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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  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. Soljačic, 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. Soljačic, 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. Soljačic, 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. Segev, "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 (2007).
    [CrossRef]

2007

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, "Transport and Anderson localization in disordered twodimensional photonic lattices," Nature (London) 446, 52-55 (2007).
[CrossRef]

2006

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

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

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, and M. Segev, "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

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

2001

J. P. Torres, C. Anastassiou, M. Segev, M. Soljačic, 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

M. Soljačic, 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. Soljačic, 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

C. Yannouleas and U. Landman, "Spontaneous symmetry breaking in single and molecular quantum dots," Phys. Rev. Lett. 82, 5325-5328 (1999).
[CrossRef]

1997

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

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

Nature (London)

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 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

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]

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]

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

Phys. Rev. Lett.

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]

M. Soljačic, 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]

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

Science

D. Kip, M. Soljačic, 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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

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

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 .

Metrics