OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 17 — Aug. 13, 2012
  • pp: 19355–19362

Solitons in parity-time symmetric potentials with spatially modulated nonlocal nonlinearity

Chengping Yin, Yingji He, Huagang Li, and Jianing Xie  »View Author Affiliations

Optics Express, Vol. 20, Issue 17, pp. 19355-19362 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1199 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We study the solitons in parity-time symmetric potential in the medium with spatially modulated nonlocal nonlinearity. It is found that the coefficient of the spatially modulated nonlinearity and the degree of the uniform nonlocality can profoundly affect the stability of solitons. There exist stable solitons in low-power region, and unstable solitons in high-power region. In the unstable cases, the solitons exhibit jump from the original site to the next one, and they can continue the motion into the other lattices. The region of the stable soliton can be expanded by increasing the coefficient of the modulated nonlocality. Finally, critical amplitude of the imaginary part of the linear PT lattices is obtained, above which solitons are unstable and decay immediately.

© 2012 OSA

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Nonlinear Optics

Original Manuscript: May 31, 2012
Revised Manuscript: June 26, 2012
Manuscript Accepted: July 6, 2012
Published: August 9, 2012

Chengping Yin, Yingji He, Huagang Li, and Jianing Xie, "Solitons in parity-time symmetric potentials with spatially modulated nonlocal nonlinearity," Opt. Express 20, 19355-19362 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. M. Bender and S. Boettcher, “Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry,” Phys. Rev. Lett.80(24), 5243–5246 (1998). [CrossRef]
  2. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical Solitons in PT Periodic Potentials,” Phys. Rev. Lett.100(3), 030402 (2008). [CrossRef] [PubMed]
  3. K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam Dynanics in PT Symmetric Optical Lattices,” Phys. Rev. Lett.100, 103904 (2008).
  4. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A81(6), 063807 (2010).
  5. C. E. Rüter, K. G. Makris, R. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys.6, 192–195 (2010).
  6. A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry Breaking in Complex Optical Potentials,” Phys. Rev. Lett.103(9), 093902 (2009). [CrossRef] [PubMed]
  7. O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially Fragile PT Symmetry in Lattices with Localized Eigenmodes,” Phys. Rev. Lett.103(3), 030402 (2009). [CrossRef] [PubMed]
  8. K. Zhou, Z. Guo, J. Wang, and S. Liu, “Defect modes in defective parity-time symmetric periodic complex potentials,” Opt. Lett.35(17), 2928–2930 (2010). [CrossRef] [PubMed]
  9. H. Wang and J. Wang, “Defect solitons in parity-time periodic potentials,” Opt. Express19(5), 4030–4035 (2011). [CrossRef] [PubMed]
  10. L. Chen, R. Li, N. Yang, D. Chen, and L. Li, “Optical modes in PT-symmetric double-channel waveguides,” Proc. Romanian Acad. A13, 46–54 (2012).
  11. S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A85(2), 023822 (2012). [CrossRef]
  12. R. Driben and B. A. Malomed, “Stability of solitons in parity-time-symmetric couplers,” Opt. Lett.36(22), 4323–4325 (2011). [CrossRef] [PubMed]
  13. S. Liu, C. Ma, Y. Zhang, and K. Lu, “Bragg gap solitons in PT symmetric lattices with competing nonlinearity,” Opt. Commun.285(7), 1934–1939 (2012). [CrossRef]
  14. F. Kh. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-Symmetric nonlinear lattices,” Phys. Rev. A83(4), 041805 (2011). [CrossRef]
  15. D. A. Zezyulin and V. V. Konotop, “Nonlinear Modes in Finite-Dimensional PT -Symmetric Systems,” Phys. Rev. Lett.108(21), 213906 (2012). [CrossRef]
  16. X. Zhu, H. Wang, L. X. Zheng, H. G. Li, and Y. J. He, “Gap solitons in parity-time complex periodic optical lattices with the real part of superlattices,” Opt. Lett.36(14), 2680–2682 (2011). [CrossRef] [PubMed]
  17. H. Li, Z. Shi, X. Jiang, and X. Zhu, “Gray solitons in parity-time symmetric potentials,” Opt. Lett.36(16), 3290–3292 (2011). [CrossRef] [PubMed]
  18. Z. Shi, X. Jiang, X. Zhu, and H. Li, “Bright spatial solitons in defousing Kerr media with PT-symmetric potentials,” Phys. Rev. A84(5), 053855 (2011). [CrossRef]
  19. Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattices solitons in PT-Symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A85(1), 013831 (2012). [CrossRef]
  20. Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Solitons in PT-symmetric optical lattices with spatially periodic modulation of nonlinearity,” Opt. Commun.285(15), 3320–3324 (2012). [CrossRef]
  21. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Lattice-supported surface solitons in nonlocal nonlinear media,” Opt. Lett.31(17), 2595–2597 (2006). [CrossRef] [PubMed]
  22. F. Ye, Y. V. Kartashov, and L. Torner, “Nonlocal surface dipoles and vortices,” Phys. Rev. A77(3), 033829 (2008). [CrossRef]
  23. Z. Xu, Y. V. Kartashov, and L. Torner, “Soliton mobility in nonlocal optical lattices,” Phys. Rev. Lett.95(11), 113901 (2005). [CrossRef] [PubMed]
  24. S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A85(4), 043826 (2012). [CrossRef]
  25. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett.33(15), 1747–1749 (2008). [CrossRef] [PubMed]
  26. Y. He, D. Mihalache, and B. Hu, “Soliton drift, rebound, penetration, and trapping at the interface between media with uniform and spatially modulated nonlinearities,” Opt. Lett.35(10), 1716–1718 (2010). [CrossRef] [PubMed]
  27. D. Blömer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tünnermann, “Nonlinear refractive index of fs-laser-written waveguides in fused silica,” Opt. Express14(6), 2151–2157 (2006). [CrossRef] [PubMed]
  28. M. Theis, G. Thalhammer, K. Winkler, M. Hellwig, G. Ruff, R. Grimm, and J. Hecker Denschlag, “Tuning the Scattering Length with an Optically Induced Feshbach Resonance,” Phys. Rev. Lett.93(12), 123001 (2004). [CrossRef] [PubMed]
  29. G. Hwang, T. I. Akylas, and J. Yang, “Solitary Waves and Their Linear Stability in Nonlinear Lattices,” Stud. Appl. Math.128(3), 275–298 (2012). [CrossRef]
  30. H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A81(1), 013624 (2010). [CrossRef]
  31. H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(4), 046610 (2005). [CrossRef] [PubMed]
  32. Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys.83(1), 247–306 (2011). [CrossRef]
  33. M. J. Ablowitz and Z. H. Musslimani, “Spectral renormalization method for computing self-localized solutions to nonlinear systems,” Opt. Lett.30(16), 2140–2142 (2005). [CrossRef] [PubMed]

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited