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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 15 — Jul. 23, 2007
  • pp: 9681–9691

The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction

Marcelo Davanço, Yaroslav Urzhumov, and Gennady Shvets  »View Author Affiliations

Optics Express, Vol. 15, Issue 15, pp. 9681-9691 (2007)

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The propagation characteristics of a subwavelength plasmonic crystal are studied based on its complex Bloch band structure. Photonic crystal bands are generated with an alternative 2D Finite Element Method formulation in which the Bloch wave problem is reduced to a quadratic eigenvalue system for the Bloch wavevector amplitude k. This method constitutes an efficient and convenient alternative to nonlinear search methods normally employed in the calculation of photonic bands when dispersive materials are involved. The method yields complex wavevector Bloch modes that determine the wave-scattering characteristics of finite crystals. This is evidenced in a comparison between the band structure of the square-lattice plasmonic crystal and scattering transfer-functions from a corresponding finite crystal slab. We report on a wave interference effect that leads to transmission resonances similar to Fano resonances, as well as on the isotropy of the crystal’s negative index band. Our results indicate that effective propagation constants obtained from scattering simulations may not always be directly related to individual crystal Bloch bands.

© 2007 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(160.4670) Materials : Optical materials
(260.2030) Physical optics : Dispersion
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Physical Optics

Original Manuscript: June 1, 2007
Revised Manuscript: July 15, 2007
Manuscript Accepted: July 16, 2007
Published: July 19, 2007

Marcelo Davanco, Yaroslav Urzhumov, and Gennady Shvets, "The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction," Opt. Express 15, 9681-9691 (2007)

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light. (Princteon University Press, 1995).
  2. K. Sakoda, Optical Properties of Photonic Crystal, ser. Optical Sciences. (New York: Springer, 2001).
  3. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001). [CrossRef] [PubMed]
  4. B. P. Hiett, B. D. H., S. J. Cox, J. M. Generowicz, M. Molinari, and K. S. Thomas, "Aplication of finite element methods to photonic crystal modelling," IEE Proc - Sci. Meas. Technol. 149, 293-296 (2002). [CrossRef]
  5. G. Shvets and Y. A. Urzhumov, "Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances," Phys. Rev. Lett. 93, 243902 (2004). [CrossRef]
  6. G. Shvets and Y. Urzhumov, "Electric and magnetic properties of sub-wavelength plasmonic crystals," J. Opt. A: Pure Appl. Opt. 7, S23-S31 (2005). [CrossRef]
  7. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005). [CrossRef] [PubMed]
  8. A. Ruhe, "Algorithms for the nonlinear eigenvalue problem," SIAM J. Numer. Anal. 10, 674-689 (1973). [CrossRef]
  9. A. Spence and C. Poulton, "Photonic band structure calculations using nonlinear eigenvalue techniques," J. Comput. Phys. 204, 65-81 (2005). [CrossRef]
  10. E. Istrate, A. A. Green, and E. H. Sargent, "Behavior of light at photonic crystal interfaces," Phys. Rev. B 71, 195122 (2005). [CrossRef]
  11. [Online]. Available: http://www.comsol.com
  12. U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1878 (1961). [CrossRef]
  13. J. Jin, The Finite Element Method in Electromagnetics, (2nd ed. Wiley, 2002).
  14. F. Tisseur and K. Meerbergen, "The quadratic eigenvalue problem," SIAM Rev. 43, 235-286 (2001). [CrossRef]
  15. G. Shvets and Y. Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A: Pure Appl. Opt. 8, S122-S130 (2006). [CrossRef]
  16. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005). [CrossRef]
  17. K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, "Nature of lossy bloch states in polaritonic photonic crystals," Phys. Rev. B 69, 195111 (2004). [CrossRef]
  18. H. G. Winful, "The meaning of group delay in barrier tunnelling: a re-examination of superluminal group velocities," New J. Phys., Phys. 8, 101 (2006). [CrossRef]

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