Abstract

We study, both numerically and experimentally, the transverse modulational instability of spatial stripe solitons in anisotropic nonlocal photorefractive media. We demonstrate that the instability scenarios depend strongly on the stripe orientation, but the anisotropy-induced features are largely suppressed for spatial solitons created by self-trapping of partially incoherent light.

© 2004 Optical Society of America

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References

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  1. V. E. Zakharov and A. M. Rubenchik, Zh. Eksp. Teor. Fiz. 65, 997 (1973) [Sov. Phys. JETP 38, 494 (1974)].
  2. See Yu. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
    [CrossRef]
  3. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).
  4. See, e.g., A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
    [CrossRef] [PubMed]
  5. K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
    [CrossRef]
  6. A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
    [CrossRef] [PubMed]
  7. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
    [CrossRef]
  8. C. Anastassiou, M. Soljacić, 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]
  9. M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
    [CrossRef]
  10. J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, Phys. Rev. E 65, 015601 (2001).
    [CrossRef]
  11. M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
    [CrossRef] [PubMed]

2001 (1)

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, Phys. Rev. E 65, 015601 (2001).
[CrossRef]

2000 (3)

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

C. Anastassiou, M. Soljacić, 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]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

1997 (1)

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

1996 (3)

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

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

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

1995 (1)

See, e.g., A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

1973 (1)

V. E. Zakharov and A. M. Rubenchik, Zh. Eksp. Teor. Fiz. 65, 997 (1973) [Sov. Phys. JETP 38, 494 (1974)].

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

Anastassiou, C.

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, Phys. Rev. E 65, 015601 (2001).
[CrossRef]

C. Anastassiou, M. Soljacić, 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]

See, e.g., A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

Chen, Z.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Christodoulides, D. N.

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, Phys. Rev. E 65, 015601 (2001).
[CrossRef]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

C. Anastassiou, M. Soljacić, 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]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Coskun, T.

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Coskun, T. H.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Eugenieva, E. D.

C. Anastassiou, M. Soljacić, 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]

Kip, D.

C. Anastassiou, M. Soljacić, 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, Yu. S.

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

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

Kos, K.

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Mamaev, A. V.

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

Meng, H.

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Mitchell, M.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Musslimani, Z. H.

C. Anastassiou, M. Soljacić, 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]

Pelinovsky, D. E.

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

Rubenchik, A. M.

V. E. Zakharov and A. M. Rubenchik, Zh. Eksp. Teor. Fiz. 65, 997 (1973) [Sov. Phys. JETP 38, 494 (1974)].

Saffman, M.

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

Salamo, G.

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Segev, M.

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, Phys. Rev. E 65, 015601 (2001).
[CrossRef]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

C. Anastassiou, M. Soljacić, 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]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Shih, M.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Soljacic, M.

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, Phys. Rev. E 65, 015601 (2001).
[CrossRef]

C. Anastassiou, M. Soljacić, 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]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Torres, J. P.

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, Phys. Rev. E 65, 015601 (2001).
[CrossRef]

C. Anastassiou, M. Soljacić, 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]

Valley, G. C.

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Vishwanath, A.

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov and A. M. Rubenchik, Zh. Eksp. Teor. Fiz. 65, 997 (1973) [Sov. Phys. JETP 38, 494 (1974)].

Zozulya, A. A.

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

See, e.g., A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

Phys. Rep. (1)

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

Phys. Rev. A (2)

See, e.g., A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

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

Phys. Rev. E (2)

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, Phys. Rev. E 65, 015601 (2001).
[CrossRef]

Phys. Rev. Lett. (4)

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

C. Anastassiou, M. Soljacić, 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]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

V. E. Zakharov and A. M. Rubenchik, Zh. Eksp. Teor. Fiz. 65, 997 (1973) [Sov. Phys. JETP 38, 494 (1974)].

Other (1)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

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Figures (4)

Fig. 1
Fig. 1

Numerical results for the coherent-stripe propagation: a–c, the soliton stripe is perpendicular to the external electric field; d–f, the soliton stripe is parallel to the field; g–i, an intermediate orientation of a tilted stripe.

Fig. 2
Fig. 2

Numerical results for the partially incoherent stripes. In a and b the stripe is perpendicular to the external field, and in c and d the stripe is parallel to the field. Shown are the (a and c) input and (b and d) output beams. The plot shows the growth rate of the transverse instability versus coherence parameter θ0.

Fig. 3
Fig. 3

Experimental observation of the transverse instability of a coherent soliton stripe. a, d, g, inputs for three orientations of the stripes. All other images are taken at the crystal output (length 7 mm) for applied voltage of b, h, 1 kV; c, i, 2 kV; c, 0.5 kV; and f, 1 kV.

Fig. 4
Fig. 4

Experimental results for the stripes oriented (a–f) perpendicular and (g–l) parallel to the electric field. a, g, input and d, j, output of the coherent light propagation (7 mm), presented for comparison; the other images correspond to partially incoherent light.

Equations (2)

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iEz+122E=φxE,
2φ+φln1+I=xln1+I,

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