Magnetism and homogenization of micro-resonators

TL;DR

This paper analyzes the effective magnetic properties of micro-resonator arrays using advanced homogenization techniques, demonstrating that the resulting bulk medium replicates the scattering behavior of the original micro-structured composite.

Contribution

It introduces a rigorous two-scale homogenization method that accurately captures the magnetic and dielectric behavior of micro-resonator arrays, improving upon traditional averaging techniques.

Findings

Effective magnetic and dielectric coefficients match scattering data

Homogenization method avoids usual cell averages

Bulk medium replicates micro-structure scattering behavior

Abstract

Arrays of cylindrical metal micro-resonators embedded in a dielectric matrix were proposed by Pendry, et. al., in 1999 as a means of creating a microscopic structure that exhibits strong bulk magnetic behavior at frequencies not realized in nature. This behavior arises for H-polarized fields in the quasi-static regime, in which the scale of the micro-structure is much smaller than the free-space wavelength of the fields. We carry out both formal and rigorous two-scale homogenization analyses, paying special attention to the appropriate method of averaging, which does not involve the usual cell averages. We show that the effective magnetic and dielectric coefficients obtained by means of such averaging characterize a bulk medium that, to leading order, produces the same scattering data as the micro-structured composite.