Biharmonic split ring resonator metamaterial: Artificially dispersive effective density in thin periodically perforated plates

Handle URI:
http://hdl.handle.net/10754/563689
Title:
Biharmonic split ring resonator metamaterial: Artificially dispersive effective density in thin periodically perforated plates
Authors:
Farhat, Mohamed; Enoch, Stefan; Guenneau, Sébastien
Abstract:
We present in this paper a theoretical and numerical analysis of bending waves localized on the boundary of a platonic crystal whose building blocks are Split Ring Resonators (SRR). We first derive the homogenized parameters of the structured plate using a three-scale asymptotic expansion in the linearized biharmonic equation. In the limit when the wavelength of the bending wave is much larger than the typical heterogeneity size of the platonic crystal, we show that it behaves as an artificial plate with an anisotropic effective Young modulus and a dispersive effective mass density. We then analyze dispersion diagrams associated with bending waves propagating within an infinite array of SRR, for which eigen-solutions are sought in the form of Floquet-Bloch waves. We finally demonstrate that this structure displays the hallmarks of All-Angle Negative Refraction (AANR) and it leads to superlensing and ultrarefraction effects, interpreted thanks to our homogenization model as a consequence of negative and vanishing effective density, respectively. © EPLA, 2014.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program
Publisher:
IOP Publishing
Journal:
EPL (Europhysics Letters)
Issue Date:
1-Aug-2014
DOI:
10.1209/0295-5075/107/44002
ARXIV:
arXiv:1408.0004
Type:
Article
ISSN:
02955075
Sponsors:
SG would like to acknowledge a funding of the European Research Council through ERC grant ANAMORPHISM.
Additional Links:
http://arxiv.org/abs/arXiv:1408.0004v1
Appears in Collections:
Articles; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorFarhat, Mohameden
dc.contributor.authorEnoch, Stefanen
dc.contributor.authorGuenneau, Sébastienen
dc.date.accessioned2015-08-03T12:06:26Zen
dc.date.available2015-08-03T12:06:26Zen
dc.date.issued2014-08-01en
dc.identifier.issn02955075en
dc.identifier.doi10.1209/0295-5075/107/44002en
dc.identifier.urihttp://hdl.handle.net/10754/563689en
dc.description.abstractWe present in this paper a theoretical and numerical analysis of bending waves localized on the boundary of a platonic crystal whose building blocks are Split Ring Resonators (SRR). We first derive the homogenized parameters of the structured plate using a three-scale asymptotic expansion in the linearized biharmonic equation. In the limit when the wavelength of the bending wave is much larger than the typical heterogeneity size of the platonic crystal, we show that it behaves as an artificial plate with an anisotropic effective Young modulus and a dispersive effective mass density. We then analyze dispersion diagrams associated with bending waves propagating within an infinite array of SRR, for which eigen-solutions are sought in the form of Floquet-Bloch waves. We finally demonstrate that this structure displays the hallmarks of All-Angle Negative Refraction (AANR) and it leads to superlensing and ultrarefraction effects, interpreted thanks to our homogenization model as a consequence of negative and vanishing effective density, respectively. © EPLA, 2014.en
dc.description.sponsorshipSG would like to acknowledge a funding of the European Research Council through ERC grant ANAMORPHISM.en
dc.publisherIOP Publishingen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1408.0004v1en
dc.titleBiharmonic split ring resonator metamaterial: Artificially dispersive effective density in thin periodically perforated platesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentElectrical Engineering Programen
dc.identifier.journalEPL (Europhysics Letters)en
dc.contributor.institutionInstitute of Condensed Matter Theory and Solid State Optics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, D-07743 Jena, Germanyen
dc.contributor.institutionAix-Marseille Université, CNRS, Campus Universitaire de Saint-Jérôme, 13013 Marseille, Franceen
dc.identifier.arxividarXiv:1408.0004en
kaust.authorFarhat, Mohameden
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