Resonances and fields near metamaterial inclusions

We consider systems of particles in two dimensions with negative dielectric permittivity and sharp corners. The field divergences near the corners of the inclusions are non-square-integrable for negative permittivities in a range depending on the corner angle, and the leading term for small distances is provided by the static term. We have developed a highly accurate numerical method which uses adaptive techniques to resolve field behaviour near the corners. We use this to elucidate the resonant spectrum associated with the effective permittivity of arrays of such particles, and in particular its behaviour as the particles approach touching.