Multipole Approach for Homogenization of Metamaterials: “Classical” Metamaterials

  • Arkadi ChipoulineEmail author
  • Franko Küppers
Part of the Springer Series in Optical Sciences book series (SSOS, volume 211)


Now the multipole expansion developed in Chap.  3 is applied to describe the widely used double-wire geometry [Shalaev et al. in Opt. Lett. 30, 3356, 2005, 1]. In what follows we assume again the geometry shown in Fig.  3.2 with the electric field \( \vec {E}_{x} \) polarized along the long axis of the wires and propagation along the y axis \( (0,\,\vec {k}_{y} ,\,0) \). Our goal is to elaborate a dispersion relation as a function of the particular parameters of the MAs using the general expressions obtained in chapter ( 3.61). In order to find the relations for the dipole, quadrupole, and magnetic dipole moments ( 3.57) it is necessary to express charge dynamics in the MAs as the functions of the averaged fields. As it was mentioned above, the microscopic interaction between charges and the electromagnetic wave is determined by the interaction with the electric field.


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Authors and Affiliations

  1. 1.Institute of Microwave Engineering and PhotonicsTechnical University of DarmstadtDarmstadtGermany
  2. 2.Department of Electrical Engineering and Information TechnologiesTechnical University of DarmstadtDarmstadtGermany

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