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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 19, Iss. 5 — May. 1, 2002
  • pp: 1216–1217

Exact soliton solutions of the nonlinear Helmholtz equation: communication

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New  »View Author Affiliations


JOSA B, Vol. 19, Issue 5, pp. 1216-1217 (2002)
http://dx.doi.org/10.1364/JOSAB.19.001216


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Abstract

Exact analytical soliton solutions of the nonlinear Helmholtz equation are reported. A lucid generalization of paraxial soliton theory that incorporates nonparaxial effects is found.

© 2002 Optical Society of America

OCIS Codes
(190.3270) Nonlinear optics : Kerr effect
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(240.4350) Optics at surfaces : Nonlinear optics at surfaces

Citation
P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, "Exact soliton solutions of the nonlinear Helmholtz equation: communication," J. Opt. Soc. Am. B 19, 1216-1217 (2002)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-5-1216


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References

  1. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Non-paraxial solitons,” J. Mod. Opt. 45, 1111–1121 (1998). [CrossRef]
  2. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Propagation properties of non-paraxial spatial solitons,” J. Mod. Opt. 47, 1877–1886 (2000). [CrossRef]
  3. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Non-paraxial beam propagation methods,” Opt. Commun. 192, 1–12 (2001). [CrossRef]
  4. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Nonparaxial solitons,” presented at the UK National Conference of Quantum Electronics, Cardiff, UK, 1997.
  5. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Exact analytical nonparaxial optical solitons,” presented at the 1998 International Conference on Quantum Electronics, San Francisco, Calif.
  6. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Nonparaxial solitons: accurate numerical methods and new results,” presented at the 1998 European Conference on Quantum Electronics, Glasgow, UK.
  7. P. Chamorro-Posada, G. S. McDonald, G. H. C. New, J. Noon, and S. Chávez-Cerda, “Fundamental properties of (1+1)D and (2+1)D nonparaxial optical solitons,” presented at the UK National Conference of Quantum Electronics, Manchester, UK, 1999.
  8. T. A. Laine and A. T. Friberg, “Self-guided waves and exact solutions of the nonlinear Helmholtz equation,” J. Opt. Soc. Am. B 17, 751–757 (2000). [CrossRef]
  9. J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media,” Suppl. Prog. Theor. Phys. 55, 284–306 (1974). [CrossRef]
  10. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Does the nonlinear Schrödinger equation correctly describe beam propagation?” Opt. Lett. 18, 411–413 (1993). [CrossRef] [PubMed]
  11. J. M. Soto-Crespo and N. Akhmediev, “Description of the self-focusing and collapse effects by a modified nonlinear Schrodinger equation,” Opt. Commun. 101, 223–230 (1993). [CrossRef]

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