OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 29, Iss. 9 — Sep. 1, 2012
  • pp: 2334–2338

Effective refractive index of the photonic crystal deduced from the oscillation model of the membrane

Ting-Hang Pei and Yang-Tung Huang  »View Author Affiliations


JOSA B, Vol. 29, Issue 9, pp. 2334-2338 (2012)
http://dx.doi.org/10.1364/JOSAB.29.002334


View Full Text Article

Enhanced HTML    Acrobat PDF (380 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The oscillation model of the circular membrane is used to calculate the effective refractive index of the two-dimensional triangular photonic crystal at normal incidence within the second photonic band. Negatively effective refractive indices deduced from this model match those calculated by equifrequency surfaces very well. The result reveals that the field distribution has relation with the effective refractive index at certain frequency regions. Besides, the field distribution described by the Bessel function is more compact than the Fourier series expansion.

© 2012 Optical Society of America

OCIS Codes
(120.5710) Instrumentation, measurement, and metrology : Refraction
(260.2065) Physical optics : Effective medium theory
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Diffraction and Gratings

History
Original Manuscript: May 22, 2012
Revised Manuscript: July 1, 2012
Manuscript Accepted: July 12, 2012
Published: August 6, 2012

Citation
Ting-Hang Pei and Yang-Tung Huang, "Effective refractive index of the photonic crystal deduced from the oscillation model of the membrane," J. Opt. Soc. Am. B 29, 2334-2338 (2012)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-9-2334


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef]
  2. A. Z. Genack and N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66, 2064–2067 (1991). [CrossRef]
  3. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998). [CrossRef]
  4. A. L. Pokrovsky and A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901 (2002). [CrossRef]
  5. M. L. Povinelli, Steven G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003). [CrossRef]
  6. C.-H. Kuo and Z. Ye, “Negative-refraction-like behavior revealed by arrays of dielectric cylinders,” Phys. Rev. E 70, 026608 (2004).
  7. D. Felbacq and G. Bouchitté, “Left-handed media and homogenization of photonic crystals,” Opt. Lett. 30, 1189–1191(2005). [CrossRef]
  8. A. Martínez and J. Martí, “Negative refraction in two-dimensional photonic crystals: role of lattice orientation and interface termination,” Phys. Rev. B 71, 235115 (2005). [CrossRef]
  9. I. Bulu, H. Caglayan, and E. Ozbay, “Negative refraction and focusing of electromagnetic waves by photonic crystals,” J. Phys. Conf. Ser. 36, 33–40 (2006). [CrossRef]
  10. T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97, 073905 (2006). [CrossRef]
  11. T.-H. Pei and Y.-T. Huang, “Analyzing the propagating waves in the two-dimensional photonic crystal by the decoupled internal-field expansion method,” AIP Advances 2, 012188(2012). [CrossRef]
  12. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000). [CrossRef]
  13. T.-H. Pei and Y.-T. Huang, “The high-transmission photonic crystal heterostructure Y-branch waveguide operating at photonic band region,” J. Appl. Phys. 109, 034504 (2011). [CrossRef]
  14. T.-H. Pei and Y.-T. Huang, “The equivalent structure and some optical properties of the periodic-defect photonic crystal,” J. Appl. Phys. 109, 073014 (2011). [CrossRef]
  15. T.-H. Pei and Y.-T. Huang, “The heterostructure photonic crystal waveguide splitter,” IEEE Photon. Technol. Lett. 23, 1145–1147 (2011). [CrossRef]
  16. A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, 2000).
  17. G. B. Arfken, H. J. Weber, and F. Harris, Mathematical Methods for Physicists: A Comprehensive Guide, 6th ed. (Academic, 2005).
  18. M. R. Spiegel and J. Liu, Mathematical Handbook of Formulas and Tables, 2nd ed. (McGraw-Hill, 1999).
  19. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007).
  20. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1990).

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