OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry M. Van Driel
  • Vol. 25, Iss. 7 — Jul. 1, 2008
  • pp: 1135–1143

Approximate analysis of two-dimensional photonic crystals with rectangular geometry. I. E polarization

Inna Nusinsky and Amos A. Hardy  »View Author Affiliations

JOSA B, Vol. 25, Issue 7, pp. 1135-1143 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (609 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Using analytical techniques the dispersion relations for two-dimensional photonic crystals with rectangular geometry are analyzed. In this part of the work E polarization is presented. By comparing with accurate numerical calculations, we show that our analysis provides a good description of the physical properties for this type of photonic crystal. Besides the significantly shorter calculation time, the analytical treatment provides an important insight into the photonic bands’ formation and their properties. The presented approach and derived analytical expressions can be useful for the investigation of photonic band structures as well as for the design of novel photonic crystal devices.

© 2008 Optical Society of America

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(160.5293) Materials : Photonic bandgap materials
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: February 14, 2008
Manuscript Accepted: March 30, 2008
Published: June 23, 2008

Inna Nusinsky and Amos A. Hardy, "Approximate analysis of two-dimensional photonic crystals with rectangular geometry. I. E polarization," J. Opt. Soc. Am. B 25, 1135-1143 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Inoue and K. Ohtaka, eds., Photonic Crystals, Physics, Fabrication and Applications (Springer, 2004).
  2. M. Plihal, A. Shambrook, and A. A. Maradudin, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199-204 (1991). [CrossRef]
  3. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  4. J. B. Pendry, “Calculating photonic band structure,” J. Phys.: Condens. Matter 8, 1085-1108 (1996). [CrossRef]
  5. S. N. Kawakami, “Analytically solvable model of photonic crystal structures and novel phenomena,” J. Lightwave Technol. 20, 1644-1650 (2002). [CrossRef]
  6. I. Ponomarev, “Separation of variables in the computation of spectra in 2-D photonic crystals,” SIAM J. Appl. Math. 61, 1202-1218 (2000). [CrossRef]
  7. K. Samokhvalova, C. Chen, and B.-L. Qian, “Analytical and numerical calculations of the dispersion characteristics of two-dimensional dielectric photonic band gap structures,” J. Appl. Phys. 99, 63104 (2006). [CrossRef]
  8. T. J. Shepherd, P. J. Roberts, and R. Loudon, “Soluble two-dimensional photonic crystal model,” Phys. Rev. E 55, 6024-6038 (1997). [CrossRef]
  9. A. Figotin and P. Kuchment, “Band gap structure of spectra of periodic dielectric and acoustic media. II. Two-dimensional photonic crystals,” SIAM J. Appl. Math. 56, 1561-1620 (1996). [CrossRef]
  10. L. Chang, C.-C. Ho, H.-S. Wei, and G. Y. Wu, “Effective medium theory with dimensionality reduction for band structures of photonic crystals,” J. Appl. Phys. 101, 053109 (2007). [CrossRef]
  11. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  12. K. Sakoda, Optical Properties of Photonic Crystals, 2nd ed. (Springer-Verlag, 2005).
  13. D. J. Griffiths, Introduction to Quantum Mechanics (Prentice-Hall, 1995).
  14. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell's equations with shifting materials boundaries,” Phys. Rev. E 65, 066611 (2002). [CrossRef]
  15. W. Magnus and S. Winkler, Hill's Equation (Wiley, 1966).
  16. I. Nusinsky and A. A. Hardy, “Band gap-analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006). [CrossRef]
  17. A. H. Nayfen, Introduction to Perturbation Techniques (Wiley, 1993).
  18. P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274-2284 (2003). [CrossRef]
  19. H. Kitahara, N. Tsumura, H. Kondo, M. W. Takeda, J. W. Haus, Z. Yuan, N. Kawai, K. Sakoda, and K. Inoue, “Terahertz wave dispersion in two-dimensional photonic crystals,” Phys. Rev. B 64, 045202 (2001). [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 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited