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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 6 — Jun. 1, 1998
  • pp: 1586–1598

Fast modeling of photonic bandgap structures by use of a diffraction-grating approach

P. Dansas and N. Paraire  »View Author Affiliations


JOSA A, Vol. 15, Issue 6, pp. 1586-1598 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001586


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Abstract

The rigorous coupled-wave method formulated by ChateauN.HugoninJ. P. [J. Opt. Soc. Am. A 11, 1321 (1994)] and revisited by PengS.MorrisG. M. [J. Opt. Soc. Am. A 12, 1087 (1995)] for one-dimensional (1D) diffraction gratings is used for the modeling of diffraction properties of photonic bandgap (PBG) structures. A two-dimensional (2D)-PBG structure is considered as a stack of 1D gratings. An original S-matrix algorithm is formulated for the modeling of any 1D grating, formed by rods that have a symmetry plane in the grating plane. Many examples—dealing with stacks of infinite rods of square (circular) sections, whose intersection with a perpendicular plane forms square, triangular, or hexagonal lattices—are studied. Particular attention is devoted to TM polarization in lossless (lossy) dielectric and metallic materials. For this polarization we take advantage of the convergence improvement formulated for 1D metallic gratings by LalanneP.MorrisG. M. [J. Opt. Soc. Am. A 13, 779 (1996)] and GranetG.GuizalR. [J. Opt. Soc. Am. A 13, 1019 (1996)]. The introduction of a periodic defect—made of dielectric material that has linear (nonlinear) optical properties—in a 2D-PBG structure and the feasibility of optical filters and switches in the 1.3–1.55 µm wavelength range are briefly studied. Limitations for the use of the modeling tool are illustrated through an example of a cubic three-dimensional (3D)-PBG structure of cubes.

© 1998 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(120.2440) Instrumentation, measurement, and metrology : Filters
(160.4670) Materials : Optical materials
(230.1950) Optical devices : Diffraction gratings
(250.5300) Optoelectronics : Photonic integrated circuits

History
Original Manuscript: July 31, 1997
Revised Manuscript: November 19, 1997
Manuscript Accepted: January 14, 1998
Published: June 1, 1998

Citation
P. Dansas and N. Paraire, "Fast modeling of photonic bandgap structures by use of a diffraction-grating approach," J. Opt. Soc. Am. A 15, 1586-1598 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-6-1586


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References

  1. E. Yablonovitch, D. F. Sievenpiper, “Knitting a finer net for photons,” Nature (London) 383, 665–666 (1996). [CrossRef]
  2. T. H. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996). [CrossRef]
  3. T. H. Krauss, R. M. De La Rue, “Optical characterization of waveguide based photonic microstructure,” Appl. Phys. Lett. 68, 1613–1615 (1996). [CrossRef]
  4. D. Cassagne, C. Jouanin, D. Bertho, “Optical properties of two-dimensional photonic crystals with graphite structure,” Appl. Phys. Lett. 70, 289–291 (1997). [CrossRef]
  5. D. Cassagne, C. Jouanin, D. Bertho, “Photonic band gaps in a two-dimensional graphite structure,” Phys. Rev. B 52, R2217–R2230 (1995). [CrossRef]
  6. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996);see also Ref. 7 herein. [CrossRef] [PubMed]
  7. S. Y. Lin, V. M. Hiettala, S. K. Lyo, “Photonic band gap quantum well and quantum box structures: a high-Q resonant cavity,” Appl. Phys. Lett. 68, 3233–3235 (1996). [CrossRef]
  8. P. R. Villeneuve, M. Piché, “Photonic bandgaps in periodic dielectric structures,” Prog. Quantum Electron. 18, 153–200 (1994). [CrossRef]
  9. See, for instance, J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals, Princeton U. Press, Princeton, N.J., 1995 and special issues on photonic bandgap structures. J. Mod. Opt. 41, 2 (1994) and J. Opt. Soc. Am. B 10, 283–413 (1993).
  10. P. R. Villeneuve, M. Piché, “Photonic bandgaps: what is the best numerical representation of periodic structure?” J. Mod. Phys. 41, 241–256 (1994).
  11. M. G. Moharam, E. B. Grann, D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995). [CrossRef]
  12. R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993). [CrossRef]
  13. R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, “Photonic bound states in periodic dielectric materials,” Phys. Rev. B 44, 13772–13774 (1991). [CrossRef]
  14. D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. Mac Call, P. M. Platzman, “Photonic band structure and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993). [CrossRef]
  15. J. B. Pendry, A. Mac Kinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992). [CrossRef] [PubMed]
  16. J. B. Pendry, “Photonic structures,” J. Mod. Opt. 41, 209–229 (1994). [CrossRef]
  17. M. M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B 48, 14121–14126 (1993). [CrossRef]
  18. M. M. Sigalas, C. M. Soukoulis, C. T. Chan, K. M. Ho. “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B 49, 11080–11087 (1994). [CrossRef]
  19. K. Sakoda, “Transmittance and Bragg reflectivity of two-dimensional photonic lattices,” Phys. Rev. B 52, 8992–9002 (1995). [CrossRef]
  20. D. Maystre, “Electromagnetic theory of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994). [CrossRef]
  21. J. M. Elson, P. Tran, “Dispersion in photonic media and diffraction from gratings: a different modal expansion for the the R-matrix propagation technique,” J. Opt. Soc. Am. A 12, 1765–1771 (1995). [CrossRef]
  22. P. Chateau, J. P. Hugonin, “Algorithm for the rigorous coupled-wave analysis of grating diffraction,” J. Opt. Soc. Am. A 11, 1321–1331 (1994). [CrossRef]
  23. S. Peng, G. M. Morris, “Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings,” J. Opt. Soc. Am. A 12, 1087–1096 (1995). [CrossRef]
  24. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996). [CrossRef]
  25. P. Dansas, N. Paraire, F. Lederer, “Fast modeling of light beam diffraction by multilayer structures including a grating coupler,” Pure Appl. Opt. 4, 139–160 (1995). [CrossRef]
  26. P. Lalanne, G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996). [CrossRef]
  27. G. Granet, R. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996). [CrossRef]
  28. V. Kuzmiak, A. A. Maradudin, F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic elements,” Phys. Rev. B 50, 16835–16844 (1994). [CrossRef]
  29. P. Dansas, N. Paraire, S. Laval, “Feasibility of optical filters and switches using plastic photonic band gap structures,” in Precision Plastic Optics for Optical Storage, Displays, Imaging and Communications, W. F. Frank, ed., Proc. SPIE3135, pp. 219–229 (1997). [CrossRef]
  30. S. Peng, G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A 13, 993–1005 (1996). [CrossRef]
  31. E. Neoponen, J. Turunen, “Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles,” J. Opt. Soc. Am. A 11, 2494–2502 (1994). [CrossRef]
  32. P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” J. Opt. Soc. Am. A 14, 1592–1598 (1997). [CrossRef]
  33. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997). [CrossRef]
  34. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef]

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