Abstract

We address the problem of the existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of 2+1-dimensional two-mode self-trapped beams, with and without a topological charge, and describe their properties analytically and numerically.

© 2000 Optical Society of America

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References

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  1. See an overview by M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
    [CrossRef]
  2. S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).
  3. J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996); Y. Barad and Y. Silberberg, Phys. Rev. Lett. 78, 3290 (1997).
    [CrossRef] [PubMed]
  4. L. Bergé, Phys. Rep. 303, 259 (1998).
    [CrossRef]
  5. Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 61 (2000).
    [CrossRef]
  6. E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. Firth, Phys. Rev. Lett. 83, 296 (1999).
    [CrossRef]
  7. See, e.g., M. Desaix, D. Anderson, and M. Lisak, J. Opt. Soc. Am. B 8, 2082 (1991).
    [CrossRef]
  8. K. Hayata and M. Koshiba, Opt. Lett. 19, 1717 (1994).
    [CrossRef] [PubMed]
  9. C. J. McKinstrie and D. A. Russell, Phys. Rev. Lett. 61, 2929 (1988).
    [CrossRef] [PubMed]
  10. See, e.g., V. Tikhonenko, J. Christou, and B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).
    [CrossRef]
  11. M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 17, 1764 (1995).
    [CrossRef]

2000 (1)

1999 (1)

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

1998 (2)

See an overview by M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

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

1996 (1)

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996); Y. Barad and Y. Silberberg, Phys. Rev. Lett. 78, 3290 (1997).
[CrossRef] [PubMed]

1995 (2)

1994 (1)

1991 (1)

1988 (1)

C. J. McKinstrie and D. A. Russell, Phys. Rev. Lett. 61, 2929 (1988).
[CrossRef] [PubMed]

1974 (1)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Aitchison, J. S.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996); Y. Barad and Y. Silberberg, Phys. Rev. Lett. 78, 3290 (1997).
[CrossRef] [PubMed]

Akhmediev, N. N.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996); Y. Barad and Y. Silberberg, Phys. Rev. Lett. 78, 3290 (1997).
[CrossRef] [PubMed]

Anderson, D.

Bergé, L.

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

Carvalho, M. I.

Christodoulides, D. N.

Christou, J.

Desaix, M.

Firth, W.

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

Hayata, K.

Kang, J. U.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996); Y. Barad and Y. Silberberg, Phys. Rev. Lett. 78, 3290 (1997).
[CrossRef] [PubMed]

Kivshar, Yu. S.

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

Koshiba, M.

Lisak, M.

Luther-Davies, B.

Manakov, S. V.

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

McKinstrie, C. J.

C. J. McKinstrie and D. A. Russell, Phys. Rev. Lett. 61, 2929 (1988).
[CrossRef] [PubMed]

Musslimani, Z. H.

Ostrovskaya, E. A.

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

Russell, D. A.

C. J. McKinstrie and D. A. Russell, Phys. Rev. Lett. 61, 2929 (1988).
[CrossRef] [PubMed]

Segev, M.

Singh, S. R.

Skryabin, D. V.

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

Stegeman, G. I.

See an overview by M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996); Y. Barad and Y. Silberberg, Phys. Rev. Lett. 78, 3290 (1997).
[CrossRef] [PubMed]

Tikhonenko, V.

Valley, G. C.

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

Opt. Lett. (3)

Phys. Rep. (1)

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

Phys. Rev. Lett. (3)

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996); Y. Barad and Y. Silberberg, Phys. Rev. Lett. 78, 3290 (1997).
[CrossRef] [PubMed]

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

C. J. McKinstrie and D. A. Russell, Phys. Rev. Lett. 61, 2929 (1988).
[CrossRef] [PubMed]

Phys. Today (1)

See an overview by M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

Sov. Phys. JETP (1)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

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Figures (5)

Fig. 1
Fig. 1

Top, existence region (hatched) for the |0,0 vector solitons. Solid curves, numerically obtained cutoff curves σ1λ and σ2λ; dashed curves, results of the variational analysis. Bottom, amplitudes of the u (solid curves) and v (dashed curves) components of |0,0 vector solitons at σ=2, corresponding to points a and b, respectively, above.

Fig. 2
Fig. 2

Total power of the |0,0 vector soliton (solid curves) and partial powers of its components (dashed and dotted–dashed curves).

Fig. 3
Fig. 3

Intensity profiles, Ir=u2+v2, of the |0,1 vector solitons (solid curves) formed by scalar components with (v; dashed–dotted curves) and without (u; dashed curves) a topological charge σ=3.

Fig. 4
Fig. 4

(a) Existence domain (hatched) for |0,1 solitons in a saturable medium. (b) Evolution of the total intensity at r=0 for three values of s. λ=0.6, z=50.

Fig. 5
Fig. 5

Typical evolution of the |0,1 solitons in a saturable medium s=0.65,λ=0.6: (a) Intensity distribution at z=0, (b) evolution of the intensity profile at y=0, (c) intensity distribution at z=100.

Equations (4)

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iE1,2z+ΔE1,2+E1,22+σE2,12E1,2=0,
E1=β1urexpiβ1zexpinφ,  E2=β1vrexpiβ2zexpimφ,
Δru-u+u2+σv2u=0,  Δrv-m2r2v-λv+v2+σu2v=0,
Δru-u+ufI=0,  Δrv-m2r2v-λv+vfI=0,

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