Abstract

We show, by performing linear stability analysis and direct numerical simulations, that dark-soliton transverse instability is significantly reduced in Kerr media by strong coupling to a bright soliton. High instability suppression can be achieved by use of large-amplitude bright solitons.

© 2001 Optical Society of America

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References

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  1. Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep.331, 117 (2000).
    [CrossRef]
  2. E. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep.142, 103 (1986).
    [CrossRef]
  3. V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).
  4. E. A. Kuznetsov and S. K. Turitsyn, Sov. Phys. JETP 76, 1583 (1988).
  5. A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
    [CrossRef] [PubMed]
  6. V. Tikhonenko, J. Christou, and B. Luther-Davis, Phys. Rev. Lett. 76, 2698 (1996).
    [CrossRef] [PubMed]
  7. V. Tikhonenko, J. Christou, and B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).
    [CrossRef]
  8. Here, the solitons were generated from the breakup of a vortex beam in a saturable self-focusing medium. See also W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
    [CrossRef]
  9. D. V. Skryabin and W. J. Firth, Phys. Rev. E 60, 1019 (1999).
    [CrossRef]
  10. G. J. Roskes, Stud. Appl. Math. 55, 231 (1976).
  11. Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
    [CrossRef] [PubMed]
  12. Z. Chen, M. Segev, T. Coskun, D. N. Christodoulides, Y. S. Kivshar, and V. Afanasjev, Opt. Lett. 21, 1821 (1996).
    [CrossRef] [PubMed]
  13. Z. Chen, M. Segev, T. Coskun, D. N. Christodoulides, and Y. S. Kivshar, J. Opt. Soc. Am. B 14, 3066 (1997).
    [CrossRef]
  14. Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
    [CrossRef]
  15. C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
    [CrossRef] [PubMed]
  16. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, Opt. Lett. 13, 871 (1988).
    [CrossRef] [PubMed]
  17. D. N. Christodoulides, Phys. Lett. A 132, 451 (1988).
    [CrossRef]
  18. A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
    [CrossRef]

2000

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

1999

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

D. V. Skryabin and W. J. Firth, Phys. Rev. E 60, 1019 (1999).
[CrossRef]

1997

A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef]

Here, the solitons were generated from the breakup of a vortex beam in a saturable self-focusing medium. See also W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Z. Chen, M. Segev, T. Coskun, D. N. Christodoulides, and Y. S. Kivshar, J. Opt. Soc. Am. B 14, 3066 (1997).
[CrossRef]

1996

1995

1988

E. A. Kuznetsov and S. K. Turitsyn, Sov. Phys. JETP 76, 1583 (1988).

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, Opt. Lett. 13, 871 (1988).
[CrossRef] [PubMed]

D. N. Christodoulides, Phys. Lett. A 132, 451 (1988).
[CrossRef]

1976

G. J. Roskes, Stud. Appl. Math. 55, 231 (1976).

1974

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

Afanasjev, V.

Anastassiou, C.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Anderson, D. Z.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

Chen, Z.

Christodoulides, D. N.

Christou, J.

V. Tikhonenko, J. Christou, and B. Luther-Davis, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).
[CrossRef]

Coskun, T.

Eugenieva, E. D.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Firth, W. J.

D. V. Skryabin and W. J. Firth, Phys. Rev. E 60, 1019 (1999).
[CrossRef]

Here, the solitons were generated from the breakup of a vortex beam in a saturable self-focusing medium. See also W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Kip, D.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Kivshar, Y. S.

Kivshar, Yu. S.

A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef]

Kuznetsov, E.

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

Kuznetsov, E. A.

E. A. Kuznetsov and S. K. Turitsyn, Sov. Phys. JETP 76, 1583 (1988).

Luther-Davies, B.

Luther-Davis, B.

V. Tikhonenko, J. Christou, and B. Luther-Davis, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Mamaev, A. V.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

Musslimani, Z. H.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

Nepomnyashchy, A.

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

Pelinovsky, D. E.

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep.331, 117 (2000).
[CrossRef]

Roskes, G. J.

G. J. Roskes, Stud. Appl. Math. 55, 231 (1976).

Rubenchik, A. M.

