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. 26, Iss. 7 — Jul. 1, 2009
  • pp: 1442–1449

Dirichlet-to-Neumann map method for analyzing periodic arrays of cylinders with oblique incident waves

Yumao Wu and Ya Yan Lu  »View Author Affiliations


JOSA B, Vol. 26, Issue 7, pp. 1442-1449 (2009)
http://dx.doi.org/10.1364/JOSAB.26.001442


View Full Text Article

Enhanced HTML    Acrobat PDF (389 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

For finite two-dimensional photonic crystals given as periodic arrays of circular cylinders in a square or triangular lattice, we develop an efficient method to compute the transmission and reflection spectra for oblique incident plane waves. The method relies on vector cylindrical wave expansions to approximate the Dirichlet-to-Neumann (DtN) map for each distinct unit cell and uses the DtN maps to derive an efficient method that works on the edges of the unit cells only. The DtN operator maps the two longitudinal field components to their derivatives on the boundary of the unit cell.

© 2009 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Numerical Approximation and Analysis

History
Original Manuscript: March 25, 2009
Manuscript Accepted: May 12, 2009
Published: June 25, 2009

Citation
Yumao Wu and Ya Yan Lu, "Dirichlet-to-Neumann map method for analyzing periodic arrays of cylinders with oblique incident waves," J. Opt. Soc. Am. B 26, 1442-1449 (2009)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-26-7-1442


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  2. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).
  3. S. Venakides, M. A. Haider, and V. Papanicolaou, “Boundary integral calculations of two-dimensional electromagnetic scattering by photonic crystal Fabry-Perot structures,” SIAM J. Appl. Math. 60, 1686-1706 (2000). [CrossRef]
  4. D. Pissoort, E. Michielssen, F. Olyslager, and D. De Zutter, “Fast analysis of 2-D electromagnetic crystal devices using a periodic Green function approach,” J. Lightwave Technol. 23, 2294-2308 (2005). [CrossRef]
  5. E. Centeno and D. Felbacq, “Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 17, 320-327 (2000). [CrossRef] [PubMed]
  6. G. H. Smith, L. C. Botten, R. C. McPhedran, and N. A. Nicorovici, “Cylinder gratings in conical incidence with applications to modes of air-cored photonic crystal fibers,” Phys. Rev. E 66, 056604 (2002). [CrossRef]
  7. G. H. Smith, L. C. Botten, R. C. McPhedran, and N. A. Nicorovici, “Cylinder gratings in conical incidence with applications to woodpile structures,” Phys. Rev. E 67, 056620 (2003). [CrossRef]
  8. L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, “Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory,” Phys. Rev. E 70, 056606 (2004). [CrossRef]
  9. K. Yasumoto, H. Toyama, and T. Kushta, “Accurate analysis of two-dimensional electromagnetic scattering from multilayered periodic arrays of circular cylinders using lattice sums technique,” IEEE Trans. Antennas Propag. 52, 2603-2611 (2004). [CrossRef]
  10. J. Yuan and Y. Y. Lu, “Photonic bandgap calculations using Dirichlet-to-Neumann maps,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 23, 3217-3222 (2006). [CrossRef] [PubMed]
  11. J. Yuan and Y. Y. Lu, “Computing photonic band structures by Dirichlet-to-Neumann maps: the triangular lattice,” Opt. Commun. 273, 114-120 (2007). [CrossRef]
  12. Y. Huang, Y. Y. Lu, and S. Li, “Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps,” J. Opt. Soc. Am. B 24, 2860-2867 (2007). [CrossRef]
  13. S. Li and Y. Y. Lu, “Computing photonic crystal defect modes by Dirichlet-to-Neumann maps,” Opt. Express 15, 14454-14466 (2007). [CrossRef] [PubMed]
  14. Y. Huang and Y. Y. Lu, “Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps,” J. Lightwave Technol. 24, 3448-3453 (2006). [CrossRef]
  15. Y. Huang and Y. Y. Lu, “Modeling photonic crystals with complex unit cells by Dirichlet-to-Neumann maps,” J. Comput. Math. 25, 337-349 (2007).
  16. Y. Wu and Y. Y. Lu, “Dirichlet-to-Neumann map method for analyzing interpenetrating cylinder arrays in a triangular lattice,” J. Opt. Soc. Am. B 25, 1466-1473 (2008). [CrossRef]
  17. Z. Hu and Y. Y. Lu, “Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps,” Opt. Express 16, 17383-17399 (2008). [CrossRef] [PubMed]
  18. J. Yuan, Y. Y. Lu, and X. Antoine, “Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps,” J. Comput. Phys. 227, 4617-4629 (2008). [CrossRef]
  19. L. Li, “A modal analysis of lamellar diffraction gratings in cornical mountings,” J. Mod. Opt. 40, 553-573 (1993). [CrossRef]
  20. S. Campbell, L. C. Botten, C. M. De Sterke, and R. C. McPhedran, “Fresnel formulation for multi-element lamellar diffraction gratings in conical mountings,” Waves Random Complex Media 17, 455-475 (2007). [CrossRef]
  21. B. Gralak, R. Pierre, G. Tayeb, and S. Enoch, “Solutions of Maxwell's equations in presence of lamellar gratings including infinitely conducting metal,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 25, 3099-3110 (2008). [CrossRef] [PubMed]
  22. P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 13, 779-784 (1996). [CrossRef]
  23. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 13, 1024-1035 (1996). [CrossRef]
  24. E. Popov and B. Bozhkov, “Differential method applied for photonic crystals,” Appl. Opt. 39, 4926-4932 (2000). [CrossRef]
  25. J. Elschner, R. Hinder, and G. Schmidt, “Finite element solution of conical diffraction problems,” Adv. Comput. Math. 16, 139-156 (2002). [CrossRef]
  26. G. Bao, Z. M. Chen, and H. J. Wu, “Adaptive finite-element method for diffraction gratings,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 22, 1106-1114 (2005). [CrossRef] [PubMed]
  27. A. Pomp, “The integral method for coated gratings--computational cost,” J. Mod. Opt. 38, 109-120 (1991). [CrossRef]
  28. D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 14, 34-43 (1997). [CrossRef]
  29. E. Popov, B. Bozhkov, D. Maystre, and J. Hoose, “Integral method for echelles covered with lossless or absorbing thin dielectric layers,” Appl. Opt. 38, 47-55 (1999). [CrossRef]
  30. A. Rathsfeld, G. Schmidt, and B. H. Kleemann, “On a fast integral equation method for diffraction gratings,” Comm. Comp. Phys. 1, 984-1009 (2006).

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