On the dispersion relation in metamaterials - An analytical approach

Jörg Petschulat, Arkadi Chipouline, Thomas Pertsch, Christoph Menzel, Carsten Rockstuhl, Falk Lederer, Andreas Tünnermann

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


An analytical description for plane wave propagation in metamaterials (MM) is presented. It follows the usual approach for describing light propagation in homogenous media on the basis of Maxwell's equations, though applied to a medium composed of metallic nanostructures. Here, as an example, these nanostructures are double (or cut) wires. In the present approach the multipole expansion technique is used to account for the electric and magnetic dipole as well as the electric quadrupole moments of the carrier distribution within the nanostructure where a model of coupled oscillators is used for the description of the internal charge density dynamics. It is shown how expressions for the effective permittivity and permeability can be derived from analytical expressions for the dispersion relation, the magnetization and the electric displacement field. Results of the analytical model are compared with rigorous simulations of Maxwell's equations yielding the limitations and applicability of the proposed model.

Original languageEnglish
Title of host publicationMetamaterials III
Publication statusPublished - 2008
Externally publishedYes
EventMetamaterials III - Strasbourg, France
Duration: 7 Apr 200810 Apr 2008

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


ConferenceMetamaterials III


  • Dispersion relation
  • Localized plasmonic eigenmodes
  • Metamaterials
  • Negative index materials


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