Abstract

We study the symmetry breaking instability of discrete solitons with even parity in a 1-D waveguide array, and find that such instability can be suppressed by adding spatial incoherence. This is true for both staggered and unstaggered modes.

© 2007 Optical Society of America

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  1. M. R. Evans, D. P. Foster, C. Godreche, and D. Mukamel, “Spontaneous symmetry breaking in a one dimensional driven diffusive system,” Phys. Rev. Lett. 74, 208–211 (1995).
    [Crossref] [PubMed]
  2. C. Yannouleas and U. Landman, “Spontaneous symmetry breaking in single and molecular quantum dots,” Phys. Rev. Lett. 82, 5325–5328 (1999).
    [Crossref]
  3. D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988).
    [Crossref] [PubMed]
  4. Y. S. Kivshar and G. P. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, San Diego, 2003).
  5. A. A. Sukhorukov and Y. S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).
    [Crossref]
  6. D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004)
    [Crossref]
  7. M. Soljac̆ic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
    [Crossref] [PubMed]
  8. D. Kip, M. Soljac̆ic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
    [Crossref] [PubMed]
  9. J. P. Torres, C. Anastassiou, M. Segev, M. Soljac̆ic, and D. N. Christodoulides, “Transverse instability of incoherent solitons in Kerr media,” Phys. Rev. E 65, 015601 (2001).
    [Crossref]
  10. C. Jeng, M. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92, 043904 (2004).
    [Crossref] [PubMed]
  11. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
    [Crossref] [PubMed]
  12. D. N. Christodoulides, T H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
    [Crossref]
  13. M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990 (1997).
    [Crossref]
  14. M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880(1997).
    [Crossref]
  15. H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, and M. Segev1, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
    [Crossref] [PubMed]
  16. O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500–503 (2005).
    [Crossref]
  17. R. Pezer, H. Buljan, J. W. Fleischer, G. Bartal, O. Cohen, and M. Segev, “Gap random-phase lattice solitons,” Opt. Express 13, 5013–5023 (2005).
    [Crossref] [PubMed]
  18. R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, “Incoherent white-light solitons in nonlinear periodic lattices,” Phys. Rev. E 73, 056608 (2006).
    [Crossref]
  19. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered twodimensional photonic lattices,” Nature (London) 446, 52–55 (200).
    [Crossref]

2006 (1)

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, “Incoherent white-light solitons in nonlinear periodic lattices,” Phys. Rev. E 73, 056608 (2006).
[Crossref]

2005 (2)

R. Pezer, H. Buljan, J. W. Fleischer, G. Bartal, O. Cohen, and M. Segev, “Gap random-phase lattice solitons,” Opt. Express 13, 5013–5023 (2005).
[Crossref] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500–503 (2005).
[Crossref]

2004 (3)

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, and M. Segev1, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[Crossref] [PubMed]

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004)
[Crossref]

C. Jeng, M. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92, 043904 (2004).
[Crossref] [PubMed]

2002 (1)

A. A. Sukhorukov and Y. S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).
[Crossref]

2001 (2)

J. P. Torres, C. Anastassiou, M. Segev, M. Soljac̆ic, and D. N. Christodoulides, “Transverse instability of incoherent solitons in Kerr media,” Phys. Rev. E 65, 015601 (2001).
[Crossref]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[Crossref] [PubMed]

2000 (2)

M. Soljac̆ic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

D. Kip, M. Soljac̆ic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

1999 (1)

C. Yannouleas and U. Landman, “Spontaneous symmetry breaking in single and molecular quantum dots,” Phys. Rev. Lett. 82, 5325–5328 (1999).
[Crossref]

1997 (3)

D. N. Christodoulides, T H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[Crossref]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990 (1997).
[Crossref]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880(1997).
[Crossref]

1995 (1)

M. R. Evans, D. P. Foster, C. Godreche, and D. Mukamel, “Spontaneous symmetry breaking in a one dimensional driven diffusive system,” Phys. Rev. Lett. 74, 208–211 (1995).
[Crossref] [PubMed]

1988 (1)

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, San Diego, 2003).

