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

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 nonmagnetic 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 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.

Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and∕or double-positive metamaterial layers

“…As is well known, such tensors relate the local electromagnetic fields ͑E loc , H loc ͒ to the induced dipole moments in a particle ͑p , m͒, 14 i.e.,…”

Evaluation of polarisability tensors of arbitrarily shaped highly conducting bodies

“…These conditions forbid the use of a homogeneous field, but allow a commonly employed excitation by linearly independent planewaves [26]. In fact, due to identity [43] 1 2π…”

Eigenfunctional representation of dyadic Green's functions in multilayered gyrotropic chiral media

“…Reduction can be made for formulating the dyadic Green's functions in a less complex medium of specific planar geometries, e.g., an anisotropic medium where ξ c = 0, a chiral medium where g = w = 0, = z and µ = µ z , a gyroelectric medium where w = 0 and µ = µ z , a chiroferrite medium where p = 0 and = z , an isotropic medium where ξ c = g = w = 0, z = and µ = µ z . When the source distribution is given, the electric field can be computed by (4), in which the local parameters of the source, the stratified layers and the materials in each layer have been taken into account systematically.…”

“…have been carried out (e.g., tensor-parameter retrieval using quasi-static Lorentz theory [4], S-parameter retrieval using the plane wave incidence [5] and constitutive relation retrieval using transmission line method [6,7]). These materials may possess backward waves [8,9], negative refraction [10,11], subwavelength focusing [12] and amplification of evanescent waves [2].…”