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

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    Type
    Article
    Authors
    Farhat, M.
    Enoch, S.
    Guenneau, S.
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Date
    2014-08-21
    Preprint Posting Date
    2014-07-28
    Online Publication Date
    2014-08-21
    Print Publication Date
    2014-08-01
    Permanent link to this record
    http://hdl.handle.net/10754/563689
    
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    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.
    Citation
    Farhat, M., Enoch, S., & Guenneau, S. (2014). Biharmonic split ring resonator metamaterial: Artificially dispersive effective density in thin periodically perforated plates. EPL (Europhysics Letters), 107(4), 44002. doi:10.1209/0295-5075/107/44002
    Sponsors
    SG would like to acknowledge a funding of the European Research Council through ERC grant ANAMORPHISM.
    Publisher
    IOP Publishing
    Journal
    EPL (Europhysics Letters)
    DOI
    10.1209/0295-5075/107/44002
    arXiv
    1408.0004
    Additional Links
    https://iopscience.iop.org/article/10.1209/0295-5075/107/44002
    http://arxiv.org/pdf/1408.0004
    ae974a485f413a2113503eed53cd6c53
    10.1209/0295-5075/107/44002
    Scopus Count
    Collections
    Articles; Electrical and Computer Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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