Abstract

We demonstrate that weak parametric interaction of a fundamental beam with its harmonic field in a Kerr medium can drastically modify the beam dynamics, giving rise to very complex bifurcation phenomena and quasi solitons. Most importantly, we reveal a novel physical mechanism of the collapse suppression in a bulk optical Kerr medium: parametric coupling to a weakly radiating harmonic field.

© 1999 Optical Society of America

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References

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  1. L. Berge, Phys. Rep. 303, 259 (1998).
    [CrossRef]
  2. M. F. Feit and J. A. Fleck, J. Opt. Soc. Am. B 5, 633 (1988); G. Fibich, Phys. Rev. Lett. 76, 4356 (1996).
    [CrossRef] [PubMed]
  3. V. Malkin, Phys. D 64, 251 (1993).
    [CrossRef]
  4. S. Chi and Q. Guo, Opt. Lett. 20, 1598 (1995).
    [CrossRef] [PubMed]
  5. O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
    [CrossRef]
  6. R. A. Sammut, A. V. Buryak, and Yu. S. Kivshar, J. Opt. Soc. Am. B 15, 1488 (1998).
    [CrossRef]
  7. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); erratum,  14, 1056 (1965).
    [CrossRef]
  8. K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
    [CrossRef] [PubMed]
  9. A. V. Buryak, Phys. Rev. E 52, 1156 (1995).
    [CrossRef]
  10. V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
    [CrossRef]
  11. A. R. Champneys and G. L. Lord, Phys. D 102, 101 (1996).
    [CrossRef]
  12. F. V. Kusmartsev, Phys. Rep. 183, 1 (1989).
    [CrossRef]
  13. This conclusion is also supported by data in X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999), in which the case of ??100???/? was considered for ?2 spatiotemporal solitons.
    [CrossRef]

1999 (1)

This conclusion is also supported by data in X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999), in which the case of ??100???/? was considered for ?2 spatiotemporal solitons.
[CrossRef]

1998 (4)

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
[CrossRef]

L. Berge, Phys. Rep. 303, 259 (1998).
[CrossRef]

R. A. Sammut, A. V. Buryak, and Yu. S. Kivshar, J. Opt. Soc. Am. B 15, 1488 (1998).
[CrossRef]

1996 (1)

A. R. Champneys and G. L. Lord, Phys. D 102, 101 (1996).
[CrossRef]

1995 (3)

K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
[CrossRef] [PubMed]

A. V. Buryak, Phys. Rev. E 52, 1156 (1995).
[CrossRef]

S. Chi and Q. Guo, Opt. Lett. 20, 1598 (1995).
[CrossRef] [PubMed]

1993 (1)

V. Malkin, Phys. D 64, 251 (1993).
[CrossRef]

1989 (1)

F. V. Kusmartsev, Phys. Rep. 183, 1 (1989).
[CrossRef]

1988 (1)

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); erratum,  14, 1056 (1965).
[CrossRef]

Bang, O.

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

Berge, L.

L. Berge, Phys. Rep. 303, 259 (1998).
[CrossRef]

Buryak, A. V.

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

R. A. Sammut, A. V. Buryak, and Yu. S. Kivshar, J. Opt. Soc. Am. B 15, 1488 (1998).
[CrossRef]

A. V. Buryak, Phys. Rev. E 52, 1156 (1995).
[CrossRef]

Champneys, A. R.

A. R. Champneys and G. L. Lord, Phys. D 102, 101 (1996).
[CrossRef]

Chi, S.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); erratum,  14, 1056 (1965).
[CrossRef]

De Rossi, A.

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

Feit, M. F.

Fleck, J. A.

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); erratum,  14, 1056 (1965).
[CrossRef]

Guo, Q.

Hayata, K.

K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
[CrossRef] [PubMed]

Kivshar, Yu. S.

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

R. A. Sammut, A. V. Buryak, and Yu. S. Kivshar, J. Opt. Soc. Am. B 15, 1488 (1998).
[CrossRef]

Koshiba, M.

K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
[CrossRef] [PubMed]

Kusmartsev, F. V.

F. V. Kusmartsev, Phys. Rep. 183, 1 (1989).
[CrossRef]

Kuznetsov, E. A.

V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
[CrossRef]

Liu, X.

This conclusion is also supported by data in X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999), in which the case of ??100???/? was considered for ?2 spatiotemporal solitons.
[CrossRef]

Lord, G. L.

A. R. Champneys and G. L. Lord, Phys. D 102, 101 (1996).
[CrossRef]

Malkin, V.

V. Malkin, Phys. D 64, 251 (1993).
[CrossRef]

Qian, L. J.

This conclusion is also supported by data in X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999), in which the case of ??100???/? was considered for ?2 spatiotemporal solitons.
[CrossRef]

Sammut, R. A.

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); erratum,  14, 1056 (1965).
[CrossRef]

Trillo, S.

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

Uehira, Y.

K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
[CrossRef] [PubMed]

Wise, F. W.

This conclusion is also supported by data in X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999), in which the case of ??100???/? was considered for ?2 spatiotemporal solitons.
[CrossRef]

Zakharov, V. E.

V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
[CrossRef]

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

JETP (1)

V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. D (2)

A. R. Champneys and G. L. Lord, Phys. D 102, 101 (1996).
[CrossRef]

V. Malkin, Phys. D 64, 251 (1993).
[CrossRef]

Phys. Rep. (2)

F. V. Kusmartsev, Phys. Rep. 183, 1 (1989).
[CrossRef]

L. Berge, Phys. Rep. 303, 259 (1998).
[CrossRef]

Phys. Rev. A (1)

K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (2)

A. V. Buryak, Phys. Rev. E 52, 1156 (1995).
[CrossRef]

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); erratum,  14, 1056 (1965).
[CrossRef]

This conclusion is also supported by data in X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999), in which the case of ??100???/? was considered for ?2 spatiotemporal solitons.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Bifurcation diagram for solitons (solid curves) and quasi solitons (dashed curves) yielded by Eqs. (4). Examples of quasi solitons and solitons corresponding to open circles A–F are shown above and below the main diagram, including enlarged plots of the third-harmonic component tails. Point G represents the self-similar solution (see text); O is the bifurcation point of two-wave solitons from the fundamental one-wave soliton family. This and other bifurcation points are shown by filled circles.

Fig. 2
Fig. 2

Hamiltonian versus power diagram for solitons and quasi solitons of Eqs. (1). The soliton families are shown by the solid curves. The family of quasi solitons with minimal radiation intensity is shown by the dashed curve. The labeling of bifurcation points and soliton examples corresponds to that of Fig. 1.

Fig. 3
Fig. 3

Examples of the evolution of the fundamental harmonic amplitude for the same initial condition, u=5.0 exp-0.695x2+y2/2, w=0, at different values of the parameter α in Eqs. (4).

Equations (4)

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iUZ+˜2U-βU+FuU+13U*2W=0,iσWZ+˜2W-α˜W+FwW+19U3=0,
QU=-U2+3σW2dXdY,
H=-U2+W2-118U4-2U2W2-92W4-29ReU3W*dXdY.
iuz+2u-u+Fuu+13u*2w=0,iσwz+2w-αw+Fww+19u3=0,

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