Phase diagram for the transition from photonic crystals to dielectric metamaterials

TL;DR

This paper introduces a phase diagram and an order parameter to distinguish photonic crystals from dielectric metamaterials, based on the physics of resonances, supported by microwave experiments and theoretical analysis.

Contribution

It presents a novel phase diagram and order parameter to classify structured materials, linking the transition from photonic crystals to metamaterials to resonance physics.

Findings

Transition occurs when Mie gap opens below the Bragg bandgap

Homogenization is valid when the effective permeability becomes negative

Experimental microwave results confirm the theoretical phase diagram

Abstract

Photonic crystals and metamaterials represent two seemingly different classes of artificial electromagnetic media but often they are composed of similar structural elements arranged in periodic lattices. The important question is how to distinguish these two types of periodic photonic structures when their parameters, such as dielectric permittivity and lattice spacing, vary continuously. Here, we discuss transitions between photonic crystals and all-dielectric metamaterials and introduce the concept of a phase diagram and an order parameter for such structured materials, based on the physics of Mie and Bragg resonances. We show that a periodic photonic structure transforms into a metamaterial when the Mie gap opens up below the lowest Bragg bandgap where the homogenization approach can be justified and the effective permeability becomes negative. Our theoretical approach is confirmed by detailed microwave experiments for a metacrystal composed of a square lattice of glass tubes filled with heated water. This analysis yields deep insight into the properties of periodic photonic structures, and it also provides a useful tool for designing different classes of electromagnetic materials in a broad range of parameters.