Faraday effect in composites

TL;DR

This paper investigates how the Faraday effect is amplified in a dielectric-metal composite near the percolation threshold, using theoretical methods to compute effective permittivity and scaling behavior.

Contribution

It introduces a combined theoretical approach to analyze the Faraday effect in composites, revealing enhanced effects near the percolation threshold.

Findings

Faraday effect is greatly enhanced near the percolation threshold.

Effective permittivity tensor computed using replica trick and variational method.

Scaling exponents near the percolation threshold are consistent across methods.

Abstract

In this article, we study the Faraday effect in a binary composite consisting of a dielectric matrix with metallic inclusions. We first use the replica trick together with a variational method in order to compute the effective permittivity tensor (in the quasi-static limit) of this composite in a static magnetic field. In order to find the scaling exponents near the percolation threshold, we use a high contrast or low frequency expansion combined with scaling. The result of the two methods are in agreement and predict that near the percolation threshold (and below, that is in the dielectric region), the Faraday effect is greatly enhanced.