Complex effective permittivity of a lossy composite material

In recent works, boundary integral equations and finite elements were used to study the (real) effective permittivity for two-component dense composite materials in the quasistatic limit. In this paper this approach is extended to investigate in detail the role of losses. We consider the special case of the axisymmetric configuration consisting of infinite circular cylinders (assumed to be parallel to the z axis and of permittivity ε1) organized into a crystalline arrangement (simple square lattice) within a homogeneous background medium of permittivity ε2=1. The intersections of the cylinders with the xy plane form a periodic two-dimensional structure. We carried out simulations taking ε1=3-0.03i or ε1=30-0.3i and ε2=1. We shall argue that the numerical results discussed here are consistent with the Bergman and Milton theory