Abstract

The nonlinear Schrödinger equation predicts conical emission that is due to spatiotemporal propagation of short pulses in normally dispersive, cubically nonlinear media. This effect is a direct consequence of a four-wave interaction.

© 1994 Optical Society of America

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References

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  1. R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970); R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989), Chap. 7, p. 333.
    [CrossRef]
  2. R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
    [CrossRef]
  3. 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); F. A. Ilkov, L. Sh. Ilkova, L. Chin, Opt. Lett. 18, 681 (1993).
    [CrossRef] [PubMed]
  4. N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986).
  5. J. E. Rothenberg, Opt. Lett. 17, 583 (1992).
    [CrossRef] [PubMed]
  6. P. Chernev, V. Petrov, Opt. Lett. 17, 172 (1992).
    [CrossRef] [PubMed]
  7. G. G. Luther, J. V. Maloney, A. C. Newell, E. M. Wright, “Self-focusing threshold in normally dispersive media,” Opt. Lett. (to be published).
  8. G. G. Luther, A. C. Newell, J. V. Maloney, “The effects of normal dispersion on collapse events,” Physica D (to be published).
  9. O. M. Phillips, Dynamics of the Upper Ocean (Cambridge U. Press, Cambridge, 1977); G. Grynberg, Opt. Commun. 66, 321 (1988).
    [CrossRef]
  10. D. U. Martin, H. C. Yuen, Phys. Fluids 23, 881 (1980); A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, Sov. J. Plasma Phys. 9, 287 (1983); L. W. Liou, X. D. Cao, C. J. McKinstrie, G. P. Agrawal, Phys. Rev. A 46, 4202 (1992), and references therein.
    [CrossRef] [PubMed]
  11. J. A. Fleck, R. L. Carman, Appl. Phys. Lett. 20, 290 (1972).
    [CrossRef]
  12. J. E. Rothenberg, Opt. Lett. 17, 1340 (1992).
    [CrossRef] [PubMed]
  13. J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 14, 99 (1977).
    [CrossRef]
  14. V. E. Zakharov, A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

1992 (3)

1989 (1)

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); F. A. Ilkov, L. Sh. Ilkova, L. Chin, Opt. Lett. 18, 681 (1993).
[CrossRef] [PubMed]

1986 (1)

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

1980 (1)

D. U. Martin, H. C. Yuen, Phys. Fluids 23, 881 (1980); A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, Sov. J. Plasma Phys. 9, 287 (1983); L. W. Liou, X. D. Cao, C. J. McKinstrie, G. P. Agrawal, Phys. Rev. A 46, 4202 (1992), and references therein.
[CrossRef] [PubMed]

1977 (1)

J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 14, 99 (1977).
[CrossRef]

1974 (1)

V. E. Zakharov, A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

1972 (1)

J. A. Fleck, R. L. Carman, Appl. Phys. Lett. 20, 290 (1972).
[CrossRef]

1970 (1)

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970); R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989), Chap. 7, p. 333.
[CrossRef]

1966 (1)

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Alfano, R. R.

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970); R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989), Chap. 7, p. 333.
[CrossRef]

Carman, R. L.

J. A. Fleck, R. L. Carman, Appl. Phys. Lett. 20, 290 (1972).
[CrossRef]

Chernev, P.

Chiao, R. Y.

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Corkum, P. B.

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); F. A. Ilkov, L. Sh. Ilkova, L. Chin, Opt. Lett. 18, 681 (1993).
[CrossRef] [PubMed]

Feit, M. D.

J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 14, 99 (1977).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 14, 99 (1977).
[CrossRef]

J. A. Fleck, R. L. Carman, Appl. Phys. Lett. 20, 290 (1972).
[CrossRef]

Garmire, E.

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Kelley, P. L.

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Litvak, A. G.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Luther, G. G.

G. G. Luther, A. C. Newell, J. V. Maloney, “The effects of normal dispersion on collapse events,” Physica D (to be published).

G. G. Luther, J. V. Maloney, A. C. Newell, E. M. Wright, “Self-focusing threshold in normally dispersive media,” Opt. Lett. (to be published).

Maloney, J. V.

G. G. Luther, J. V. Maloney, A. C. Newell, E. M. Wright, “Self-focusing threshold in normally dispersive media,” Opt. Lett. (to be published).

G. G. Luther, A. C. Newell, J. V. Maloney, “The effects of normal dispersion on collapse events,” Physica D (to be published).

Martin, D. U.

