OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 35, Iss. 27 — Sep. 20, 1996
  • pp: 5369–5380

Effective medium theory applied to photonic crystals composed of cubic or square cylinders

Philippe Lalanne  »View Author Affiliations

Applied Optics, Vol. 35, Issue 27, pp. 5369-5380 (1996)

View Full Text Article

Enhanced HTML    Acrobat PDF (477 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Using the effective medium theory, I interpret the band-gap opening in photonic crystals with simple geometries as an interference effect between alternating layers of high and low optical indices and introduce the interesting concept of multidimensional quarter-wave stacks. The interpretation provides a simple insight into band-gap opening processes. For several simple crystal geometries, I analyze the variations of the gap width and depth with respect to the light polarization, the incident angle, and contrast inversion. For two- and three-dimensional structures composed of cubic and square cylinders, I show that the effective medium theory can be used to predict accurately the gap width, the central wavelength, and the attenuation at the central wavelength. The validity domain of the effective medium theory predictions is checked with results from rigorous computations.

© 1996 Optical Society of America

Original Manuscript: November 7, 1995
Revised Manuscript: April 1, 1996
Published: September 20, 1996

Philippe Lalanne, "Effective medium theory applied to photonic crystals composed of cubic or square cylinders," Appl. Opt. 35, 5369-5380 (1996)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]
  3. See, for example, recent special issues on photonic band structures: J. Mod. Opt. 41(2) (1994)and J. Opt. Soc. Am. B 10(2) (1993).
  4. J. W. Haus, “A brief review of theoretical results for photonic band structures,” J. Mod. Opt. 41, 195–207 (1994). [CrossRef]
  5. W. H. Southwell, “Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces,” J. Opt. Soc. Am. A 8, 549–553 (1991). [CrossRef]
  6. R. Brauer, A. Bryngdahl, “Design of antireflection gratings with approximate and rigorous methods,” Appl. Opt. 33, 7875–7882 (1994). [CrossRef] [PubMed]
  7. E. B. Grann, M. G. Moharam, D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994). [CrossRef]
  8. R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983). [CrossRef] [PubMed]
  9. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983). [CrossRef]
  10. F. T. Chen, H. G. Craighhead, “Diffractive phase elements on two-dimensional artificial dielectrics,” Opt. Lett. 20, 121–123 (1995). [CrossRef] [PubMed]
  11. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  12. R. C. McPhedran, L. C. Botten, M. S. Craig, M. Nevière, D. Maystre, “Lossy lamellar gratings in the quasi-static limit,” Opt. Acta 29, 289–312 (1982). [CrossRef]
  13. G. Bouchitté, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985). [CrossRef]
  14. J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasi-static limit,” Opt. Acta 29, 1475–1489 (1982). [CrossRef]
  15. Ph. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt., to be published.
  16. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995). [CrossRef]
  17. Ph. Lalanne, G. M. Morris, “Highly improved convergence rate of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996). [CrossRef]
  18. M. G. Moharam, D. A. Pommet, E. B. Grann, T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995). [CrossRef]
  19. M. Born, E. Wolf, Principles of Optics, 6th ed. (Macmillan, New York, 1964), Chap. 1, p. 55.
  20. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chap. 5, p. 102.
  21. Ref. 20, Chap. 7, p. 144.
  22. R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Nature of photonic band gap: some insights from a field analysis,” J. Opt. Soc. Am. B 10, 328–332 (1993). [CrossRef]
  23. M. Plihal, A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991). [CrossRef]
  24. R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Existence of a photonic bandgap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992). [CrossRef]
  25. D. Maystre, “Electromagnetic study of photonic bandgaps,” Pure Appl. Opt. 3, 975–993 (1994). [CrossRef]
  26. Y. Ono, Y. Kimura, Y. Otha, N. Nishida, “Antireflection effects in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987). [CrossRef] [PubMed]
  27. D. H. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993). [CrossRef] [PubMed]
  28. S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1977).
  29. J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995). [CrossRef]
  30. In fact, as was confirmed by RCWA, the structure of Fig. 17, similar to its corresponding 3-D version, does not present any gap in the x and y directions. In that particular case, the EMT does not fail, but, in general, the conclusion derived here holds. For a discussion regarding the 3-D chessboard crystal see E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173–194 (1994). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited