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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 1 — Jan. 1, 2013
  • pp: 113–122

Three-dimensional spatiotemporal vector solitary waves in coupled nonlinear Schrödinger equations with variable coefficients

Si-Liu Xu, Milivoj R. Belić, and Wei-Ping Zhong  »View Author Affiliations


JOSA B, Vol. 30, Issue 1, pp. 113-122 (2013)
http://dx.doi.org/10.1364/JOSAB.30.000113


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Abstract

We introduce three-dimensional (3D) spatiotemporal vector solitary waves in coupled (3+1)D nonlinear Schrödinger equations with variable diffraction and nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing for novel localized solutions. Using the Hirota bilinear method, 3D approximate but analytical spatiotemporal vector solitary waves are built with the help of spherical harmonics, including multipole solutions and necklace rings. Variable diffraction and nonlinearity allow utilization of soliton management methods. The comparison with numerical solutions is provided and the behavior of relative error is displayed. It is demonstrated that the spatiotemporal soliton profiles found are stable in propagation.

© 2012 Optical Society of America

OCIS Codes
(190.3270) Nonlinear optics : Kerr effect
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: July 19, 2012
Revised Manuscript: October 19, 2012
Manuscript Accepted: November 7, 2012
Published: December 12, 2012

Citation
Si-Liu Xu, Milivoj R. Belić, and Wei-Ping Zhong, "Three-dimensional spatiotemporal vector solitary waves in coupled nonlinear Schrödinger equations with variable coefficients," J. Opt. Soc. Am. B 30, 113-122 (2013)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-1-113


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References

  1. B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997). [CrossRef]
  2. H. He and P. D. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998). [CrossRef]
  3. D. Mihalache, D. Mazilu, J. Dōrring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999). [CrossRef]
  4. M. Blaauboer, B. A. Malomed, and G. Kurizki, “Temporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000). [CrossRef]
  5. L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001). [CrossRef]
  6. P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003). [CrossRef]
  7. X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634(1999). [CrossRef]
  8. G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999). [CrossRef]
  9. X. Liu, K. Beckwitt, and F. W. Wise, “Noncollinear generation of optical spatiotemporal solitons and application to ultrafast digital logic,” Phys. Rev. E 61, R4722–R4725 (2000). [CrossRef]
  10. V. E. Lobanov, Y. V. Kartashov, and L. Torner, “Light bullets by synthetic diffraction-dispersion matching,” Phys. Rev. Lett. 105, 033901 (2010). [CrossRef]
  11. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007). [CrossRef]
  12. A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991). [CrossRef]
  13. W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373, 296–298 (2009). [CrossRef]
  14. I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009). [CrossRef]
  15. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008). [CrossRef]
  16. A. S. Desyatnikov and Yu. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87, 033901 (2001). [CrossRef]
  17. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002). [CrossRef]
  18. D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, “Interface discrete light bullets in waveguide arrays,” Opt. Lett. 32, 2091–2093 (2007). [CrossRef]
  19. L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1131 (2009). [CrossRef]
  20. W. P. Zhong, M. Belic, R. H. Xie, and G. Chen, “Two-dimensional Whittaker solitons in nonlocal nonlinear media,” Phys. Rev. A 78, 013826 (2008). [CrossRef]
  21. S. K. Adhikari, “Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose–Einstein condensate by temporal modulation of the scattering length,” Phys. Rev. A 69, 063613 (2004). [CrossRef]
  22. S. K. Adhikari, “Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity,” Phys. Rev. E 70, 036608 (2004). [CrossRef]
  23. S. K. Adhikari, “Stabilization of a (3+1)D soliton in a Kerr medium by a rapidly oscillating dispersion coefficient,” Phys. Rev. E 71, 016611 (2005). [CrossRef]
  24. J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005). [CrossRef]
  25. D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E 70, 055603R (2004). [CrossRef]
  26. D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005). [CrossRef]
  27. H. Leblond, B. A. Malomed, and D. Mihalache, “Three-dimensional vortex solitons in quasi-two-dimensional lattices,” Phys. Rev. E 76, 026604 (2007). [CrossRef]
  28. J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007). [CrossRef]
  29. J. He and Y. Li, “Designable integrability of the variable coefficient nonlinear Schrödinger equations,” Stud. Appl. Math. 126, 1–15 (2011). [CrossRef]
  30. W. Ping Zhong, M. Belić, G. Assanto, and T. Huang, “Three-dimensional spatiotemporal vector solitary waves,” J. Phys. B 44, 095403 (2011). [CrossRef]
  31. M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008). [CrossRef]
  32. W. P. Zhong, L. Yi, R. H. Xie, M. Belić, and G. Chen, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. B 41, 025402 (2008). [CrossRef]
  33. R. Hirota, “Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons,” Phys. Rev. Lett. 27, 1192–1194 (1971). [CrossRef]
  34. B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2005).
  35. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose–Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999). [CrossRef]

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