OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 17 — Aug. 22, 2005
  • pp: 6587–6596

Perturbation analysis of plane-wave transmission through a dielectric slab with Kerr-type nonlinearity

Kiarash Zamani Aghaie and Mahmoud Shahabadi  »View Author Affiliations


Optics Express, Vol. 13, Issue 17, pp. 6587-6596 (2005)
http://dx.doi.org/10.1364/OPEX.13.006587


View Full Text Article

Enhanced HTML    Acrobat PDF (223 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Multiple-scale analysis is employed for the analysis of plane-wave refraction at a nonlinear slab. It will be demonstrated that the perturbation method will lead to a nonuniformly valid approximation to the solution of the nonlinear wave equation. To construct a uniformly valid approximation, we will exploit multiple-scale analysis. Using this method, we will derive the zeroth-order approximation to the solution of the nonlinear wave equation analytically. This approximate solution clearly shows the effects of self-phase modulation (SPM) and cross-phase modulation (XPM) on plane-wave refraction at the nonlinear slab. As will be shown, the proposed method can be generalized to the rigorous study of nonlinear wave propagation in one-dimensional photonic band-gap structures.

© 2005 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(190.3270) Nonlinear optics : Kerr effect
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

ToC Category:
Research Papers

History
Original Manuscript: May 19, 2005
Revised Manuscript: August 14, 2005
Published: August 22, 2005

Citation
Kiarash Zamani Aghaie and Mahmoud Shahabadi, "Perturbation analysis of plane-wave transmission through a dielectric slab with Kerr-type nonlinearity," Opt. Express 13, 6587-6596 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-17-6587


Sort:  Journal  |  Reset  

References

  1. H. G. Winful, J. H. Marburger, and E. Garmire, �??Theory of bistability in nonlinear distributed feedback structures,�?? Appl. Phys. Lett. 35, 379-381 (1979). [CrossRef]
  2. D. N. Christodoulides and R. I. Joseph, �??Slow Bragg solitons in nonlinear periodic structures,�?? Phys. Rev. Lett. 62, 1746-1749 (1989). [CrossRef] [PubMed]
  3. N. G. R. Broderick, D. J. Richardson, and M. Ibsen, �??Nonlinear switching in a 20-cm long fiber Bragg grating,�?? Opt. Lett. 25, 536�??538 (2000). [CrossRef]
  4. K. Senthilnathan, P. Malathi, and K. Porsezian, �??Dynamics of nonlinear pulse propagation through a fiber Bragg grating with linear coupling,�?? J. Opt. Soc. Am. B 20, 366�??372 (2003). [CrossRef]
  5. R. E. Slusher and B. J. Eggleton, eds., Nonlinear Photonic Crystals (Springer-Verlag Berlin Heidelberg, Berlin, 2003).
  6. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, �??Interaction between light waves in a nonlinear dielectric,�?? Phys. Rev. 127, 1918�??1939 (1962). [CrossRef]
  7. N. Bloembergen and P. S. Pershan, �??Light waves at the boundary of nonlinear media,�?? Phys. Rev. 128, 606�??622 (1962). [CrossRef]
  8. M. M. Carroll, �??Plane waves of constant amplitude in nonlinear dielectrics,�?? Phys. Rev. A 6, 1977�??1980 (1972). [CrossRef]
  9. Th. Peschel, P. Dannberg, U. Langbein, and F. Lederer, �??Investigation of optical tunneling through nonlinear films,�?? J. Opt. Soc. Am. B 5, 5�??36 (1988). [CrossRef]
  10. K. Hayata, M. Nagai, and M. Koshiba, �??Finite-element formalism for noninear slab-guided waves,�?? IEEE Trans. Microwave Theory Tech. 36, 1207�??1215 (1988). [CrossRef]
  11. S. V. Polstyanko, R. Dyczij-Edlinger, and J. F. Lee, �??A full vectorial analysis of a nonlinear slab waveguide based on the nonlinear hybrid vector finite-element method,�?? Opt. Lett. 21, 98�??100 (1996). [CrossRef] [PubMed]
  12. V. Van and S. K. Chaudhuri, �??A hybrid implicit-explicit FDTD scheme for nonlinear optical waveguide modeling,�?? IEEE Trans. Microwave Theory Tech. 47, 540�??545 (1999). [CrossRef]
  13. R. M. Joseph and A. Taflove, �??FDTD Maxwell�??s equations models for nonlinear electrodynamics and optics,�?? IEEE Trans. Microwave Theory Tech. 45, 364�??374 (1997).
  14. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, Singapore, 1978).
  15. K. Ogusu, �??Self-switching in hollow waveguides with a Kerrlike nonlinear permittivity,�?? IEEE J. Lightwave Technol. 8, 1541�??1547 (1990). [CrossRef]
  16. U. Trutschel, F. Lederer, and M. Golz, �??Nonlinear guided waves in multilayer systems,�?? IEEE J. Quantum Electron. 25, 194�??200 (1989). [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. Fig. 3.
 
Fig. 4.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited