OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: G. I. Stegeman
  • Vol. 23, Iss. 10 — Oct. 1, 2006
  • pp: 2249–2256

Numerical method based on the solution of integral equations for the calculation of the band structure and reflectance of one- and two-dimensional photonic crystals

Alberto Mendoza-Suárez, Francisco Villa-Villa, and Jorge A. Gaspar-Armenta  »View Author Affiliations

JOSA B, Vol. 23, Issue 10, pp. 2249-2256 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (617 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose a method for the determination of the band structure, reflectance, and transmittance of one- and two-dimensional photonic crystals that is based on the solution of integral equations. The results of this method are compared with those obtained by other well-known algorithms, and good agreement between them is found. The method is also tested by considering systems that possess a complex structure in their unit cell such as fractal geometries.

© 2006 Optical Society of America

OCIS Codes
(290.0290) Scattering : Scattering

ToC Category:
Photonic Crystals

Original Manuscript: February 15, 2006
Revised Manuscript: May 9, 2006
Manuscript Accepted: June 2, 2006

Alberto Mendoza-Suárez, Francisco Villa-Villa, and Jorge A. Gaspar-Armenta, "Numerical method based on the solution of integral equations for the calculation of the band structure and reflectance of one- and two-dimensional photonic crystals," J. Opt. Soc. Am. B 23, 2249-2256 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. C. Schroden, M. Al-Daous, C. F. Blanford, and A. Stein,"Optical properties of inverse opal photonic crystals," Chem. Mater. 14, 3305-3315 (2002). [CrossRef]
  2. A. F. Koenderink and W. L. Vos, "Optical properties of real photonic crystals," J. Opt. Soc. Am. B 22, 1075-1084 (2005). [CrossRef]
  3. L. Florescu, K. Busch, and S. John, "Semiclassical theory of lasing in photonic crystals," J. Opt. Soc. Am. B 19, 2215-2223 (2002). [CrossRef]
  4. P. Kramper, A. Birner, M. Agio, C. M. Soukoulis, F. Müller, U. Gösele, J. Mlynek, and V. Sandoghdar, "Direct spectroscopy of a deep two-dimensional photonic crystal microresonator," Phys. Rev. B 64, 233102 (2001). [CrossRef]
  5. M. Mengens, J. E. G. J. Wijnhoven, A. Lagendijk, and W. L. Vos, "Light sources inside photonic crystals," J. Opt. Soc. Am. B 16, 1403-1408 (1999). [CrossRef]
  6. M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, "Nonlinear photonic crystal microdevices for optical integration," Opt. Lett. 28, 637-639 (2005). [CrossRef]
  7. S. F. Mingaleev and K. Busch, "Scattering matrix approach to large-scale photonic crystal circuits," Opt. Lett. 28, 619-621 (2003). [CrossRef] [PubMed]
  8. K. Busch, S. F. Mingaleev, A. García-Martin, M. Schillinger, and D. Hermann, "The Wannier functions approach to photonic crystal circuits," J. Phys. Condens. Matter 15, R1233-R1256 (2003). [CrossRef]
  9. D. Bria, B. Djafari-Rouhani, A. Akjouj, L. Dobrzynski, J. P. Vigneron, E. H. El Boudoti, and A. Nougaoui, "Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials," Phys. Rev. E 69, 066613 (2004). [CrossRef]
  10. F. Villa-Villa and J. A. Gaspar-Armenta, "Brewster angle and optical tunneling in one-dimensional photonic crystals composed of left- and right-handed materials," J. Opt. Soc. Am. B 23, 375-380 (2006). [CrossRef]
  11. F. Ramos-Mendieta and P. Halevi, "Surface modes in a 2D array of square dielectric cylinders," Solid State Commun. 100, 311-314 (1996). [CrossRef]
  12. J. B. Pendry, "Calculating the photonic band structure," J. Phys. Condens. Matter 8, 1085-1108 (1996). [CrossRef]
  13. A. J. Ward and J. B. Pendry, "A program for calculating the photonic band structures, Green's functions and transmission/reflection coefficients using a non-orthogonal FDTD method," Comput. Phys. Commun. 128, 590-621 (2000). [CrossRef]
  14. R. M. Josephand and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propag. 45, 364-374 (1997). [CrossRef]
  15. A. Lavrinenko, P. I. Borel, L. H. Fransen, M. Thorhauge, A. Harpoth, M. Kristensen, and T. Niemi, "Comprehensive FDTD modeling of photonic crystal waveguide components," Opt. Express 12, 234-248 (2004). [CrossRef] [PubMed]
  16. C. T. Chan, Q. L. Yu, and K. M. Ho, "Order-N spectral method for electromagnetic waves," Phys. Rev. B 51, 16635-16642 (1995). [CrossRef]
  17. M. Qui and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268-8275 (2000). [CrossRef]
  18. S. Fan, P. R. Villeeuve, and J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B 54, 11245-11251 (1996). [CrossRef]
  19. O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998). [CrossRef]
  20. O. J. F. Martin, C. Girard, D. R. Smith, and S. Schultz, "Generalized field propagator for arbitrary finite-size photonic band gap structures," Phys. Rev. Lett. 82, 315-318 (1999). [CrossRef]
  21. A. I. Rahachou and I. V. Zozoulenko, "Light propagation in finite photonic crystals: the recursive Green's function technique," Phys. Rev. B 72, 155117 (2005). [CrossRef]
  22. L.-M. Zhao, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, "Green's functions for photonic crystal slabs," Phys. Rev. E 72, 026614 (2005). [CrossRef]
  23. F. Villa, J. A. Gaspar-Armenta, and F. Ramos-Mendieta, "One-dimensional photonic crystals: equivalent systems to single layers with a classical oscillator like dielectric function," Opt. Commun. 216, 361-367 (2003). [CrossRef]
  24. J. A. Gaspar-Armenta and F. Villa, "Band-structure properties of one-dimensional photonic crystals under the formalism of equivalent systems," J. Opt. Soc. Am. B 21, 405-412 (2004). [CrossRef]
  25. A. A. Maradudin, E. R. Mendez, and T. Michel, "Enhanced backscattering of light from a random grating," Ann. Phys. (N.Y.) 203, 255-307 (1990). [CrossRef]
  26. A. Mendoza-Suárez and E. R. Mendez, "Light scattering by a reentrant fractal surface," Appl. Opt. 36, 3521-3531 (1997). [CrossRef] [PubMed]
  27. A. Mendoza-Suárez, R. Espinosa-Luna, J. Cruz-Mandujano, and J. Espinosa-Luna, "Numerical technique to calculate modes in waveguides of arbitrarily cross-sectional shape," J. Opt. Soc. Am. A 18, 961-965 (2001). [CrossRef]
  28. M. Plihal, A. Shamrock, A. A. Maradudin, and P. Sheng, "Two-dimensional photonic band structures," Opt. Commun. 80, 199-204 (1991). [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