OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 10 — Oct. 1, 2000
  • pp: 1791–1797

Plane waves in regular arrays of dipole scatterers and effective-medium modeling

S. A. Tretyakov and A. J. Viitanen  »View Author Affiliations

JOSA A, Vol. 17, Issue 10, pp. 1791-1797 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (154 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A simple analytical theory for finding eigensolutions for plane electromagnetic waves propagating along an axis in infinite regular arrays of small dipole particles is presented. The spacing between dipoles in every plane is assumed to be smaller than the wavelength; separation between the planes is arbitrary. The influence of evanescent modes is taken into account. This theory gives a model for an effective propagation constant that can be applied in a wide frequency range from the quasi-static regime to the Bragg reflection (photonic bandgap) region.

© 2000 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(160.4760) Materials : Optical properties
(260.2030) Physical optics : Dispersion
(260.2110) Physical optics : Electromagnetic optics

Original Manuscript: November 10, 1999
Revised Manuscript: May 23, 2000
Manuscript Accepted: May 23, 2000
Published: October 1, 2000

S. A. Tretyakov and A. J. Viitanen, "Plane waves in regular arrays of dipole scatterers and effective-medium modeling," J. Opt. Soc. Am. A 17, 1791-1797 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Sihvola, Electromagnetic Mixing Formulas and Applications (IEE Publishing, London, 1999).
  2. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-isotropic Media (Artech House, Boston, Mass, 1994).
  3. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford, UK, 1984; first Russian edition, Gostechizdat, Moscow, 1957).
  4. J. Slater, Insulators, Semiconductors, and Metals (McGraw-Hill, New York, 1967).
  5. H. F. Contopanagos, C. A. Kyriazidou, W. M. Merrill, “Effective response functions for photonic bandgap materials,” J. Opt. Soc. Am. A 16, 1682–1699 (1999). [CrossRef]
  6. C. A. Moses, N. Engheta, “An idea for electromagnetic ‘feedforward-feedbackward’ media,” IEEE Trans. Antennas Propag. 47, 918–928 (1999). [CrossRef]
  7. G. D. Mahan, G. Obermair, “Polaritons at surfaces,” Phys. Rev. 183, 834–841 (1961). [CrossRef]
  8. R. C. McPhedran, D. R. McKenzie, “The conductivity of lattices of spheres. 1. Simple cubic lattice,” Proc. R. Soc. London, Ser. A 359, 45–63 (1978). [CrossRef]
  9. A. P. Vinogradov, Yu. N. Dmitriev, V. E. Romanenko, “Transition from planar to bulk properties in multi-layer system,” Electromagnetics 17, 563–571 (1997). [CrossRef]
  10. C. R. Simovski, S. A. Tretyakov, A. H. Sihvola, M. M. Popov, “On the surface effect in thin molecular or composite layers,” Eur. Phys. J. Appl. Phys. 9, 195–204 (2000). [CrossRef]
  11. S. A. Tretyakov, A. J. Viitanen, S. I. Maslovski, I. E. Saarela, “Impedance boundary conditions for regular dense arrays of dipole scatterers,” , Electromagnetics Laboratory Report Series (Helsinki U. Technology, Helsinki Finland, 1999).
  12. S. I. Maslovski, S. A. Tretyakov, “Full-wave interaction field in two-dimensional arrays of dipole scatterers,” Int. J. Electron. Commun. 53, 135–139 (1999).
  13. R. E. Collin, Field Theory of Guided Waves, 2nd ed. (IEEE Press, Piscataway, N.J., 1991).
  14. R. E. Collin, Foundations for Microwave Engineering (McGraw-Hill, Tokyo, 1966).
  15. V. Yatsenko, S. Maslovski, S. Tretyakov, “Electromagnetic interaction of parallel arrays of dipole scatterers,” in Progress in Electromagnetics Research (EMW, Cambridge, Mass., 2000, pp. 285–307. [Abstract also in J. Electromagn. Waves Appl. 14, 79–80 (2000)]. [CrossRef]
  16. J. I. Peltoniemi, “Variational volume integral equation method for electromagnetic scattering by irregular grains,” J. Quant. Spectrosc. Radiat. Transf. 55, 637–647 (1996). [CrossRef]
  17. A. Sihvola, R. Sharma, “Scattering corrections for the Maxwell Garnett mixing rule,” Microwave Opt. Technol. Lett. 22, 229–231 (1999). [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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited