On the dispersion relation in metamaterials: an analytic approach

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

doi:10.1117/12.781047

6 May 2008 On the dispersion relation in metamaterials: an analytic approach

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

Author Affiliations +

Proceedings Volume 6987, Metamaterials III; 69871T (2008) https://doi.org/10.1117/12.781047
Event: SPIE Photonics Europe, 2008, Strasbourg, France

Abstract

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.

Citation Download Citation

Jörg Petschulat, Arkadi Chipouline, Thomas Pertsch, Christoph Menzel, Carsten Rockstuhl, Falk Lederer, and Andreas Tünnermann "On the dispersion relation in metamaterials: an analytic approach", Proc. SPIE 6987, Metamaterials III, 69871T (6 May 2008); https://doi.org/10.1117/12.781047

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