Low-Frequency Scattering Analysis and Homogenisation of Split-Ring Elements

Abstract

Abstract-A key structure in so-called metamaterial mediums is the elementary split-ring resonator. We consider in this paper the lowfrequency electromagnetic scattering by a split-ring particle modelled as a perfectly conducting wire ring, furnished with a narrow gap, and derive analytical solutions for the electric and magnetic dipole moments for different kinds of incidence and polarisation in the quasistatic approximation. Through a vectorial homogenisation process, the expressions discovered for the dipole moments and the related polarisability dyadics are linked with the macroscopic constitutive equations for the medium. We further show that the condition for resonance of a medium consisting of simple split-rings cannot be achieved by means of the given quasi-static terms without violating the underlying assumptions of homogenisation. Nevertheless, the results are applicable for sparse medium of rings, and we derive numerical guidelines for the applicability with some examples of the effect of the considered split-ring medium on electromagnetic wave propagation.

Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials

“…For the case of passive materials (and metamaterials), these multipoles will have been induced by normally incident plane-wave radiation. We assume that the multipole moments can either be extracted from the numerical simulation of the induced currents, or calculated from the dynamics of charge and current densities anticipated for the metamolecules of a known geometry [48][49][50][51][52]. In the interest of brevity, only the key steps of the derivation will be demonstrated, yielding the expression for the radiation from a two-dimensional array of toroidal dipoles, before giving the full expression that includes all leading multipoles.…”

Magnetic Response of Metamaterials

“…Many theoretical descriptions of the magnetic response of SRR systems are given in terms of the inductance and capacitance of the structure, while only few studies have dealt with the microscale electrodynamic problem, mostly focusing on the asymptotic region of the scattered fields. The effective permeability may be deduced experimentally from comparison of reflectance measurements to model calculations or by fitting transmission and reflection amplitudes to standard expressions derived by assuming the system to be non‐spatially dispersive .…”