Geometry-function relationships in meta-foils

Abstract

Meta-foils are all-metal free-standing electromagnetic metamaterials based on interconnected S-string architecture. They provide a versatile applications' platform. Lacking any substrate or embedding matrix, they feature arrays of parallel upright S-strings with each string longitudinally shifted by half an S compared to its neighbour to form capacitance-inductance loops. Geometric parameters include length a, width b, thickness t, and height h of an S, the gap between adjacent S-strings d, and the periodicity p of the interconnecting lines. Equidistant strings at p=1 form a 1SE meta-foil. Grouped in pairs of gap d, exhibiting a gap d(p) between pairs, they are named 2SP. Geometric parameters a, b, t, h, d, d(p), pS(E or P) and materials' properties like electric conductivity, Young's modulus, thermal expansion coefficient, and heat capacity determine the electromagnetic, mechanical, and thermal properties of meta-foils including the spectral dependence of resonance frequencies, refractive index, transmission, reflection, and bending. We show how the frequency and transmission of left-handed pass-bands depend on a, p, and d(p), the pSP geometry exhibiting higher resonance frequency and transmission. Equivalent circuit considerations serve to explain physical reasons. We also demonstrate mechanical behavior versus p and d(p) justifying the design of a cylindrical hyperlens depending on bent meta-foils.