Mathematical Institute, University of Oxford, UK

Homogenisation and resonance effects in Faraday cages

Faraday cages are used to shield regions from electrostatic or electromagnetic fields. They usually comprise a mesh of conducting wires, and are routinely used in electronic components and microwave ovens. There is increasing interest in their use at smaller scales to provide optical shielding. I will discuss mathematical models to quantify the efficiency of a two-dimensional Faraday cage and how it depends on the properties of the cage. The models combine numerical methods and homogenization theory, using matched asymptotic expansions. The analysis reveals resonance effects, when a cage subjected to incident waves of a certain frequency can actually amplify the field rather than shield from it. I will discuss how such resonance effects can be understood and controlled. This is joint work with David Hewett.