Homogenization of composites: dynamic and static theories

We study the homogenization of arrays of cylinders, treating both the cases of non-dispersive cylinders, and cylinders dispersive according to a power law. In the latter case, we exhibit the critical value of the dispersion i ndex, below which the composite homogenizes satisfactorily, and above which homogenization is not possible. We also discuss the link between homogeniz ation and the lowest band in the photonic dispersion diagram for an array o f cylinders. We contrast the situations when the lowest band does and does not pass through the origin. (C) 2000 Elsevier Science B.V. All rights rese rved.