OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 15, Iss. 5 — May. 1, 1998
  • pp: 1488–1496

Bright and dark solitary waves in the presence of third-harmonic generation

Rowland A. Sammut, Alexander V. Buryak, and Yuri S. Kivshar  »View Author Affiliations

JOSA B, Vol. 15, Issue 5, pp. 1488-1496 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (289 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We analyze the effect of phase-matched third-harmonic generation on the existence and stability of (1+1)-dimensional bright and dark spatial solitary waves in optical media with a cubic (or Kerr) nonlinear response. We demonstrate that parametric coupling of the fundamental beam with the third harmonic leads to the existence of two-color solitary waves resembling those in a χ(2) medium and that it can modify drastically the properties of solitary waves due to effective non-Kerr nonlinearities. In particular, we find a power threshold for the existence of two-frequency parametric bright solitons and also reveal the soliton multistability in a Kerr medium that becomes possible owing to a higher-order nonlinear phase shift caused by cascaded third-order processes. We also analyze dark solitary waves and their stabilities. We show that, in a certain parameter domain, parametric χ(3) dark solitons may become unstable owing to the modulational instability of the supporting background or to other instability mechanisms caused by the parametric coupling between the harmonics.

© 1998 Optical Society of America

OCIS Codes
(190.3270) Nonlinear optics : Kerr effect
(190.4160) Nonlinear optics : Multiharmonic generation
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

Rowland A. Sammut, Alexander V. Buryak, and Yuri S. Kivshar, "Bright and dark solitary waves in the presence of third-harmonic generation," J. Opt. Soc. Am. B 15, 1488-1496 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. L. Mills, Nonlinear Optics: Basic Concepts (Springer-Verlag, Berlin, 1991); R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
  2. I. V. Tomov and M. C. Richardson, IEEE J. Quantum Electron. 12, 521 (1976). [CrossRef]
  3. See, for example, the recent review paper on cascading in χ(2) materials, G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996). [CrossRef]
  4. Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976); A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981); R. Schiek, J. Opt. Soc. Am. B JOBPDE 10, 1848 (1993); A. V. Buryak and Yu. S. Kivshar, Opt. Lett. OPLEDP 19, 1612 (1994); L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. OPLEDP 19, 1615 (1994). [CrossRef] [PubMed]
  5. A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995). [CrossRef]
  6. D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995). [CrossRef] [PubMed]
  7. A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996). [CrossRef] [PubMed]
  8. A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997). [CrossRef]
  9. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996); R. A. Furst, D. M. Baboiu, B. L. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. PRLTAO 78, 2756 (1997). [CrossRef] [PubMed]
  10. S. Saltiel, S. Tanev, and A. D. Boardman, Opt. Lett. 22, 148 (1997). [CrossRef] [PubMed]
  11. See, e.g., R. W. Micallef, V. V. Afanasjev, Yu. S. Kivshar, and J. D. Love, Phys. Rev. E 54, 2936 (1996) and references therein. [CrossRef]
  12. N. A. Ansari, R. A. Sammut, and H. T. Tran, J. Opt. Soc. Am. B 13, 1419 (1996); 14, 298 (1997). [CrossRef]
  13. This exact solution has been presented previously in the papers by K. Hayata and M. Koshiba, Opt. Lett. 19, 1717 (1994), and Y. Chen, Phys. Rev. A 50, 5145 (1994). However, unlike the theory of solitary waves in quadratic media, in the case of third-harmonic generation the exact hyperbolic-secant-like solution does not give any useful information about the families of proper (stable) two-wave solitary waves. [CrossRef] [PubMed]
  14. A. E. Kaplan, Phys. Rev. Lett. 55, 1291 (1985); IEEE J. Quantum Electron. 21, 1538 (1985). [CrossRef] [PubMed]
  15. A. W. Snyder, D. J. Mitchell, and A. V. Buryak, J. Opt. Soc. Am. B 13, 1146 (1996). [CrossRef]
  16. Yu. S. Kivshar and W. Krolikowski, Opt. Lett. 20, 1527 (1995); Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996); D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E PLEEE8 54, 2015 (1996). [CrossRef] [PubMed]
  17. See the review paper by Yu. S. Kivshar and B. Luther-Davies, “Dark optical solitons:physics and applications,” Phys. Rep. (to be published).
  18. A. V. Buryak, Phys. Rev. E 52, 1156 (1995); “Solitons due to second harmonic generation,” Ph.D. dissertation (The Australian National University, Canberra, Australia, 1996). [CrossRef]
  19. A. V. Buryak and Yu. S. Kivshar, Phys. Rev. A 51, R41 (1995). [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