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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 6 — Mar. 24, 2003
  • pp: 541–551

Moving least-square method for the band-structure calculation of 2D photonic crystals

Sukky Jun, Young-Sam Cho, and Seyoung Im  »View Author Affiliations


Optics Express, Vol. 11, Issue 6, pp. 541-551 (2003)
http://dx.doi.org/10.1364/OE.11.000541


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Abstract

The moving least-square (MLS) basis is implemented for the real-space band-structure calculation of 2D photonic crystals. A value-periodic MLS shape function is thus proposed in order to represent the periodicity of crystal lattice. Through numerical examples, this MLS method is proved to be a promising scheme for predicting band gaps of photonic crystals.

© 2003 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Research Papers

History
Original Manuscript: February 6, 2003
Revised Manuscript: March 12, 2003
Published: March 24, 2003

Citation
Sukky Jun, Young-Sam Cho, and Seyoung Im, "Moving least-square method for the band-structure calculation of 2D photonic crystals," Opt. Express 11, 541-551 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-6-541


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References

  1. J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).
  2. Y. Xia, �??Photonic crystals,�?? Adv. Mater. 13, 369 (2001) and papers in this special issue. [CrossRef]
  3. K. Busch, "Photonic band structure theory: assesment and perspectives,�?? C. R. Physique 3, 53-66 (2002). [CrossRef]
  4. D. Cassagne, "Photonic band gap materials,�?? Ann. Phys. Fr. 23(4), 1-91 (1998). [CrossRef]
  5. J.B. Pendry, �??Calculating photonic band structure,�?? J. Phys.: Condens. Matter 8, 1085-1108 (1996). [CrossRef]
  6. H.S. Sozuer, J.W. Haus, and R. Inguva, �??Photonic bands: Convergence problems with the planewave method,�?? Phys. Rev. B 45, 13962-13972 (1992). [CrossRef]
  7. R.D. Meade, A.M. Rappe, K.D. Brommer, J.D. Joannopoulos, O.L. Alerhand, �??Accurate theoretical analysis of photonic band-gap materials,�?? Phys. Rev. B 48, 8434-8437 (1993). [CrossRef]
  8. 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]
  9. A.J. Ward and J.B. Pendry, �??Calculating photonic Green�??s functions using a nonorthogonal finite difference time-domain method,�?? Phys. Rev. B 58, 7252-7259 (1998). [CrossRef]
  10. M. Qiu 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]
  11. K.M. Leung and Y. Qiu, �??Multiple-scattering calculation of the two-dimensional photonic band structure,�?? Phys. Rev. B 48, 7767-7771 (1993). [CrossRef]
  12. X. Wang, X.G. Zhang, Q. Yu, and B.N. Harmon, �??Multiple-scattering theory for electromagnetic waves,�?? Phys. Rev. B 47, 4161-4167 (1993). [CrossRef]
  13. J.B. Pendry and A. MacKinnon, �??Calculation of photon dispersion relations,�?? Phys. Rev. Lett. 69, 2772-2775 (1992). [CrossRef] [PubMed]
  14. L. Shen, S. He, and S. Xiao, �??A finite-difference eigenvalue algorithm for calculating the band structure of a photonic crystal,�?? Comput. Phys. Comm. 143, 213-221 (2002). [CrossRef]
  15. W. Axmann and P. Kuchment, �??An efficient finite element method for computing spectra of photonic and acoustic band-gap materials: I. Scalar case,�?? J. Comput. Phys. 150, 468-481 (1999). [CrossRef]
  16. D.C. Dobson, �??An efficient band structure calculations in 2D photonic crystals,�?? J. Comput. Phys. 149, 363-376 (1999). [CrossRef]
  17. C. Mias, J.P. Webb and R.L. Ferrari, �??Finite element modelling of electromagnetic waves in doubly and triply periodic structures,�?? IEE Proc. Optoelectron. 146(2), 111-118 (1999). [CrossRef]
  18. M. Marrone, V.F. Rodriguez-Esquerre, and H.E. Hernandez-Figueroa, �??Novel numerical method for the analysis of 2D photonic crystals: the cell method,�?? Opt. Express 10, 1299-1304 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1299">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1299</a> [CrossRef] [PubMed]
  19. S. Li and W.K. Liu, �??Meshfree and particle methods and their applications,�?? Appl. Mechanics Rev. 55, 1-34 (2002). [CrossRef]
  20. D.W. Kim and Y. Kim, �??Point collocation method using the fast moving least-square reproducing kernel approximation,�?? Int. J. Numer. Methods Engrg. 56, 1445 - 1464 (2003). [CrossRef]
  21. L.W. Cordes and B. Moran, �??Treatment of material discontinuity in the Element-Free Galerkin method,�?? Comput. Meth. Appl. Mech. Eng. 139, 75-89 (1996). [CrossRef]

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