D. U. Martin, H. C. Yuen, Phys. Fluids 23, 881 (1980); A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, Sov. J. Plasma Phys. 9, 287 (1983); L. W. Liou, X. D. Cao, C. J. McKinstrie, G. P. Agrawal, Phys. Rev. A 46, 4202 (1992), and references therein.
[CrossRef] [PubMed]

Morris, J. R.

J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 14, 99 (1977).
[CrossRef]

Newell, A. C.

G. G. Luther, A. C. Newell, J. V. Maloney, “The effects of normal dispersion on collapse events,” Physica D (to be published).

G. G. Luther, J. V. Maloney, A. C. Newell, E. M. Wright, “Self-focusing threshold in normally dispersive media,” Opt. Lett. (to be published).

Petrov, V.

Petrova, T. A.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Phillips, O. M.

O. M. Phillips, Dynamics of the Upper Ocean (Cambridge U. Press, Cambridge, 1977); G. Grynberg, Opt. Commun. 66, 321 (1988).
[CrossRef]

Rolland, C.

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); F. A. Ilkov, L. Sh. Ilkova, L. Chin, Opt. Lett. 18, 681 (1993).
[CrossRef] [PubMed]

Rothenberg, J. E.

Rubenchik, A. M.

V. E. Zakharov, A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Sergeev, A. M.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Shapiro, S. L.

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970); R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989), Chap. 7, p. 333.
[CrossRef]

Wright, E. M.

G. G. Luther, J. V. Maloney, A. C. Newell, E. M. Wright, “Self-focusing threshold in normally dispersive media,” Opt. Lett. (to be published).

Yuen, H. C.

D. U. Martin, H. C. Yuen, Phys. Fluids 23, 881 (1980); A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, Sov. J. Plasma Phys. 9, 287 (1983); L. W. Liou, X. D. Cao, C. J. McKinstrie, G. P. Agrawal, Phys. Rev. A 46, 4202 (1992), and references therein.
[CrossRef] [PubMed]

Yunakovskii, A. D.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Zakharov, V. E.

V. E. Zakharov, A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Zharova, N. A.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 14, 99 (1977).
[CrossRef]

Appl. Phys. Lett. (1)

J. A. Fleck, R. L. Carman, Appl. Phys. Lett. 20, 290 (1972).
[CrossRef]

IEEE J. Quantum Electron. (1)

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); F. A. Ilkov, L. Sh. Ilkova, L. Chin, Opt. Lett. 18, 681 (1993).
[CrossRef] [PubMed]

JETP Lett. (1)

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Opt. Lett. (3)

Phys. Fluids (1)

D. U. Martin, H. C. Yuen, Phys. Fluids 23, 881 (1980); A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, Sov. J. Plasma Phys. 9, 287 (1983); L. W. Liou, X. D. Cao, C. J. McKinstrie, G. P. Agrawal, Phys. Rev. A 46, 4202 (1992), and references therein.
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970); R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989), Chap. 7, p. 333.
[CrossRef]

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zakharov, A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Other (3)

G. G. Luther, J. V. Maloney, A. C. Newell, E. M. Wright, “Self-focusing threshold in normally dispersive media,” Opt. Lett. (to be published).

G. G. Luther, A. C. Newell, J. V. Maloney, “The effects of normal dispersion on collapse events,” Physica D (to be published).

O. M. Phillips, Dynamics of the Upper Ocean (Cambridge U. Press, Cambridge, 1977); G. Grynberg, Opt. Commun. 66, 321 (1988).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Intensity |A(x, y = 0, t)|2 (top) and far-field frequency spectrum log[|A(κx, κy = 0, ω)|] (bottom) of a light pulse displayed at positions (a) just before it enters the medium, z = 0.0LDF; (b) just before pulse splitting, z = 1.1LDF; (c) just after pulse splitting, z = 1.5LDF. The four-wave interaction redistributes the pulse energy onto bands near k2 ∝ Ω2.

Fig. 2
Fig. 2

Time-integrated far-field image of a light pulse at z = 1.1LDF just before a splitting event and (b) the time-integrated far-field image of the pulse after it passes through a narrow-band filter shifted from the center frequency of the pulse, |A(Ω = 19500 cm−1, θx, θy)|.

Fig. 3
Fig. 3

Axial pulse amplitude profile |A(x = 0, y = 0, z, t)| (top) and instantaneous frequency shifts (bottom) for LDFk″/tp2 = 0.1 and P/Pc = 1.5 for z = 0.0LDF (curve a), z = 1.1LDF (curve b), z = 1.3LDF (curve c), z = 2.0LDF (curve d).

Equations (1)

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2 i k ( A z + k ω A t ) + 2 A - k 2 k ω 2 2 A t 2 + 2 k 2 n 2 n 0 A 2 A = 0 ,

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