Abstract

We investigate the propagation of intense Gaussian beams in materials with quadratic nonlinearity. Excitation of (2 + 1) solitons is numerically predicted at finite phase mismatch and in the presence of linear walk-off between the fundamental and second-harmonic waves. The numerical results are interpreted in terms of the conserved quantities of the wave evolution, and the appropriate conditions for the experimental observation of the solitons are discussed.

© 1995 Optical Society of America

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References

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  1. Q. Guo, Quantum Opt. 5, 133 (1993); A. G. Kalocsai, J. W. Haus, Opt. Commun. 97, 239 (1993); Phys. Rev. A 49, 574 (1994); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); M. J. Werner, P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993); Opt. Lett. 19, 613 (1994).
    [CrossRef] [PubMed]
  2. L. Torner, C. R. Menyuk, G. I. Stegeman, Opt. Lett. 19, 1615 (1994).
    [CrossRef] [PubMed]
  3. C. R. Menyuk, R. Schiek, L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).
    [CrossRef]
  4. Yu. N. Karamzin, A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).
  5. A. A. Kanashov, A. M. Rubenchik, Physica D 4, 122 (1981).
    [CrossRef]
  6. K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
    [CrossRef] [PubMed]
  7. V. E. Zakharov, E. A. Kuznetzov, Sov. Phys. JETP 39, 285 (1975).
  8. E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 103 (1986).
    [CrossRef]
  9. I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
    [CrossRef]

1994 (2)

1993 (2)

Q. Guo, Quantum Opt. 5, 133 (1993); A. G. Kalocsai, J. W. Haus, Opt. Commun. 97, 239 (1993); Phys. Rev. A 49, 574 (1994); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); M. J. Werner, P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993); Opt. Lett. 19, 613 (1994).
[CrossRef] [PubMed]

K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

1990 (1)

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

1986 (1)

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

1981 (1)

A. A. Kanashov, A. M. Rubenchik, Physica D 4, 122 (1981).
[CrossRef]

1976 (1)

Yu. N. Karamzin, A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

1975 (1)

V. E. Zakharov, E. A. Kuznetzov, Sov. Phys. JETP 39, 285 (1975).

Badan, J.

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

Guo, Q.

Q. Guo, Quantum Opt. 5, 133 (1993); A. G. Kalocsai, J. W. Haus, Opt. Commun. 97, 239 (1993); Phys. Rev. A 49, 574 (1994); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); M. J. Werner, P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993); Opt. Lett. 19, 613 (1994).
[CrossRef] [PubMed]

Hayata, K.

K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Kanashov, A. A.

A. A. Kanashov, A. M. Rubenchik, Physica D 4, 122 (1981).
[CrossRef]

Karamzin, Yu. N.

Yu. N. Karamzin, A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Koshiba, M.

K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Kuznetsov, E. A.

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

Kuznetzov, E. A.

V. E. Zakharov, E. A. Kuznetzov, Sov. Phys. JETP 39, 285 (1975).

Ledoux, I.

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

Lepers, C.

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

Menyuk, C. R.

Périgaud, A.

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

Rubenchik, A. M.

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

A. A. Kanashov, A. M. Rubenchik, Physica D 4, 122 (1981).
[CrossRef]

Schiek, R.

Stegeman, G. I.

Sukhorukov, A. P.

Yu. N. Karamzin, A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Torner, L.

Zakharov, V. E.

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

V. E. Zakharov, E. A. Kuznetzov, Sov. Phys. JETP 39, 285 (1975).

Zyss, J.

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

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

Opt. Commun. (1)

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

Phys. Rev. Lett. (1)

K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Physica D (1)

A. A. Kanashov, A. M. Rubenchik, Physica D 4, 122 (1981).
[CrossRef]

Quantum Opt. (1)

Q. Guo, Quantum Opt. 5, 133 (1993); A. G. Kalocsai, J. W. Haus, Opt. Commun. 97, 239 (1993); Phys. Rev. A 49, 574 (1994); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); M. J. Werner, P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993); Opt. Lett. 19, 613 (1994).
[CrossRef] [PubMed]

Sov. Phys. JETP (2)

Yu. N. Karamzin, A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

V. E. Zakharov, E. A. Kuznetzov, Sov. Phys. JETP 39, 285 (1975).

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Figures (2)

Fig. 1
Fig. 1

Evolution of the amplitude of the fundamental wave. Dashed curves show the evolution of the beams in absence of nonlinearity. Dotted curves show the evolution of a beam governed by the nonlinear Schrödinger equation. All values are scaled to the input amplitudes. (a) β = 3, (b) β = −3.

Fig. 2
Fig. 2

Detail of the beam evolution in the presence of walk-off. The plots show a slice of the beams along the walk-off axis. Dashed curves, ξ = 0; solid curves, ξ = 5. (a) δ = 0, (b) δ = 1. In both cases β = −3, A = 4, and B = 4.

Equations (5)

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i a 1 ξ + 1 2 2 a 1 + a 1 * a 2 exp ( - i β ξ ) = 0 , i a 2 ξ + α 2 2 a 2 - i δ a 2 x + a 1 2 exp ( i β ξ ) = 0 ,
I = { a 1 2 + a ^ 2 2 } d r ,
H = 1 2 { a 1 2 + α 2 a ^ 2 2 + β a ^ 2 2 - i δ 2 ( a ^ 2 a ^ 2 * x - a ^ 2 * a ^ 2 x ) - ( a 1 * 2 a ^ 2 + a 1 2 a ^ 2 * ) } d r ,
H - 1 4 ( β - β ) I - I 2 .
a 1 ( ξ = 0 ) = A exp ( - r 2 ) , a 2 ( ξ = 0 ) = B exp ( - r 2 ) .

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