%0 Journal Article
%T Extension of the Multipole Approach to Random Metamaterials
%A A. Chipouline
%A S. Sugavanam
%A J. Petschulat
%A T. Pertsch
%J Advances in OptoElectronics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/161402
%X Influence of the short-range lateral disorder in the meta-atoms positioning on the effective parameters of the metamaterials is investigated theoretically using the multipole approach. Random variation of the near field quasi-static interaction between metaatoms in form of double wires is shown to be the reason for the effective permittivity and permeability changes. The obtained analytical results are compared with the known experimental ones. 1. Introduction Metamaterials are artificial media that allow tailoring the macroscopic properties of the light propagation by a careful choice of a design for the microscopic unit cell (called the meta-atom). By controlling the geometrical shape and the material dispersion of the meta-atom, novel effects such as negative refraction [1¨C3], optical cloaking [4¨C9], as well as series of optical analogues to phenomena known from different disciplines in physics could be observed [10¨C14]. Despite the possibility to rely on rigorous computations for describing the light propagation on the microscopic level, an enduring problem in metamaterial research is the question on how the effective material tensor looks like for a certain metamaterial. A simple and versatile analytical model describing propagation of electromagnetic waves in metamaterials has been recently developed following classical approach of Maxwell equation averaging procedure [15]. This transition from the microscopic to macroscopic system of Maxwell equations takes into account all peculiarities of carriers dynamics under the action of the resulted electromagnetic field through the introduction of multipole moments which are supposed to be represented as the functions of the macroscopic electric and magnetic fields [16]. One of the great advantages of this model is the ability to evaluate straightforwardly influence of the charge dynamics of the meta-atoms on the effective properties of the metamaterials. In fact, the multipole moments are calculated through the averaged charge dynamics in the meta-atoms. Any factors influencing the charge dynamics (e.g., interaction between the meta-atoms, extra coupling of the meta-atoms with the other objects, etc.) cause the changes in the multipole expressions, which in turn change the effective parameters. It is important for the analysis presented here that the interaction between the meta-atoms and hence its influence on the effective permittivity and permeability can be straightforwardly taken into account [17]. The interaction between the small particles, both dielectric and metallic, and propagation of an
%U http://www.hindawi.com/journals/aoe/2012/161402/