OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 9 — Sep. 1, 2007
  • pp: 2537–2544

Hermite–Gaussian breathers and solitons in strongly nonlocal nonlinear media

Dongmei Deng, Xin Zhao, Qi Guo, and Sheng Lan  »View Author Affiliations


JOSA B, Vol. 24, Issue 9, pp. 2537-2544 (2007)
http://dx.doi.org/10.1364/JOSAB.24.002537


View Full Text Article

Enhanced HTML    Acrobat PDF (928 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Based on the Snyder–Mitchell model in the Cartesian coordinate system, exact analytical Hermite–Gaussian (HG) solutions are obtained in strongly nonlocal nonlinear media. The comparisons of analytical solutions with numerical simulations of the nonlocal nonlinear Schrödinger equation show that the analytical HG solutions are in good agreement with the numerical simulations in the case of strong nonlocality. Furthermore, we demonstrate that HG functions can be expressed as a linear superposition of individual Gaussian functions with a π phase difference under the appropriate conditions.

© 2007 Optical Society of America

OCIS Codes
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers
(190.4360) Nonlinear optics : Nonlinear optics, devices
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 5, 2007
Revised Manuscript: June 21, 2007
Manuscript Accepted: July 13, 2007
Published: August 31, 2007

Citation
Dongmei Deng, Xin Zhao, Qi Guo, and Sheng Lan, "Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media," J. Opt. Soc. Am. B 24, 2537-2544 (2007)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-9-2537


Sort:  Year  |  Journal  |  Reset  

References

  1. A. W. Snyder and D. J. Mitchell, "Accessible solitons," Science 276, 1538-1541 (1997). [CrossRef]
  2. M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, "All-optical switching and logic gating with spatial solitons in liquid crystals," Appl. Phys. Lett. 81, 3335-3337 (2002). [CrossRef]
  3. G. Assanto, M. Peccianti, and C. Conti, "Nematicons: optical spatial solitons in nematic liquid crystals," Opt. Photonics News 14, 44-48 (2003). [CrossRef]
  4. D. J. Mitchell and A. W. Snyder, "Soliton dynamics in a nonlocal medium," J. Opt. Soc. Am. B 16, 236-239 (1999). [CrossRef]
  5. W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E 64, 016612 (2001). [CrossRef]
  6. C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003). [CrossRef] [PubMed]
  7. C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004). [CrossRef] [PubMed]
  8. Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E 69, 016602 (2004). [CrossRef]
  9. Q. Guo, "Nonlocal spatial solitons and their interactions," in Optical Transmission, Switching, and Subsystems, C.F.Lam, C.Fan, N.Hanik, and K.Oguchi, eds., Proc. SPIE 5281, 581-594 (2004).
  10. Y. Xie and Q. Guo, "Phase modulations due to collisions of beam pairs in nonlocal nonlinear media," Opt. Quantum Electron. 36, 1335-1351 (2004). [CrossRef]
  11. A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, "Bound dipole solitary solutions in anisotropic nonlocal self-focusing media," Phys. Rev. A 56, R1110-R1113 (1997). [CrossRef]
  12. M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002). [CrossRef]
  13. X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, "Single-component higher-order mode solitons in liquid crystals," Opt. Commun. 233, 211-217 (2004). [CrossRef]
  14. Z. Xu, Y. V. Kartashov, and L. Torner, "Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media," Opt. Lett. 30, 3171-3173 (2005). [CrossRef] [PubMed]
  15. S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, "Stability of two-dimensional spatial solitons in nonlocal nonlinear media," Phys. Rev. E 73, 066603 (2006). [CrossRef]
  16. A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, "Dynamics of two-dimensional coherent structures in nonlocal nonlinear media," Phys. Rev. E 73, 066605 (2006). [CrossRef]
  17. N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical solitons," Opt. Lett. 29, 286-288 (2004). [CrossRef] [PubMed]
  18. A. Dreischuh, D. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between dark solitons," Phys. Rev. Lett. 96, 043901 (2006). [CrossRef] [PubMed]
  19. D. W. McLaughlin, D. J. Muraki, M. J. Shelley, "Self-focussed optical structures in a nematic liquid crystal," Physica D 97, 471-497 (1996). [CrossRef]
  20. C. Rotschild, M. Segev, Z. Y. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312-3314 (2006). [CrossRef] [PubMed]
  21. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite soliton clusters in nonlocal nonlinear media," Phys. Rev. Lett. 98, 053901 (2007). [CrossRef] [PubMed]
  22. A. W. Snyder and Y. Kivshar, "Bright spatial solitons in non-Kerr media: stationary beams and dynamical evolution," J. Opt. Soc. Am. B 11, 3025-3031 (1997). [CrossRef]
  23. S. Abe and A. Ogura, "Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response," Phys. Rev. E 57, 6066-6070 (1998). [CrossRef]
  24. B. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "Sub-wavelength non-local spatial solitons," Opt. Commun. 166, 121-126 (1999). [CrossRef]
  25. W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: exact solutions," Phys. Rev. E 63, 016610 (2000). [CrossRef]
  26. S. G. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E 74, 036622 (2006). [CrossRef]
  27. P. D. Rasmusen, O. Bang, W. Królikowski, "Theory of nonlocal soliton interaction in nematic liquid crystals," Phys. Rev. E 72, 066611 (2005). [CrossRef]
  28. X. P. Zhang and Q. Guo, "Analytical solution in the Hermite-Gaussian form of the beam propagating in the strong nonlocal media," Acta Phys. Sin. 54, 3178-3182 (2005) (in Chinese).
  29. X. P. Zhang and Q. Guo, "Analytical solution to the spatial optical solitons propagating in the strong nonlocal media," Acta Phys. Sin. 54, 5189-5193 (2005) (in Chinese).
  30. W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006). [CrossRef]
  31. Y. R. Shen, "Optical physics--solitons made simple," Science 276, 1520-1520 (1997). [CrossRef]
  32. W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, "Anomalous interaction of spatial solitons in photorefractive media," Phys. Rev. Lett. 80, 3240-3243 (1998). [CrossRef]
  33. G. E. Andrews, R. Askey, and R. Roy, Special Functions (Cambridge U. Press, 2000), Sec. 6.1.

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