OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 15, Iss. 3 — Mar. 1, 1998
  • pp: 1061–1068

Exact representations for coupled bright and dark solitary waves of quadratically nonlinear systems

D. F. Parker  »View Author Affiliations

JOSA B, Vol. 15, Issue 3, pp. 1061-1068 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (285 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A thorough search is performed for all cases in which solutions of the quadratically coupled nonlinear equations for χ(2) cascading may be expressed in terms of hyperbolic functions. This reveals two new classes (IV and VI) in addition to classes I–III, which have appeared in many recent papers. These new solutions describe pulses with a nonzero cw background in one or both modes. They include bright–dark, brighter–brighter, twin-hole, and dark–dark solutions, and each contains an adjustable parameter related to the phase shift across the pulse. For a planar waveguide, any of the class VI profiles may arise for any choice of pulse orientation parameters κJ giving pp˜>0, whereas any of the class IV profiles may arise if pp˜<0. In each case, the choice then determines the remaining pulse parameters in the exact representation.

© 1998 Optical Society of America

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(190.0190) Nonlinear optics : Nonlinear optics
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(230.7390) Optical devices : Waveguides, planar
(250.5530) Optoelectronics : Pulse propagation and temporal solitons

D. F. Parker, "Exact representations for coupled bright and dark solitary waves of quadratically nonlinear systems," J. Opt. Soc. Am. B 15, 1061-1068 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988). [CrossRef] [PubMed]
  2. M. V. Tratnik and J. E. Sipe, “Bound solitary waves in a birefringent optical fibre,” Phys. Rev. A 38, 2011–2017 (1988). [CrossRef] [PubMed]
  3. C. R. Menyuk, “Pulse propagation in an elliptically birefringent Kerr medium,” IEEE J. Quantum Electron. QE-25, 2674–2682 (1989). [CrossRef]
  4. D. F. Parker and G. K. Newboult, “Coupled nonlinear Schrödinger equations arising in fibre optics,” J. Phys. Colloq. 50, 137–146 (1989). [CrossRef]
  5. L. Wang and C. C. Yang, “Existence of coupled solitary waves in optical fibers owing to mutual support between bright and dark pulses,” Opt. Lett. 15, 474–476 (1990). [CrossRef] [PubMed]
  6. Yu. S. Kivshar, “Stable vector solitons composed of bright and dark pulses,” Opt. Lett. 17, 1322–1324 (1992). [CrossRef] [PubMed]
  7. Yu. S. Kivshar, A. V. Buryak, and D. F. Parker, “Coupling between bright and dark solitons,” Phys. Lett. A 215, 57–62 (1996). [CrossRef]
  8. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992). [CrossRef] [PubMed]
  9. K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear media,” Phys. Rev. Lett. 71, 3275–3278 (1993). [CrossRef] [PubMed]
  10. M. J. Werner and P. D. Drummond, “Simulton solutions for the parametric amplifier,” J. Opt. Soc. Am. B 10, 2390–2393 (1993). [CrossRef]
  11. M. J. Werner and P. D. Drummond, “Strongly coupled nonlinear parametric solitary waves,” Opt. Lett. 19, 613–615 (1994). [CrossRef] [PubMed]
  12. A. V. Buryak and Yu. S. Kivshar, “Solitons due to second harmonic generation,” Phys. Lett. A 197, 407–412 (1995). [CrossRef]
  13. C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ(2): χ(2) cascading,” J. Opt. Soc. Am. B 11, 2434–2443 (1994). [CrossRef]
  14. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal-processing, mode-locking, pulse-compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996). [CrossRef]
  15. A. V. Buryak, “Solitons due to quadratic nonlinearities,” Ph.D. thesis (Australian National University, Canberra, 1996).
  16. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871–873 (1988). [CrossRef] [PubMed]
  17. V. V. Afanasjev, Yu. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright solitons,” Opt. Lett. 14, 805–807 (1989). [CrossRef]
  18. P. Ferro and S. Trillo, “Periodical waves, domain walls, and modulational instability in dispersive quadratic media,” Phys. Rev. E 51, 4944–4951 (1995). [CrossRef]
  19. A. V. Buryak and Yu. S. Kivshar, “Dark solitons in dispersive quadratic media,” Opt. Lett. 20, 834–836 (1995). [CrossRef] [PubMed]
  20. H. He, P. D. Drummond, and B. A. Malomed, “Modulational stability in dispersive optical systems with cascaded nonlinearity,” in Proceedings of the Twentieth Australian Conference on Optical Fibre Technology (IREE Society, Milsons Point, Australia, 1995), pp. 259–262.
  21. Yu. N. Karamzin and A. P. Sukhorukov, “Nonlinear interaction of diffracted beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters,” JETP Lett. 20, 339–342 (1974).
  22. Yu. S. Kivshar and V. V. Afanasjev, “Drift instability of dark solitons in saturable media,” Opt. Lett. 21, 1135–1137 (1996). [CrossRef] [PubMed]
  23. A. V. Porubov and D. F. Parker, “Some general periodic solutions to coupled nonlinear Schrödinger equations,” submitted to Wave Motion.

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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited