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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 19027–19041

Complex k band diagrams of 3D metamaterial/photonic crystals.

Chris Fietz, Yaroslav Urzhumov, and Gennady Shvets  »View Author Affiliations

Optics Express, Vol. 19, Issue 20, pp. 19027-19041 (2011)

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A finite element method (FEM) for solving a complex valued k(ω) vs. ω dispersion curve of a 3D metamaterial/photonic crystal system is presented. This 3D method is a generalization of a previously reported 2D eigenvalue method [Opt. Express 15, 9681 (2007)]. This method is particularly convenient for analyzing periodic systems containing dispersive (e.g., plasmonic) materials, for computing isofrequency surfaces in the k-space, and for calculating the decay length of the evanescent waves. Two specific examples are considered: a photonic crystal comprised of dielectric spheres and a plasmonic fishnet structure. Hybridization and avoided crossings between Mie resonances and propagating modes are numerically demonstrated. Negative index propagation of four electromagnetic modes distinguished by their symmetry is predicted for the plasmonic fishnets. By calculating the isofrequency contours, we also demonstrate that the fishnet structure is a hyperbolic medium.

© 2011 OSA

OCIS Codes
(160.3918) Materials : Metamaterials
(160.5298) Materials : Photonic crystals

ToC Category:

Original Manuscript: May 31, 2011
Revised Manuscript: July 1, 2011
Manuscript Accepted: July 14, 2011
Published: September 15, 2011

Chris Fietz, Yaroslav Urzhumov, and Gennady Shvets, "Complex k band diagrams of 3D metamaterial/photonic crystals.," Opt. Express 19, 19027-19041 (2011)

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