Low-frequency scattering analysis and homogenisation of split-ring elements

Johan Stén, Daniel Sjöberg (Corresponding Author)

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

A key structure in so-called metamaterial mediums is the elementary split-ring resonator. We consider in this paper the low-frequency 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 quasi-static 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.
Original languageEnglish
Pages (from-to)187-212
JournalProgress In Electromagnetics Research B
Volume35
DOIs
Publication statusPublished - 2011
MoE publication typeA1 Journal article-refereed

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Electric dipole moments
Electromagnetic wave propagation
Dipole moment
Metamaterials
homogenizing
Constitutive equations
Magnetic moments
Resonators
Wire
Scattering
Polarization
low frequencies
rings
scattering
dipole moments
dyadics
electromagnetic scattering
constitutive equations
magnetic dipoles
electric dipoles

Cite this

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Low-frequency scattering analysis and homogenisation of split-ring elements. / Stén, Johan; Sjöberg, Daniel (Corresponding Author).

In: Progress In Electromagnetics Research B, Vol. 35, 2011, p. 187-212.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Low-frequency scattering analysis and homogenisation of split-ring elements

AU - Stén, Johan

AU - Sjöberg, Daniel

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AB - A key structure in so-called metamaterial mediums is the elementary split-ring resonator. We consider in this paper the low-frequency 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 quasi-static 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.

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