OSA's Digital Library

Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Alan E. Willner
  • Vol. 33, Iss. 18 — Sep. 15, 2008
  • pp: 2101–2103

Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method

Oleg V. Belai, Leonid L. Frumin, Evgeny V. Podivilov, and David A. Shapiro  »View Author Affiliations


Optics Letters, Vol. 33, Issue 18, pp. 2101-2103 (2008)
http://dx.doi.org/10.1364/OL.33.002101


View Full Text Article

Enhanced HTML    Acrobat PDF (193 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The inverse scattering problem for the one-dimensional Helmholtz wave equation is studied. The equation is reduced to a Fresnel set that describes multiple bulk reflection and is similar to the coupled-wave equations. The inverse scattering problem is equivalent to coupled Gel’fand–Levitan–Marchenko integral equations. In the discrete representation its matrix has Töplitz symmetry, and the fast inner bordering method can be applied for its inversion. Previously the method was developed for the design of fiber Bragg gratings. The testing example of a short Bragg reflector with deep modulation demonstrates the high efficiency of refractive-index reconstruction.

© 2008 Optical Society of America

OCIS Codes
(060.3735) Fiber optics and optical communications : Fiber Bragg gratings
(100.3200) Image processing : Inverse scattering

ToC Category:
Image Processing

History
Original Manuscript: February 26, 2008
Revised Manuscript: July 30, 2008
Manuscript Accepted: August 5, 2008
Published: September 11, 2008

Citation
Oleg V. Belai, Leonid L. Frumin, Evgeny V. Podivilov, and David A. Shapiro, "Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method," Opt. Lett. 33, 2101-2103 (2008)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-18-2101


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  2. R. Kashyap, Fiber Bragg Gratings (Academic, 1999).
  3. P. Sacks, J. Math. Phys. 45, 1699 (2004). [CrossRef]
  4. D. W. Huang and C. C. Yang, Appl. Opt. 38, 4494 (1999). [CrossRef]
  5. K. O. Hill and G. Meltz, J. Lightwave Technol. 15, 1263 (1997). [CrossRef]
  6. G. N. Balanis, J. Math. Phys. 23, 2562 (1982). [CrossRef]
  7. S. H. Gray, J. Math. Phys. 24, 1148 (1983). [CrossRef]
  8. A. M. Bruckstein and T. Kailath, SIAM Rev. 29, 359 (1987). [CrossRef]
  9. Y. Chen and V. Rokhlin, Inverse Probl. 8, 365 (1992). [CrossRef]
  10. Y. Zhang, J. A. Kong, and A. K. Jordan, Microwave Opt. Technol. Lett. 15, 277 (1998). [CrossRef]
  11. V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971).
  12. O. V. Belai, L. L. Frumin, E. V. Podivilov, and D. A. Shapiro, J. Opt. Soc. Am. B 24, 1451 (2007). [CrossRef]
  13. H. Bremmer, Physica (Amsterdam) 15, 593 (1949). [CrossRef]
  14. R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999). [CrossRef]
  15. G. B. Xiao and K. Yashiro, IEEE Trans. Antennas Propag. 50, 807 (2002). [CrossRef]
  16. C. M. de Sterke, D. G. Salinas, and J. E. Sipe, Phys. Rev. E 54, 1969 (1996). [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
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited