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. 16, Iss. 4 — Apr. 1, 1999
  • pp: 845–852

Exact theory of electromagnetic scattering by a heterogeneous multilayer sphere in the infinite-layer limit: effective-media approach

B. R. Johnson  »View Author Affiliations


JOSA A, Vol. 16, Issue 4, pp. 845-852 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000845


View Full Text Article

Enhanced HTML    Acrobat PDF (284 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

An exact theory is presented for calculating electromagnetic scattering by a model heterogeneous particle. The model is a multilayer sphere composed of alternating layers of different dielectric constants in the limit where the number of layers approaches infinity and the layer thickness approaches zero. The scattering analysis for this limiting case is based on a formulation of scattering theory known as the variable-phase method (VPM). A derivation of the VPM formulation is presented. Analytic formulas are derived for the scattering coefficients of the heterogeneous sphere that are generalizations of similar Mie theory formulas for scattering by a homogeneous sphere. The optical properties of the layered heterogeneous mixture are exactly described in this theory by the two effective-media parameters. The solution in the long-wavelength limit is used to derive a new formula for the effective dielectric constant for heterogeneous mixtures.

© 1999 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(160.4760) Materials : Optical properties
(290.4020) Scattering : Mie theory
(290.5850) Scattering : Scattering, particles

History
Original Manuscript: June 18, 1998
Revised Manuscript: November 9, 1998
Manuscript Accepted: September 21, 1998
Published: April 1, 1999

Citation
B. R. Johnson, "Exact theory of electromagnetic scattering by a heterogeneous multilayer sphere in the infinite-layer limit: effective-media approach," J. Opt. Soc. Am. A 16, 845-852 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-4-845


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. L. Dourneuf, V. K. Lan, “The variable-phase method in multichannel electron-atom or electron-ion scattering,” J. Phys. B 10, L35–L42 (1977). [CrossRef]
  2. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 9.
  3. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), Chap. 3.
  4. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Interscience, New York, 1981), Pt. 1.
  5. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), 563–573 and 392–395.
  6. P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962);erratum 134, AB1 (1964). [CrossRef]
  7. C. T. Tai, “The electromagnetic theory of the spherical Luneberg lens,” Appl. Sci. Res., Sect. B 7, 113–130 (1958). [CrossRef]
  8. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).
  9. B. R. Johnson, “Invariant imbedding T matrix approach to electromagnetic scattering,” Appl. Opt. 27, 4861–4873 (1988). [CrossRef] [PubMed]
  10. B. R. Johnson, “Light scattering by a multilayer sphere,” Appl. Opt. 35, 3286–3296 (1996). [CrossRef] [PubMed]
  11. W. F. Brown, “Dielectrics,” in Encyclopedia of physics, Vol. 17, S. Flügge, ed. (Springer-Verlag, Heidelberg, 1956), Chap. 1, Sec. 53.
  12. D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982). [CrossRef]
  13. R. Landauer, in Proceedings of the First Conference on the Electrical and Transport Properties of Inhomogeneous Media, J. C. Garland, D. B. Tanner, eds., AIP Conf. Proc. No. 40 (American Institute of Physics, New York, 1978), pp. 2–43.
  14. G. B. Smith, “Dielectric constants for mixed media,” J. Phys. D 10, L39–L42 (1977). [CrossRef]
  15. G. A. Niklasson, C. G. Granqvist, O. Hunderi, “Effective medium models for the optical properties of inhomogeneous materials,” Appl. Opt. 20, 26–30 (1981). [CrossRef] [PubMed]
  16. G. W. Milton, “Bounds on the complex dielectric constant of a composite material,” Appl. Phys. Lett. 37, 300–302 (1980). [CrossRef]
  17. D. J. Bergman, “Exactly solvable microscopic geometries and rigorous bounds for the complex dielectric constant of a two-component composite material,” Phys. Rev. Lett. 44, 1285–1287 (1980). [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