OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 15 — Jul. 26, 2004
  • pp: 3297–3306

Spectral limits for periodic pattern propagation in Kerr media

N. Korneev and E. Morales Rodríguez  »View Author Affiliations


Optics Express, Vol. 12, Issue 15, pp. 3297-3306 (2004)
http://dx.doi.org/10.1364/OPEX.12.003297


View Full Text Article

Enhanced HTML    Acrobat PDF (171 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We consider the propagation of periodic waves with initially narrow spatial spectra in a Kerr medium. The set of constants of motion closely related to the order amplitudes is introduced. It is shown that the spatial spectrum remains uniformly narrow with propagation for both self-focusing and self-defocusing nonlinearity. In addition, for sufficiently weak nonlinearity, initially strong orders always remain strong. Thus the problem is shown to be essentially finite dimensional and well approximated by a proper set of coupled ordinary differential equations.

© 2004 Optical Society of America

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

ToC Category:
Research Papers

History
Original Manuscript: May 17, 2004
Revised Manuscript: June 21, 2004
Published: July 26, 2004

Citation
N. Korneev and E. Rodriguez, "Spectral limits for periodic pattern propagation in Kerr media," Opt. Express 12, 3297-3306 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-15-3297


Sort:  Journal  |  Reset  

References

  1. Y. C. Ma and M. J. Ablowitz, �??The periodic cubic Schrödinger equation,�?? Stud. Appl. Math. 65, 113-158 (1981).
  2. N. Korneev, A. Apolinar-Iribe, and J. J. Sanchéz -Mondragon, �??Theory of multiple beam interaction in photorefractive media,�?? J. Opt. Soc. Am. B 16, 580-586 (1999). [CrossRef]
  3. A. Thyagaraja �??Recurrent motions in certain continuum dynamical systems,�?? Phys. Fluids 22, 2093-2096 (1979). [CrossRef]
  4. D. U. Martin and H. C. Yuen �??Spreading of energy in solutions of the nonlinear Schrödinger equation,�?? Phys. Fluids 23, 1269-1271 (1980). [CrossRef]
  5. L. A. Takhtajan and L. D. Faddeev Hamiltonian Methods in the Theory of Solitons (Springer-Verlag, 1987).
  6. V. E. Zakharov and A. B. Shabat, �??Exact theory of two-dimensional self-focusing and one-dimensional selfmodulation of waves in nonlinear media,�?? Sov. Phys. JETP 61, 62-69 (1972).
  7. M. J. Ablowitz and J. F. Ladik, �??Nonlinear differential-difference equations and Fourier analysis,�?? J. Math. Phys. 17, 1011-1018 (1976). [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.

Figures

Fig. 1. Fig. 2.
 

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited