Modeling of Isotropic Backward-Wave Materials Composed of Resonant Spheres

TL;DR

This paper presents a theoretical analysis and improved modeling of isotropic backward-wave materials made of resonant dielectric spheres, validated by simulations and considering size distribution effects on losses.

Contribution

It introduces an improved mixing rule for effective permittivity and validates it with Mie theory and numerical simulations.

Findings

Validated mixing rule for effective permittivity

Size distribution increases losses in the frequency band

Theoretical analysis supports design of backward-wave materials

Abstract

A possibility to realize isotropic artificial backward-wave materials is theoretically analyzed. An improved mixing rule for the effective permittivity of a composite material consisting of two sets of resonant dielectric spheres in a homogeneous background is presented. The equations are validated using the Mie theory and numerical simulations. The effect of a statistical distribution of sphere sizes on the increasing of losses in the operating frequency band is discussed and some examples are shown.