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[Crossref] [PubMed]

Anastassiou, C.

J. P. Torres, C. Anastassiou, M. Segev, M. Soljac̆ic, and D. N. Christodoulides, “Transverse instability of incoherent solitons in Kerr media,” Phys. Rev. E 65, 015601 (2001).
[Crossref]

Bartal, G.

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, “Incoherent white-light solitons in nonlinear periodic lattices,” Phys. Rev. E 73, 056608 (2006).
[Crossref]

R. Pezer, H. Buljan, J. W. Fleischer, G. Bartal, O. Cohen, and M. Segev, “Gap random-phase lattice solitons,” Opt. Express 13, 5013–5023 (2005).
[Crossref] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500–503 (2005).
[Crossref]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered twodimensional photonic lattices,” Nature (London) 446, 52–55 (200).
[Crossref]

Buljan, H.

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, “Incoherent white-light solitons in nonlinear periodic lattices,” Phys. Rev. E 73, 056608 (2006).
[Crossref]

R. Pezer, H. Buljan, J. W. Fleischer, G. Bartal, O. Cohen, and M. Segev, “Gap random-phase lattice solitons,” Opt. Express 13, 5013–5023 (2005).
[Crossref] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500–503 (2005).
[Crossref]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, and M. Segev1, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[Crossref] [PubMed]

Carmon, T.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500–503 (2005).
[Crossref]

Christodoulides, D. N.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500–503 (2005).
[Crossref]

J. P. Torres, C. Anastassiou, M. Segev, M. Soljac̆ic, and D. N. Christodoulides, “Transverse instability of incoherent solitons in Kerr media,” Phys. Rev. E 65, 015601 (2001).
[Crossref]

D. Kip, M. Soljac̆ic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

M. Soljac̆ic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

D. N. Christodoulides, T H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[Crossref]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990 (1997).
[Crossref]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988).
[Crossref] [PubMed]

Cohen, O.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500–503 (2005).
[Crossref]

R. Pezer, H. Buljan, J. W. Fleischer, G. Bartal, O. Cohen, and M. Segev, “Gap random-phase lattice solitons,” Opt. Express 13, 5013–5023 (2005).
[Crossref] [PubMed]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, and M. Segev1, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[Crossref] [PubMed]

Coskun, T H.

D. N. Christodoulides, T H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[Crossref]

Coskun, T.

M. Soljac̆ic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990 (1997).
[Crossref]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[Crossref] [PubMed]

Eugenieva, E.

D. Kip, M. Soljac̆ic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Evans, M. R.

M. R. Evans, D. P. Foster, C. Godreche, and D. Mukamel, “Spontaneous symmetry breaking in a one dimensional driven diffusive system,” Phys. Rev. Lett. 74, 208–211 (1995).
[Crossref] [PubMed]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered twodimensional photonic lattices,” Nature (London) 446, 52–55 (200).
[Crossref]

Fleischer, J. W.

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, “Incoherent white-light solitons in nonlinear periodic lattices,” Phys. Rev. E 73, 056608 (2006).
[Crossref]

R. Pezer, H. Buljan, J. W. Fleischer, G. Bartal, O. Cohen, and M. Segev, “Gap random-phase lattice solitons,” Opt. Express 13, 5013–5023 (2005).
[Crossref] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500–503 (2005).
[Crossref]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, and M. Segev1, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[Crossref] [PubMed]

Foster, D. P.

M. R. Evans, D. P. Foster, C. Godreche, and D. Mukamel, “Spontaneous symmetry breaking in a one dimensional driven diffusive system,” Phys. Rev. Lett. 74, 208–211 (1995).
[Crossref] [PubMed]

Godreche, C.

M. R. Evans, D. P. Foster, C. Godreche, and D. Mukamel, “Spontaneous symmetry breaking in a one dimensional driven diffusive system,” Phys. Rev. Lett. 74, 208–211 (1995).
[Crossref] [PubMed]

Jeng, C.

C. Jeng, M. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92, 043904 (2004).
[Crossref] [PubMed]

Joseph, R. I.

Kip, D.

