Abstract

We demonstrate that a weak defocusing Kerr effect in an optical medium with predominantly quadratic [or χ2] nonlinear response can eliminate the parametric modulational instability of plane waves, leading to the existence of stable two-wave dark and vortex spatial solitons.

© 1998 Optical Society of America

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References

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  1. Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 288, 81 (1998).
    [CrossRef]
  2. B. Luther-Davies and X. Yang, Opt. Lett. 17, 496 (1992).
    [CrossRef] [PubMed]
  3. M. Shih, Z. Chen, M. Mitchell, M. Segev, H. Lee, R. S. Feigelson, and J. P. Wilde, J. Opt. Soc. Am. B 14, 3091 (1997).
    [CrossRef]
  4. See, e.g., G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
    [CrossRef]
  5. For a classfication of bright and dark solitary waves in diffractive ?2 media, see, e.g., A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
    [CrossRef]
  6. S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995).
    [CrossRef] [PubMed]
  7. A. V. Buryak and Yu. S. Kivshar, Phys. Rev. A 51, R41 (1995); Opt. Lett. 20, 834 (1995).
    [CrossRef]
  8. A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995); S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Opt. Commun. 122, 200 (1996); O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).
    [CrossRef] [PubMed]
  9. C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
    [CrossRef]
  10. D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E 54, 2015 (1996); Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996).
    [CrossRef] [PubMed]
  11. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996); A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
    [CrossRef]
  12. C. Fiorini, F. Charra, P. Raimond, A. Lorin, and J-M. Nunzi, Opt. Lett. 22, 1846 (1997); H. Nakayama, O. Sugihara, and N. Okamoto, Opt. Lett. 22, 1541 (1997).
    [CrossRef]

1998 (1)

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 288, 81 (1998).
[CrossRef]

1997 (3)

1996 (3)

See, e.g., G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E 54, 2015 (1996); Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996).
[CrossRef] [PubMed]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996); A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

1995 (4)

For a classfication of bright and dark solitary waves in diffractive ?2 media, see, e.g., A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
[CrossRef]

S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995).
[CrossRef] [PubMed]

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. A 51, R41 (1995); Opt. Lett. 20, 834 (1995).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995); S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Opt. Commun. 122, 200 (1996); O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).
[CrossRef] [PubMed]

1992 (1)

Afanasjev, V. V.

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E 54, 2015 (1996); Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996).
[CrossRef] [PubMed]

Allen, L.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996); A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

Bang, O.

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Buryak, A. V.

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. A 51, R41 (1995); Opt. Lett. 20, 834 (1995).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995); S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Opt. Commun. 122, 200 (1996); O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).
[CrossRef] [PubMed]

For a classfication of bright and dark solitary waves in diffractive ?2 media, see, e.g., A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
[CrossRef]

Charra, F.

Chen, Z.

Clausen, C. B.

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Dholakia, K.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996); A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

Feigelson, R. S.

Ferro, P.

Fiorini, C.

Hagan, D. J.

See, e.g., G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Kivshar, Yu. S.

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 288, 81 (1998).
[CrossRef]

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E 54, 2015 (1996); Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996).
[CrossRef] [PubMed]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995); S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Opt. Commun. 122, 200 (1996); O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).
[CrossRef] [PubMed]

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. A 51, R41 (1995); Opt. Lett. 20, 834 (1995).
[CrossRef]

For a classfication of bright and dark solitary waves in diffractive ?2 media, see, e.g., A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
[CrossRef]

Lee, H.

Lorin, A.

Luther-Davies, B.

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 288, 81 (1998).
[CrossRef]

B. Luther-Davies and X. Yang, Opt. Lett. 17, 496 (1992).
[CrossRef] [PubMed]

Mitchell, M.

Nunzi, J-M.

Padgett, M. J.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996); A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

Pelinovsky, D. E.

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E 54, 2015 (1996); Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996).
[CrossRef] [PubMed]

Raimond, P.

Segev, M.

Shih, M.

Simpson, N. B.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996); A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

Stegeman, G. I.

See, e.g., G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Torner, L.

See, e.g., G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Trillo, S.

Wilde, J. P.

Yang, X.

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

Opt. Lett. (4)

Opt. Quantum Electron. (1)

See, e.g., G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Phys. Lett. A (1)

For a classfication of bright and dark solitary waves in diffractive ?2 media, see, e.g., A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
[CrossRef]

Phys. Rep. (1)

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 288, 81 (1998).
[CrossRef]

Phys. Rev. A (2)

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. A 51, R41 (1995); Opt. Lett. 20, 834 (1995).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996); A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

Phys. Rev. E (1)

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E 54, 2015 (1996); Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Existence domains for the modulationally stable PW’s: (a) r=+1, (b) r=-1.

Fig. 2
Fig. 2

Amplitudes of the modulationally stable PW’s versus χ at α=-2.0. (a), (b), Figs.  1(a) and 1(b), respectively. The limit χ0 is singular.

Fig. 3
Fig. 3

Examples of dark solitons of Eqs.  (1) at r=+1: (a) α=-2.5 and χ=-0.1, (b) α=-4.0 and χ=-0.1, (c) α=-1.0 and χ=-0.1, (d) α=4.0 and χ=-0.05.

Fig. 4
Fig. 4

Existence domains for dark solitons of Eqs.  (1) at r=+1. The curve χ=1/4α is defined by the exact solution  [Eq.  (3)]. Points A, B, C, and D correspond to the dark solitons presented in Figs.  3(a), 3(b), 3(c), and 3(d), respectively.

Fig. 5
Fig. 5

Two-wave single-charged vortex soliton for χ=-0.1, α=-2.5, and r=+1. (a) Intensity profile for the FH. (b) Radial dependence for the FH and the SH.

Equations (3)

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iuz+r2u-u+wu*+χ14u2+ρw2u=0, 2iwz+r2w-αw+12u2+χ4w2+ρu2w=0,
rd2udx2-u+wu+χ14u2+2w2u=0, rd2wdx2-αω+12u2+χ4w2+2u2w=0,
u=4χ+1ρχ21/2tanhx-r2-r8ρχ1/2, w=-1/2ρχ,

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