On the dispersion relation in metamaterials - an analyticalapproach

摘要

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.