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

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

Saffman, M.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

Segev, M.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

Z. Chen, M. Segev, T. Coskun, D. N. Christodoulides, and Y. S. Kivshar, J. Opt. Soc. Am. B 14, 3066 (1997).
[CrossRef]

Z. Chen, M. Segev, T. Coskun, D. N. Christodoulides, Y. S. Kivshar, and V. Afanasjev, Opt. Lett. 21, 1821 (1996).
[CrossRef] [PubMed]

Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef] [PubMed]

Sheppard, A. P.

A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef]

Skryabin, D. V.

D. V. Skryabin and W. J. Firth, Phys. Rev. E 60, 1019 (1999).
[CrossRef]

Here, the solitons were generated from the breakup of a vortex beam in a saturable self-focusing medium. See also W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Soljacic, M.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Stegeman, G. I.

Tikhonenko, V.

V. Tikhonenko, J. Christou, and B. Luther-Davis, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).
[CrossRef]

Torres, J. P.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Trillo, S.

Turitsyn, S. K.

E. A. Kuznetsov and S. K. Turitsyn, Sov. Phys. JETP 76, 1583 (1988).

Wabnitz, S.

Wright, E. M.

Zakharov, V. E.

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

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

Zozulya, A. A.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Lett. A

D. N. Christodoulides, Phys. Lett. A 132, 451 (1988).
[CrossRef]

Phys. Rev. A

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

Phys. Rev. E

A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Y. S. Kivshar, Phys. Rev. E 60, R1170 (1999).
[CrossRef]

D. V. Skryabin and W. J. Firth, Phys. Rev. E 60, 1019 (1999).
[CrossRef]

Phys. Rev. Lett.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davis, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Here, the solitons were generated from the breakup of a vortex beam in a saturable self-focusing medium. See also W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Sov. Phys. JETP

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

E. A. Kuznetsov and S. K. Turitsyn, Sov. Phys. JETP 76, 1583 (1988).

Stud. Appl. Math.

G. J. Roskes, Stud. Appl. Math. 55, 231 (1976).

Other

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep.331, 117 (2000).
[CrossRef]

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

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Figures (3)

Fig. 1
Fig. 1

Growth rate of the TI of a dark–bright-soliton pair for all transverse-wave numbers at three selected a values.

Fig. 2
Fig. 2

(a) Dark–bright-soliton solution  (2) at a=0.6. (b) Most-unstable eigenfunctions ϕ1x,ϕ2x,ψ1x,ψ2x for the dark–bright-soliton in (a). Here, a=0.6, q=0.4, and unstable eigenvalue iω=0.1113.

Fig. 3
Fig. 3

Evolution of the dark-soliton TI (a)–(c) for the scalar case a=1, (d)–(f) in the presence of bright component with peak intensity 0.6 a=0.8, and (g)–(i) for higher bright-soliton amplitude 0.8 a=0.6. Snapshots are taken at z=8,16,24LD for each a value. Black indicates low solution values, and white represents high solution values. The x and y scales are -8<x<8 and -40<y<40, respectively.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

iUz+122U-U2+V2U=0,iVz+122V-U2+V2V=0,
usx=1-a2sechax,vsx=tanhax,
Uz,x,y=usx+ϵU1z,x,yexpiμz,Vz,x,y=vsx+ϵV1z,x,yexpiνz,
U1=ϕ1xexpiωz+iqy+ϕ2*xexp-iω*z-iqy,V1=ψ1xexpiωz+iqy+ψ2*xexp-iω*z-iqy.
12d2ϕ+dx2-Rμ+q22ϕ+-ωϕ--2usvsψ+=0,12d2ψ+dx2-Rν+q22ψ+-ωψ--2usvsϕ+=0,12d2ϕ-dx2-μ+q22+us2+vs2ϕ--ωϕ+=0,12d2ψ-dx2-ν+q22+us2+vs2ψ--ωψ+=0,
ϕ±ϕ0±+qϕ1±+q2ϕ2±+,ψ±ψ0±+qψ1±+q2ψ2±+,ωq=qω1+q2ω2+,
iω=a23-a23a2+11/2q.
U0,x,y=usx+ϵdus/dxcosq0y,V0,x,y=vsx+ϵdvs/dxcosq0y,

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