Effective complex permittivity tensor of a periodic array of cylinders

TL;DR

This paper derives efficient formulas for the effective complex permittivity tensor of a 2D periodic array of cylinders, revealing non-monotonic behavior of its real and imaginary parts with volume fraction.

Contribution

It introduces new formulas for calculating the effective complex permittivity tensor of periodic composites with complex dielectric properties.

Findings

Formulas agree well with numerical calculations.

Real and imaginary parts can behave non-monotonically.

Effective tensor can differ significantly from constituent properties.

Abstract

We determine the effective complex permittivity of a two-dimensional composite, consisting of an arbitrary doubly periodic array of identical circular cylinders in a homogeneous matrix, and whose dielectric properties are complex-valued. Efficient formulas are provided to determine the effective complex permittivity tensor which are in excellent agreement with numerical calculations. We also show that in contrast to the real-valued case, the real and imaginary parts of the effective complex-valued tensor can exhibit non-monotonic behavior as functions of volume fraction of cylinders, and can be either greater or less than that of the constituents.