OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 5 — Feb. 28, 2011
  • pp: 4030–4035

Defect solitons in parity-time periodic potentials

Hang Wang and Jiandong Wang  »View Author Affiliations


Optics Express, Vol. 19, Issue 5, pp. 4030-4035 (2011)
http://dx.doi.org/10.1364/OE.19.004030


View Full Text Article

Enhanced HTML    Acrobat PDF (761 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this article, properties of solitons in a parity-time periodical lattices with a single-sited defect are investigated. Both of the negative and positive defects are considered. Linear stability analyses show that, when the defect is positive, in the semi-infinite gap, the solitons are always stable, while in the first gap, the solitons are unstable in most of their existence region except for those near the edge of the second band; when the defect is negative, in the semi-infinite gap, other than those near the edge of the first band, most solitons are stable, but in the first gap, all solitons are unstable. Such stability analyses are corroborated by numerical simulations.

© 2011 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 5, 2011
Revised Manuscript: February 5, 2011
Manuscript Accepted: February 7, 2011
Published: February 15, 2011

Citation
Hang Wang and Jiandong Wang, "Defect solitons in parity-time periodic potentials," Opt. Express 19, 4030-4035 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-5-4030


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998). [CrossRef]
  2. C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002). [CrossRef]
  3. C. M. Bender, D. C. Brody, and H. F. Jones, “Must a Hamiltonian be Hermitian?” Am. J. Phys. 71, 1095–1102 (2003). [CrossRef]
  4. Z. Ahmed, “Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT - invariant potential,” Phys. Lett. A 282, 343–348 (2001). [CrossRef]
  5. C. M. Bender, D. C. Brody, H. F. Jones, and B. K. Meister, “Faster than Hermitian quantum mechanics,” Phys. Rev. Lett. 98, 040403 (2007). [CrossRef] [PubMed]
  6. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008). [CrossRef] [PubMed]
  7. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008). [CrossRef] [PubMed]
  8. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010). [CrossRef]
  9. C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity -time symmetry in optics,” Nat. Phys. 6, 192–195 (2010). [CrossRef]
  10. A. A. Sukhorukov and Yu. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001). [CrossRef] [PubMed]
  11. I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. 96, 223903 (2006). [CrossRef] [PubMed]
  12. M. Skorobogatiy and J. Yang, Fundamentals of Photonic Crystal Guiding (Cambridge University Press, 2009).
  13. L. M. Molina and R. A. Vicencio, “Trapping of discrete solitons by defects in nonlinear waveguide arrays,” Opt. Lett. 31, 966–968 (2006). [CrossRef]
  14. P. P. Belicev, I. Ilic, M. Stepic, A. Maluckov, Y. Tan, and F. Chen, “Observation of linear and nonlinear strongly localized modes at phase-slip defects in one-dimensional photonic lattices,” Opt. Lett. 35, 3099–3101 (2010). [CrossRef] [PubMed]
  15. A. Szameit, M. I. Molina, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, and Y. S. Kivshar, “Observation of localized modes at phase slips in two-dimensional photonic lattices,” Opt. Lett. 35, 2738–2740 (2010). [CrossRef] [PubMed]
  16. F. Fedele, J. Yang, and Z. Chen, “Properties of defect modes in one-dimensional optically induced photonic lattices,” Stud. Appl. Math. 115, 279–301 (2005). [CrossRef]
  17. J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73, 026609 (2006). [CrossRef]
  18. X. Wang, J. Young, Z. Chen, D. Weinstein, and J. Yang, “Observation of lower to higher bandgap transition of one-dimensional defect modes,” Opt. Express 14, 7362–7367 (2006). [CrossRef] [PubMed]
  19. J. Wang, J. Yang, and Z. Chen, “Two-dimensional defect modes in optically induced photonic lattices,” Phys. Rev. A 76, 013828 (2007). [CrossRef]
  20. W. H. Chen, X. Zhu, T. W. Wu, and R. H. Li, “Defect solitons in two-dimensional optical lattices,” Opt. Express 18, 10956–10961 (2010). [CrossRef] [PubMed]
  21. A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34, 797–799 (2009). [CrossRef] [PubMed]
  22. W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271–11276 (2006). [CrossRef] [PubMed]
  23. W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect linear modes in one-dimensional photonic lattices,” Phys. Lett. A 372, 3525–3530 (2008). [CrossRef]
  24. K. Zhou, Z. Guo, J. Wang, and S. Liu, “Defect modes in defective parity-time symmetric periodic complex potentials,” Opt. Lett. 35, 2928–2930 (2010). [CrossRef] [PubMed]
  25. J. Yang and T. I. Lakoba, “Universally convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations,” Stud. Appl. Math. 118, 153–197 (2007). [CrossRef]
  26. J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 227, 6862–6876 (2008). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited