Effective Macroscopic Response of a Composite with Small Deviations from Periodicity: Application to Colloidal Crystals

Abstract

Using the spectral approach, we analyze the effective properties of a composite which deviates slightly from periodicity. We find that, when the inclusions are randomly displaced from their equilibrium positions, the sharp resonances seen in the periodic case are broadened, and an additional branch cut appears. We use these results to analyze the effective dielectric constant of a colloidal crystal.