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