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

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

http://dx.doi.org/10.1364/OE.19.019027

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### Abstract

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:**

Metamaterials

**History**

Original Manuscript: May 31, 2011

Revised Manuscript: July 1, 2011

Manuscript Accepted: July 14, 2011

Published: September 15, 2011

**Citation**

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

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19027

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