynaud, Opt. Commun. 66, 325 (1988); J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, Opt. Lett. 15, 471 (1990).
[Crossref] [PubMed]

V. M. Malkin, JETP Lett. 48, 653 (1988); S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

M. D. Feit and J. A. Fleck, J. Opt. Soc. Am. B 5, 633 (1988).
[Crossref]

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

1975 (1)

V. E. Zakharov and V. S. Synakh, Sov. Phys. JETP 41, 465 (1975); V. E. Zakharov, N. E. Kosmatov, and V. F. Shvets, JETP Lett. 49, 492 (1989).

1972 (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

1965 (1)

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[Crossref]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Akhmanov, S. A.

For reviews of self-focusing, see S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi and E. O. Schulz-DuBois, eds. (North-Holland, Amsterdam, 1972); Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975); J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[Crossref]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Feit, M. D.

Fleck, J. A.

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Gordon, J. P.

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and A. H. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
[Crossref]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Haus, A. H.

Kelley, P. L.

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[Crossref]

Khokhlov, R. V.

For reviews of self-focusing, see S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi and E. O. Schulz-DuBois, eds. (North-Holland, Amsterdam, 1972); Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975); J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[Crossref]

Malkin, V. M.

V. M. Malkin, JETP Lett. 48, 653 (1988); S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

Maneuf, S.

S. Maneuf and F. Reynaud, Opt. Commun. 66, 325 (1988); J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, Opt. Lett. 15, 471 (1990).
[Crossref] [PubMed]

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Reynaud, F.

S. Maneuf and F. Reynaud, Opt. Commun. 66, 325 (1988); J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, Opt. Lett. 15, 471 (1990).
[Crossref] [PubMed]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Stolen, R. H.

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and A. H. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
[Crossref]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Sukhorukov, A. P.

For reviews of self-focusing, see S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi and E. O. Schulz-DuBois, eds. (North-Holland, Amsterdam, 1972); Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975); J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[Crossref]

Synakh, V. S.

V. E. Zakharov and V. S. Synakh, Sov. Phys. JETP 41, 465 (1975); V. E. Zakharov, N. E. Kosmatov, and V. F. Shvets, JETP Lett. 49, 492 (1989).

Tomlinson, W. J.

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Zakharov, V. E.

V. E. Zakharov and V. S. Synakh, Sov. Phys. JETP 41, 465 (1975); V. E. Zakharov, N. E. Kosmatov, and V. F. Shvets, JETP Lett. 49, 492 (1989).

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

J. Opt. Soc. Am. B (2)

JETP Lett. (1)

V. M. Malkin, JETP Lett. 48, 653 (1988); S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

Opt. Commun. (1)

S. Maneuf and F. Reynaud, Opt. Commun. 66, 325 (1988); J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, Opt. Lett. 15, 471 (1990).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[Crossref]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Sov. Phys. JETP (2)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

V. E. Zakharov and V. S. Synakh, Sov. Phys. JETP 41, 465 (1975); V. E. Zakharov, N. E. Kosmatov, and V. F. Shvets, JETP Lett. 49, 492 (1989).

Other (2)

The self-trapped beam power in 2d calculated here is different by 1.5% from the value given in Ref.2.

For reviews of self-focusing, see S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi and E. O. Schulz-DuBois, eds. (North-Holland, Amsterdam, 1972); Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975); J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[Crossref]

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Figures (1)

Fig. 1
Fig. 1

Radial dependence of the field of the self-trapped beam in 1, 2, and 3 transverse dimensions. The field is normalized to unity at ρ = 0. The 1d solution is U = sech(ρ).

Equations (8)

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2 ik ( z + 1 ν g t ) E + 2 E x 2 + 2 E y 2 k 2 h ω 2 2 E t 2 + 2 k 2 n 2 n 0 | E | 2 E = 0 ,
i u ζ + 1 2 ( 2 u ξ 2 + 2 u η 2 + 2 u τ 2 ) + | u | 2 u = 0 .
1 2 [ 2 ρ 2 + ( d 1 ) ρ ρ ] U βU + U 3 = 0 ,
P ˜ U 2 d S t = { 2 . 000 β = 0 . 5000 ( 1 d ) , 5 . 850 β = 0 . 2055 ( 2 d ) , 28 . 87 β = 0 . 05316 ( 3 d ) ,
d 2 ρ d ζ 2 = V ρ = 1 2 ρ ( ρ 2 A A + 2 A 2 ) .
A ( ρ , ζ ) = A 0 [ w 0 w ( ζ ) ] d / 2 exp [ ρ 2 2 w 2 ( ζ ) ] ,
d 2 w d ζ 2 = V w ,
V d 2 w 2 ( 1 2 U 0 2 w 0 d w 2 d d ) .

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