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, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, 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, 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, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  5. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  6. S. Maneuf, 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, 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, V. S. Synakh, Sov. Phys. JETP 41, 465 (1975); V. E. Zakharov, N. E. Kosmatov, V. F. Shvets, JETP Lett. 49, 492 (1989).
  9. V. M. Malkin, JETP Lett. 48, 653 (1988); S. N. Vlasov, L. V. Piskunova, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).
  10. M. D. Feit, J. A. Fleck, J. Opt. Soc. Am. B 5, 633 (1988).
    [Crossref]
  11. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, A. H. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
    [Crossref]

1989 (1)

1988 (3)

S. Maneuf, 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, 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, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

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

1980 (1)

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

1975 (1)

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

1972 (1)

V. E. Zakharov, 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, 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, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, 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, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Feit, M. D.

Fleck, J. A.

Garmire, E.

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

Gordon, J. P.

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

L. F. Mollenauer, R. H. Stolen, 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, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, 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, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

Maneuf, S.

S. Maneuf, 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, P. W. E. Smith, Opt. Lett. 15, 471 (1990).
[Crossref] [PubMed]

Mollenauer, L. F.

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

Reynaud, F.

S. Maneuf, 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, P. W. E. Smith, Opt. Lett. 15, 471 (1990).
[Crossref] [PubMed]

Shabat, A. B.

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

Stolen, R. H.

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

L. F. Mollenauer, R. H. Stolen, 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, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, 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, V. S. Synakh, Sov. Phys. JETP 41, 465 (1975); V. E. Zakharov, N. E. Kosmatov, V. F. Shvets, JETP Lett. 49, 492 (1989).

Tomlinson, W. J.

Townes, C. H.

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

Zakharov, V. E.

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

V. E. Zakharov, 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, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

Opt. Commun. (1)

S. Maneuf, 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, P. W. E. Smith, Opt. Lett. 15, 471 (1990).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

R. Y. Chiao, E. Garmire, 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, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Sov. Phys. JETP (2)

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

V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1975); V. E. Zakharov, N. E. Kosmatov, 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, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, 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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