D. Kip, M. Soljac̆ic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Kivshar, Y.

C. Jeng, M. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92, 043904 (2004).
[Crossref] [PubMed]

Kivshar, Y. S.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004)
[Crossref]

A. A. Sukhorukov and Y. S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).
[Crossref]

Y. S. Kivshar and G. P. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, San Diego, 2003).

Landman, U.

C. Yannouleas and U. Landman, “Spontaneous symmetry breaking in single and molecular quantum dots,” Phys. Rev. Lett. 82, 5325–5328 (1999).
[Crossref]

Mitchell, M.

D. N. Christodoulides, T H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[Crossref]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880(1997).
[Crossref]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990 (1997).
[Crossref]

Morandotti, R.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[Crossref] [PubMed]

Motzek, K.

C. Jeng, M. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92, 043904 (2004).
[Crossref] [PubMed]

Mukamel, D.

M. R. Evans, D. P. Foster, C. Godreche, and D. Mukamel, “Spontaneous symmetry breaking in a one dimensional driven diffusive system,” Phys. Rev. Lett. 74, 208–211 (1995).
[Crossref] [PubMed]

Pelinovsky, D. E.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004)
[Crossref]

Pezer, R.

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, “Incoherent white-light solitons in nonlinear periodic lattices,” Phys. Rev. E 73, 056608 (2006).
[Crossref]

R. Pezer, H. Buljan, J. W. Fleischer, G. Bartal, O. Cohen, and M. Segev, “Gap random-phase lattice solitons,” Opt. Express 13, 5013–5023 (2005).
[Crossref] [PubMed]

Schwartz, T.

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, and M. Segev1, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[Crossref] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered twodimensional photonic lattices,” Nature (London) 446, 52–55 (200).
[Crossref]

Segev, M.

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, “Incoherent white-light solitons in nonlinear periodic lattices,” Phys. Rev. E 73, 056608 (2006).
[Crossref]

R. Pezer, H. Buljan, J. W. Fleischer, G. Bartal, O. Cohen, and M. Segev, “Gap random-phase lattice solitons,” Opt. Express 13, 5013–5023 (2005).
[Crossref] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500–503 (2005).
[Crossref]

J. P. Torres, C. Anastassiou, M. Segev, M. Soljac̆ic, and D. N. Christodoulides, “Transverse instability of incoherent solitons in Kerr media,” Phys. Rev. E 65, 015601 (2001).
[Crossref]

D. Kip, M. Soljac̆ic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

M. Soljac̆ic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered twodimensional photonic lattices,” Nature (London) 446, 52–55 (200).
[Crossref]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990 (1997).
[Crossref]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880(1997).
[Crossref]

D. N. Christodoulides, T H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[Crossref]

Segev1, M.

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, and M. Segev1, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[Crossref] [PubMed]

Shih, M.

C. Jeng, M. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92, 043904 (2004).
[Crossref] [PubMed]

Silberberg, Y.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[Crossref] [PubMed]

Soljac?ic, M.

J. P. Torres, C. Anastassiou, M. Segev, M. Soljac̆ic, and D. N. Christodoulides, “Transverse instability of incoherent solitons in Kerr media,” Phys. Rev. E 65, 015601 (2001).
[Crossref]

D. Kip, M. Soljac̆ic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

M. Soljac̆ic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[Crossref] [PubMed]

Sukhorukov, A. A.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004)
[Crossref]

A. A. Sukhorukov and Y. S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).
[Crossref]

Torres, J. P.

J. P. Torres, C. Anastassiou, M. Segev, M. Soljac̆ic, and D. N. Christodoulides, “Transverse instability of incoherent solitons in Kerr media,” Phys. Rev. E 65, 015601 (2001).
[Crossref]

Vishwanath, A.

M. Soljac̆ic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

Yannouleas, C.

