Generalized constitutive relations for metamaterials based on the quasi-static lorentz theory

14 October 2003

journal article
research article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation

Vol. 51 (10) , 2550-2557
https://doi.org/10.1109/tap.2003.817565

Abstract

This paper presents a method of calculating the elements of the generalized matrix representation of the macroscopic constitutive relations for a three-dimensional (3-D) array of non-magnetic inclusions with arbitrary shape. The derivation is based on the quasi-static Lorentz theory and the inclusions are represented by electric and magnetic dipole moments. The 6/spl times/6 constitutive relation matrix is expressed in terms of the interaction matrix and the polarizability matrix, which can be numerically calculated using the sum and the difference of opposing plane wave excitations. Numerical examples are given for split ring resonators and a chiral medium consisting of an array of helices to illustrate the usefulness of the formula and to verify the consistency constraint and reciprocity relations for a bianisotropic medium.

Keywords

This publication has 20 references indexed in Scilit:

Constitutive relations
Published by SPIE-Intl Soc Optical Eng ,2002
Role of bianisotropy in negative permeability and left-handed metamaterials
Physical Review B, 2002
On Perfect Lenses and Nihility
International Journal of Infrared and Millimeter Waves, 2002
Negative Refraction Makes a Perfect Lens
Physical Review Letters, 2000
Analytical antenna model for chiral scatterers: comparison with numerical and experimental data
IEEE Transactions on Antennas and Propagation, 1996
Isotropic chiral composite modeling: Comparison between analytical, numerical, and experimental results
Microwave and Optical Technology Letters, 1994
An approximate model for artificial chiral material
IEEE Transactions on Antennas and Propagation, 1994
Electromagnetic waves in Faraday chiral media
IEEE Transactions on Antennas and Propagation, 1992
Equivalent dipole moments of helical arrangements of small, isotropic, point-polarizable scatters: Application to chiral polymer design
Journal of Applied Physics, 1988
THE ELECTRODYNAMICS OF SUBSTANCES WITH SIMULTANEOUSLY NEGATIVE VALUES OF $\epsilon$ AND μ
Soviet Physics Uspekhi, 1968