OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 15, Iss. 2 — Feb. 1, 1998
  • pp: 607–616

Temporal modulation instabilities of counterpropagating waves in a finite dispersive Kerr medium. I. Theoretical model and analysis

M. Yu, C. J. McKinstrie, and Govind P. Agrawal  »View Author Affiliations

JOSA B, Vol. 15, Issue 2, pp. 607-616 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (280 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



This paper presents a comprehensive analytical study of temporal modulation instabilities in a finite, nonlinear, dispersive medium in which two counterpropagating pump beams interact through a Kerr-type nonlinearity. The analysis includes self- and cross-phase modulations, group-velocity dispersion, four-wave mixing, and reflections occurring at the two facets of the dispersive Kerr medium. The use of a new method based on a small-parameter analysis has resulted in a physically transparent model in terms of a doubly resonant optical parametric oscillator that allows characterization of the complicated nonlinear system in a familiar language. The effects of boundary reflections are shown to be very important. In the low-frequency limit, in which dispersive effects are negligible, our results reduce to those obtained previously. At high frequencies, dispersive effects lead to new instabilities both in the normal- and anomalous-dispersion regions of the dispersive Kerr medium. The anomalous-dispersion case is discussed in detail after including weak boundary reflections. The growth rate and the threshold for the absolute instability are obtained in an analytical form for arbitrary pump–power ratios. Our analytic results are in agreement with previous numerical work done by neglecting boundary reflections and assuming equal powers for the counterpropagating pump beams.

© 1998 Optical Society of America

OCIS Codes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(190.0190) Nonlinear optics : Nonlinear optics
(190.3270) Nonlinear optics : Kerr effect
(270.3100) Quantum optics : Instabilities and chaos

M. Yu, C. J. McKinstrie, and Govind P. Agrawal, "Temporal modulation instabilities of counterpropagating waves in a finite dispersive Kerr medium. I. Theoretical model and analysis," J. Opt. Soc. Am. B 15, 607-616 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. W. J. Firth, Opt. Commun. 39, 343 (1981). [CrossRef]
  2. Y. Silberberg and I. Bar-Joseph, J. Opt. Soc. Am. B 1, 662 (1984). [CrossRef]
  3. W. J. Firth and C. Paré, Opt. Lett. 13, 1096 (1989); W. J. Firth, C. Paré, and A. FitzGerald, J. Opt. Soc. Am. B 7, 1087 (1990). [CrossRef]
  4. C. T. Law and A. E. Kaplan, Opt. Lett. 14, 734 (1989); J. Opt. Soc. Am. B 8, 58 (1991). [CrossRef] [PubMed]
  5. W. J. Firth and C. Penman, Opt. Commun. 94, 183 (1992). [CrossRef]
  6. R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992).
  7. K. Ikeda, Opt. Commun. 30, 257 (1979). [CrossRef]
  8. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  9. R. Vallée, Opt. Commun. 81, 419 (1991); Opt. Commun. 93, 389 (1992). [CrossRef]
  10. M. B. van der Mark, J. M. Schins, and A. Lagendijk, Opt. Commun. 98, 120 (1993). [CrossRef]
  11. G. Steinmeyer, D. Jaspert, and F. Mitschke, Opt. Commun. 104, 379 (1994). [CrossRef]
  12. M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989); M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989). [CrossRef]
  13. M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992); Opt. Lett. 17, 745 (1992). [CrossRef]
  14. D. W. McLaughlin, J. V. Moloney, and A. C. Newell, Phys. Rev. Lett. 54, 681 (1985). [CrossRef] [PubMed]
  15. M. Haelterman, Opt. Lett. 17, 792 (1992). [CrossRef]
  16. A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981).
  17. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, New York, 1993), Chap. 7.
  18. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 9.
  19. Y. Yu, C. McKinstrie, and G. P. Agrawal, J. Opt. Soc. Am. B 14, 617 (1998). [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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited