Biharmonic Split Ring Resonator Metamaterial: Artificially dispersive effective density in thin periodically perforated plates

TL;DR

This paper develops a theoretical and numerical model of a metamaterial with split ring resonators that exhibits artificial dispersive effective density, enabling phenomena like negative refraction and superlensing in thin perforated plates.

Contribution

It introduces a homogenization approach for biharmonic plates with SRR structures, revealing dispersive effective parameters and novel wave phenomena.

Findings

Demonstrates negative and vanishing effective density in the structured plates.

Shows the structure supports all-angle negative refraction.

Predicts superlensing and ultrarefraction effects due to effective parameters.

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.