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

Autor: Mohamed Farhat, Sébastien Guenneau, Stefan Enoch
Přispěvatelé: King Abdullah University of Science and Technology (KAUST), Institut FRESNEL (FRESNEL), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), CLARTE (CLARTE), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), EPSILON (EPSILON), CONCEPT (CONCEPT), European Project, Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)
Rok vydání: 2014
Předmět:
Zdroj: EPL-Europhysics Letters
EPL-Europhysics Letters, 2014, 107, pp.44002. ⟨10.1209/0295-5075/107/44002⟩
EPL-Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2014, 107, pp.44002. ⟨10.1209/0295-5075/107/44002⟩
ResearcherID
ISSN: 1286-4854
0295-5075
DOI: 10.1209/0295-5075/107/44002
Popis: 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.
Comment: 17 pages, 6 figures
Databáze: OpenAIRE