Unified Homogenization Theory for Magnetoinductive and Electromagnetic Waves in Split Ring Metamaterials

TL;DR

This paper introduces a unified homogenization theory for split ring metamaterials that accounts for time and spatial dispersion, enabling accurate characterization of electromagnetic and magnetoinductive wave propagation.

Contribution

It presents a novel homogenization approach combining circuit models and Maxwell equations to describe wave spectra in split ring metamaterials.

Findings

The theory accurately predicts wave propagation in metamaterials.

Good agreement with full wave simulations.

Accounts for complete wave spectrum including magnetoinductive waves.

Abstract

A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the metamaterial as a cubic arrangement of coupled LC circuits, giving the relation between currents and local magnetic field. The second equation comes from macroscopic Maxwell equations, and gives the relation between the macroscopic magnetic field and the average magnetization of the metamaterial. It is shown that electromagnetic and magnetoinductive waves propagating in the metamaterial are obtained from this analysis. Therefore, the proposed time and spatially dispersive permeability accounts for the characterization of the complete spectrum of waves of the metamaterial. Finally, it is shown that the proposed theory is in good quantitative and qualitative agreement with full wave simulations.