Four definitions of magnetic permeability for periodic metamaterials

TL;DR

This paper compares four different definitions of magnetic permeability in periodic metamaterials, analyzing their relationships and properties such as causality, passivity, and symmetry, specifically for linear, nonmagnetic constituents.

Contribution

It provides a detailed comparison and analysis of four definitions of magnetic permeability in metamaterials, clarifying their differences and properties.

Findings

Different definitions have distinct properties and implications.

The analysis clarifies the connection between the definitions.

Properties like causality and passivity are discussed in detail.

Abstract

We state and compare four different definitions of magnetic permeability for periodic, artificial media, or metamaterials. The connection between them, and properties in general, are discussed in detail, including causality, passivity, symmetry, asymptotic behavior, and origin dependence. The analysis is limited to metamaterials made from linear and nonmagnetic constituents.