Dispersion in media containing resonant inclusions: where does it come from?

TL;DR

This paper investigates the origin of dispersion in media with resonant inclusions, revealing that far field coupling and Fano interference are key factors, and provides a unified formalism applicable across various metamaterial domains.

Contribution

It introduces a simple formalism linking the dispersion relation to the far field response of a single resonator, unifying different types of resonant media.

Findings

Far field coupling explains dispersion in resonant media.

Fano interference causes phase shifts at resonance.

The formalism applies to metamaterials, band gap materials, and plasmons.

Abstract

We study the propagation of waves in a quasi 1D homogeneous host medium filled with various resonators. We first prove that a far field coupling between the elements explains its dispersive nature. This coupling is interpreted as a Fano interference between the incoming wave and the waves re-radiated by each resonator, which experience a phase shift at resonance. We propose a simple formalism that gives the complete dispersion relation of the medium in terms of the far field response of a single resonator. We prove that our approach applies to and unifies various domains such as metamaterials, hybridization band gap materials and designer's plasmons. Finally we show that those media, spatially random or organized on a scale larger than the wavelength, also present very interesting properties, which broadens the range of man made exotic materials.