Complex k band diagrams of 3D metamaterial/photonic crystals

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 fo...

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Bibliographic Details
Published in:Optics express 2011-09, Vol.19 (20), p.19027-19041
Main Authors: Fietz, Chris, Urzhumov, Yaroslav, Shvets, Gennady
Format: Article
Language:English
Subjects:
Computer Simulation
Crystallization - instrumentation
Equipment Design
Manufactured Materials
Models, Theoretical
Optics and Photonics
Photons
Refractometry - instrumentation
Scattering, Radiation
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Summary: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.
ISSN:1094-4087
1094-4087
DOI:10.1364/OE.19.019027