OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 14 — Jul. 7, 2008
  • pp: 10189–10199

Trapping dynamics in nonlinear wave scattering by local guiding defects

Yoav Linzon, Yaron Shavit, and Shimshon Bar-Ad  »View Author Affiliations

Optics Express, Vol. 16, Issue 14, pp. 10189-10199 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (1146 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We study numerically the trapping dynamics of nonlinear waves scattered by local guiding photonic centers with normal eigenmodes which are embedded in uniform nonlinear Kerr waveguides. The linear and nonlinear scattering from a local defect may be treated from either a wave optics approach or a ray optics approach. The former provides a better understanding of the wave dynamics while the latter enables one to perform quasi-analytical estimates of the extent of trapping in a given structure. In the presence of a single-site multi-mode local scattering center, power may localize in a certain normal mode of the center, or periodically oscillate between different normal modes. The degree of trapping and mode of localization can be controlled as function of both the input power and the angle of incidence. With multi-site local scattering centers, the trapping dynamics are strongly dependent on the degree of coupling between the neighboring sites. In the scattering by a local multi-site defect with strongly coupled adjacent sites, two possibilities for nonlinear trapping arise. At intermediate nonlinear powers, periodic tunneling of power between adjacent sites and their normal modes is observed. At highly nonlinear powers, but still within experimental feasibility, the radiation can become strongly localized in a single site. The scattering and trapping dynamics are also described in the context of nonlinear Fabry-Perot etalons, as a function of the local defect’s refractive index.

© 2008 Optical Society of America

OCIS Codes
(190.4360) Nonlinear optics : Nonlinear optics, devices
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(290.0290) Scattering : Scattering
(240.3695) Optics at surfaces : Linear and nonlinear light scattering from surfaces

ToC Category:
Nonlinear Optics

Original Manuscript: May 9, 2008
Manuscript Accepted: June 10, 2008
Published: June 23, 2008

Yoav Linzon, Yaron Shavit, and Shimshon Bar-Ad, "Trapping dynamics in nonlinear wave scattering by local guiding defects," Opt. Express 16, 10189-10199 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. See, for example:P. P. Banerjee, Nonlinear Optics: Theory, Numerical Modeling and Applications (Taylor and Francis, London, 2007).
  2. Z. V. Vardeny and M. Raikh, "Photonics: Light localized on the lattice," Nature 446, 37-38 (2007). [CrossRef] [PubMed]
  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. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998). [CrossRef]
  5. F. Geniet and J. Leon, "Energy transmission in the forbidden band gap of a nonlinear chain," Phys. Rev. Lett. 89, 134102 (2002). [CrossRef] [PubMed]
  6. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 093904 (2004). [CrossRef] [PubMed]
  7. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-2468 (2005). [CrossRef] [PubMed]
  8. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006). [CrossRef] [PubMed]
  9. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Bragg-type soliton mirror," Opt. Express 14, 1576-1581 (2006). [CrossRef] [PubMed]
  10. X. D. Cao and B. A. Malomed, "Soliton-defect collisions in the nonlinear Schrodinger equation," Phys. Lett. A 206, 177-182 (1995). [CrossRef]
  11. A. E. Miroshnichenko, S. Flach, and B. Malomed, "Resonant scattering of solitons," Chaos 13, 874-879 (2003). [CrossRef] [PubMed]
  12. H. Sakaguchi and M. Tamura, "Scattering and trapping of nonlinear schrodinger solitons in external potentials," J. Phys. Soc. Jpn. 73, 503-506 (2004). [CrossRef]
  13. R. H. Goodman, P. J. Holmes, and M. I. Weinstein, "Strong NLS soliton-defect interactions," Physica D 192, 215-248 (2004). [CrossRef]
  14. K. T. Stoychev, M. T. Primatarowa, and R. S. Kamburova, "Resonant scattering of nonlinear Schrdinger solitons from potential wells," Phys. Rev. E 70, 066622 (2004). [CrossRef]
  15. H. Sakaguchi and M. Tamura, "Scattering of solitons and dark solitons by potential walls in the nonlinear schrodinger equation," J. Phys. Soc. Jpn. 74, 292-298 (2005). [CrossRef]
  16. B. Piette, W. J. Zakrzewski, and J. Brand, "Scattering of topological solitons on holes and barriers," J. Phys. A 38, 1040310412 (2005). [CrossRef]
  17. J. Garnier and F. Kh. Abdullaev, "Transmission of matter-wave solitons through nonlinear traps and barriers," Phys. Rev. A 74, 013604 (2006). [CrossRef]
  18. C. Lee and J. Brand, "Enhanced quantum reflection of matter-wave solitons," Europhys. Lett. 73, 321-327 (2006). [CrossRef]
  19. K. Rapedius, D. Witthaut, and H. J. Korsch, "Analytical study of resonant transport of Bose-Einstein condensates," Phys. Rev. A 73, 033608 (2006). [CrossRef]
  20. Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, "Nonlinear scattering and trapping by local photonic potentials," Phys. Rev. Lett. 99, 133901 (2007). [CrossRef] [PubMed]
  21. Y. Shavit, Y. Linzon, S. Bar-Ad, R. Morandotti, M. Volatier, V. Aimez, and R. Ares, "Power-dependent switching of nonlinear trapping by local photonic potentials," Opt. Lett. 33, 1056-1058 (2008). [CrossRef] [PubMed]
  22. D. Mandelik, Y. Lahini, and Y. Silberberg, "Nonlinearly induced relaxation to the ground state in a two-level system," Phys. Rev. Lett. 95, 073902 (2005). [CrossRef] [PubMed]
  23. A. Soffer and M. I. Weinstein, "Theory of nonlinear dispersive waves and selection of the ground state," Phys. Rev. Lett. 95, 213905 (2005). [CrossRef] [PubMed]
  24. J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907 (2003). [CrossRef] [PubMed]
  25. Y. Linzon, Y. Shavit, M. Elazar, R. Morandotti, M. Volatier-Ravat, V. Aimez, R. Ares, and S. Bar-Ad, "Single beam mapping of nonlinear phase shift profiles in planar waveguides with an embedded mirror," Opt. Express 15, 12068-12075 (2007). [CrossRef] [PubMed]
  26. J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The nonlinear optical properties of AlGaAs at the half band gap," IEEE J. Quant. Electron. 33, 341-348 (1997). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited