2018
DOI: 10.1007/s00205-018-1237-1
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Effective Maxwell’s Equations for Perfectly Conducting Split Ring Resonators

Abstract: We analyze the time harmonic Maxwell's equations in a geometry containing perfectly conducting split rings. We derive the homogenization limit in which the typical size η of the rings tends to zero. The split rings act as resonators and the assembly can act, effectively, as a magnetically active material. The frequency dependent effective permeability of the medium can be large and/or negative.

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Cited by 11 publications
(20 citation statements)
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“…The notion of a geometric average was first introduced by Bouchitté, Bourel, and Felbacq in [5]. The notion turned out to be very useful, it was extended in [17] to more general geometries. Although we focus on simple Helmholtz domains in the main part of this work, we define the geometric average for general geometries.…”
Section: The Geometric Averagementioning
confidence: 99%
See 1 more Smart Citation
“…The notion of a geometric average was first introduced by Bouchitté, Bourel, and Felbacq in [5]. The notion turned out to be very useful, it was extended in [17] to more general geometries. Although we focus on simple Helmholtz domains in the main part of this work, we define the geometric average for general geometries.…”
Section: The Geometric Averagementioning
confidence: 99%
“…Proof. Thanks to the preparations of the last section, we can essentially follow [17] to derive (4.5a)-(4.5c). The remaining relations (4.5d) and (4.5e) follow from the characterisation of the solution spaces of the cell problems.…”
Section: Derivation Of the Effective Equationsmentioning
confidence: 99%
“…In order to analyze split ring geometries for perfectly conducting inclusions, the concept of a geometric average was extended in [18] to cover the case of compactly contained inclusions without the assumption of simple connectedness. The concept of a geometric average was extended further in [22] in order to cover the case that the inclusions touch the boundary of the periodicity cell (0, 1) 3 .…”
Section: Introductionmentioning
confidence: 99%
“…We treat here properties of the three-dimensional solutions. We emphasize that the transmission properties of a high-contrast medium cannot be captured in the framework of perfect conductors, since the latter excludes resonances on the scale of the periodicity (except if three different length-scales are considered as in [28]).…”
Section: Introductionmentioning
confidence: 99%