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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 7 — Jul. 1, 2009
  • pp: 1598–1605

Accurate determination of band structures of two-dimensional dispersive anisotropic photonic crystals by the spectral element method

Ma Luo and Qing Huo Liu  »View Author Affiliations

JOSA A, Vol. 26, Issue 7, pp. 1598-1605 (2009)

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The spectral element method (SEM) is used to calculate band structures of two-dimensional photonic crystals (PCs) consisting of dispersive anisotropic materials. As in the conventional finite element method, for a dispersive PC, the resulting eigenvalue problem in the SEM is nonlinear and the eigenvalues are in general complex frequencies. We develop an efficient way of incorporating the dispersion in the system matrices. The band structures of a PC with a square lattice of dispersive cylindrical rods are first analyzed. The imaginary part of the complex frequency is the time-domain decay rate of the eigenmode, which is very useful for tracing a band from discrete numerical data. Modification of the band structure of TE mode by an external static magnetic field in the out-of-plane direction is explored for this square lattice. A plasmon resonance mode is found near the plasmon frequency when the magnetic field is nonzero. The band structure of a PC with a triangular lattice is also calculated with the SEM. Other types of lattices can also be treated readily by the SEM.

© 2009 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(160.5298) Materials : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: March 3, 2009
Revised Manuscript: May 8, 2009
Manuscript Accepted: May 14, 2009
Published: June 18, 2009

Ma Luo and Qing Huo Liu, "Accurate determination of band structures of two-dimensional dispersive anisotropic photonic crystals by the spectral element method," J. Opt. Soc. Am. A 26, 1598-1605 (2009)

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  3. J. D. Joannopoulos, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton U. Press, 2008).
  4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003). [CrossRef] [PubMed]
  5. K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. Principle of calculation and accuracy,” Phys. Rev. B 64, 045116 (2001). [CrossRef]
  6. T. Ito and K. Sakoda, “Photonic bands of metallic systems. II. Features of surface plasmon polaritons,” Phys. Rev. B 64, 045117 (2001). [CrossRef]
  7. E. Moreno, D. Erni, and C. Hafner, “Band structure computations of metallic photonic crystals with the multiple multipole method,” Phys. Rev. B 65, 155120 (2002). [CrossRef]
  8. M. Davanco, Y. Urzhumov, and G. Shvets, “The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction,” Opt. Express 15, 9681-9691 (2007). [CrossRef] [PubMed]
  9. S. Liu, J. Du, Z. Lin, R. X. Wu, and S. T. Chui, “Formation of robust and completely tunable resonant photonic band gaps,” Phys. Rev. B 78, 155101 (2008). [CrossRef]
  10. R. L. Chern, “Surface plasmon modes for periodic lattices of plasmonic hole waveguides,” Phys. Rev. B 77, 045409 (2008). [CrossRef]
  11. P.-J. Chiang, C.-P. Yu, and H.-C. Chang, “Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method,” Phys. Rev. E 75, 026703 (2007). [CrossRef]
  12. M. Luo, Q. H. Liu, and Z. Li, “A spectral element method for band structures of two-dimensional anisotropic photonic crystals,” Phys. Rev. E 79, 026705 (2009). [CrossRef]
  13. G. C. Cohen, Higher-Order Numerical Methods for Transient Wave Equations (Springer, 2001).
  14. J.-H. Lee and Q. H. Liu, “An efficient 3-D spectral element method for Schrödinger equation in nanodevice simulation,” IEEE Trans. Comput.-Aided Des. 24, 1848-1858 (2005). [CrossRef]
  15. J.-H. Lee, T. Xiao, and Q. H. Liu, “A 3-D spectral element method using mixed-order curl conforming vector basis functions for electromagnetic fields,” IEEE Trans. Microwave Theory Tech. 54, 437-444 (2006). [CrossRef]
  16. R. P. Brent, Algorithms for Minimization without Derivatives (Prentice-Hall, 1973), Chaps. 3 and 4.
  17. R. B. Lehoucq and D. C. Sorensen, “Deflation techniques for an implicitly re-started Arnoldi iteration,” SIAM J. Matrix Anal. Appl. 17, 789-821 (1996). [CrossRef]
  18. E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005). [CrossRef]
  19. Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100, 023902 (2008). [CrossRef] [PubMed]
  20. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999), p. 316.
  21. J. M. Pitarke, J. E. Inglesfield, and N. Giannakis, “Surface-plasmon polaritons in a lattice of metal cylinders,” Phys. Rev. B 75, 165415 (2007). [CrossRef]

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