Bounds on the transport and optical properties of a two-component composite material

Abstract

An infinite set of bounds on the effective permittivity εe of two-component composite materials is derived. All the bounds can be expressed in terms of a single function g. Analogous bounds apply to the other transport properties of the composite, such as the thermal and electrical conductivities and the magnetic permeability. The work also applies to the optical properties of the composite, provided the wavelength is sufficiently large compared with the structure of the composite. In all cases we find εe is confined to a region of the complex plane bounded by arcs of circles. The appropriate region is determined by what is known about the composite and as more information is known the region becomes progressively smaller. We show that in many cases the region is the most restrictive which can be found using only the known information about the composite material.