Symmetry breaking of discrete solitons and its suppression by partial incoherence
Optics Express, Vol. 15, Issue 16, pp. 10446-10451 (2007)
http://dx.doi.org/10.1364/OE.15.010446
Acrobat PDF (502 KB)
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
1. Introduction
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]
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]
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]
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]
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]
2. Discrete solitons and symmetry breaking
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]
3. Partially coherent discrete solitons and symmetry breaking
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]
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]
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]
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]
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]
4. Conclusion
References and links
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] |
OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(190.3100) Nonlinear optics : Instabilities and chaos
(190.5940) Nonlinear optics : Self-action effects
ToC Category:
Nonlinear Optics
History
Original Manuscript: July 18, 2007
Revised Manuscript: July 28, 2007
Manuscript Accepted: August 1, 2007
Published: August 2, 2007
Citation
Shao-Chuan Wang and Ming-Feng Shih, "Symmetry breaking of discrete solitons and its suppression by partial
incoherence," Opt. Express 15, 10446-10451 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-16-10446
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References
- 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]
- D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988). [CrossRef] [PubMed]
- Y. S. Kivshar and G. P. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, San Diego, 2003).
- 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]
- 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]
- 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]
- 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. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature (London) 387, 880 (1997). [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]
- 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]
- 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]
- 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]
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