OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 2, Iss. 11 — Nov. 1, 1985
  • pp: 1916–1921

Renormalization of an inverse-scattering theory for inhomogeneous dielectrics

H. D. Ladouceur and A. K. Jordan  »View Author Affiliations


JOSA A, Vol. 2, Issue 11, pp. 1916-1921 (1985)
http://dx.doi.org/10.1364/JOSAA.2.001916


View Full Text Article

Enhanced HTML    Acrobat PDF (764 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Renormalized solutions are obtained for an inverse-scattering problem that are equivalent to the second-order regular perturbation approximations for the exact (Gel’fand-Levitan-Marchenko) theory. We have developed an inversion method for reconstruction the permittivity profiles of inhomogeneous dielectric slabs from reflection-coefficient data. Solutions with increased radii of convergence are obtained. Numerical examples are demonstrated for simulated-scattering data from Gaussian and parabolic profiles and homogeneous slabs.

© 1985 Optical Society of America

History
Original Manuscript: May 6, 1985
Manuscript Accepted: July 25, 1985
Published: November 1, 1985

Citation
H. D. Ladouceur and A. K. Jordan, "Renormalization of an inverse-scattering theory for inhomogeneous dielectrics," J. Opt. Soc. Am. A 2, 1916-1921 (1985)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-2-11-1916


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. I. Kay, “The inverse scattering problem,” Rep. No. EM-74 (Institute of Mathematical Sciences, New York University, N.Y., 1955).
  2. H. E. Moses, “Calculation of the scattering potential from reflection coefficients,” Phys. Rev. 102, 559–567 (1956). [CrossRef]
  3. I. Kay, H. E. Moses, Inverse Scattering Papers: 1955–1963 (Math Sci, Brookline, Mass., 1982).
  4. I. M. Gel’fand, B. M. Levitan, “On the determination of a differential equation by its spectral function,” Transl. Am. Math. Soc. Ser. 2 1, 253 (1955).
  5. V. A. Marchenko, “Concerning the theory of a differential operator of second order,”Dokl. Akad. Nauk SSSR 72, 457 (1950).
  6. M. Nayfeh, Perturbation Methods (Wiley, New York, 1973), p. 315.
  7. H. Bremmer, “The W.K.B. approximation as the first term of a geometrical-optical series,” Comm. Pure Appl. Math. 3, S169–S179 (1951).
  8. M. Nayfeh, Comm. Pure Appl. Math. 3, 315 (1951).
  9. A. K. Jordan, “Inverse scattering theory: exact and approximate solutions,” in Mathematical Methods and Applications of Scattering Theory, J. A. DeSanto, A. W. Saenz, W. W. Zachary, eds. (Springer-Verlag, New York, 1980), p. 318–326. [CrossRef]
  10. J. Hirsch, “An analytic solution to the synthesis problem for dielectric thin-film layers,” Opt. Acta 26, 1273–1279 (1979). [CrossRef]
  11. H. Kaiser, H. C. Kaiser, “Mathematical methods in the synthesis and identification of thin-film systems: errata,” Appl. Opt. 20, 1043–1049 (1981). [CrossRef] [PubMed]
  12. M. Nayfeh, Perturbation Methods (Wiley, New York, 1973), p. 367.
  13. R. B. Barrar, R. M. Redheffer, “On nonuniform dielectric media,” IEEE Trans. Antennas Propag. AP-7, 101–1071955).
  14. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 132.

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