C. Yannouleas and U. Landman, “Spontaneous symmetry breaking in single and molecular quantum dots,” Phys. Rev. Lett. 82, 5325–5328 (1999).
[Crossref]

Nature (London) (3)

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880(1997).
[Crossref]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500–503 (2005).
[Crossref]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered twodimensional photonic lattices,” Nature (London) 446, 52–55 (200).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E (4)

A. A. Sukhorukov and Y. S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).
[Crossref]

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004)
[Crossref]

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, “Incoherent white-light solitons in nonlinear periodic lattices,” Phys. Rev. E 73, 056608 (2006).
[Crossref]

J. P. Torres, C. Anastassiou, M. Segev, M. Soljac̆ic, and D. N. Christodoulides, “Transverse instability of incoherent solitons in Kerr media,” Phys. Rev. E 65, 015601 (2001).
[Crossref]

Phys. Rev. Lett. (8)

C. Jeng, M. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92, 043904 (2004).
[Crossref] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[Crossref] [PubMed]

D. N. Christodoulides, T H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[Crossref]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990 (1997).
[Crossref]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, and M. Segev1, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[Crossref] [PubMed]

M. Soljac̆ic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).
[Crossref] [PubMed]

M. R. Evans, D. P. Foster, C. Godreche, and D. Mukamel, “Spontaneous symmetry breaking in a one dimensional driven diffusive system,” Phys. Rev. Lett. 74, 208–211 (1995).
[Crossref] [PubMed]

C. Yannouleas and U. Landman, “Spontaneous symmetry breaking in single and molecular quantum dots,” Phys. Rev. Lett. 82, 5325–5328 (1999).
[Crossref]

Science (1)

D. Kip, M. Soljac̆ic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Other (1)

Y. S. Kivshar and G. P. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, San Diego, 2003).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Refractive index (b) The dimensionless potential function. The waveguide displacement is d=7 µm. Note that the center is the potential barrier. (c) The bandgap structure. (solid line) The diffraction relation with periodically modulated refractive index. (dotted-line) The diffraction relation in a homogeneous medium. The gray area shows the forbidden band. In the first band, normal diffraction occurs at the central region (kx ~0), while anomalous diffraction occurs near the edge (kx π/d).

Fig. 2.
Fig. 2.

The symmetry breaking of the unstaggered discrete solitons. The input (gray) and output (black) intensity profiles (upper row) and evolution of the beam along z-direction (lower row). (a) n′ 2=0.000585 and Mout =0.0318. (b) n′ 2=0.000729 and Mout =0.2107. (c) Higher nonlinearity results in higher Mout , and higher Mout means more unstable discrete solitons.

Fig. 3.
Fig. 3.

The symmetry breaking of the staggered discrete solitons. The input (gray) and output (black) intensity profiles (upper row) and evolution of the beam along z-direction (lower row). (a) n′ 2=-0.000744 andMout =0.0182. (b) n′ 2=-0.000912 Mout =0.3811. (c) Stronger self-defocusing nonlinear effect leads to more unstable staggered discrete solitons.

Fig. 4.
Fig. 4.

The symmetry breaking of coherent and partially incoherent discrete solitons. The input (gray) and output (black) intensity profiles (upper row) and evolution of the beam along z-direction (lower row). (a) The coherent unstaggered discrete soliton, with n′ 2=0.000639 and Mout =0.0707. (b) The partially incoherent (θ 0=0.0025) unstaggered discrete soliton, with n′ 2=0.000639 and Mout =0.0021. (d) The coherent staggered discrete soliton, with n′ 2=-0.000936 and Mout =0.5048. (e) The partially incoherent (θ 0=0.0025 rad) staggered discrete soliton, with n′ 2=-0.000936 and Mout =0.0304. (c)(f) The Mout versus the strength of nonlinearity under different spatial incoherence. (c) for unstaggered and (f) for staggered modes.

Equations (3)

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i A ( x , z ) z + 1 2 k 2 A ( x , z ) x 2 + k 2 [ n 2 A 2 A ( x , z ) ν ( x ) A ( x , z ) ] = 0 ,
M = I pr I pl I pr + I pl ,
i [ A j ( x , z ) z + ( j Δ θ ) A j ( x , z ) x ] + 1 2 k 2 A j ( x , z ) x 2 + k 2 [ n 2 I ( x , z ) A j ( x , z ) ν ( x ) A j ( x , z ) ] = 0 .

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