Scattering electromagnetic eigenstates of a two-constituent composite and their exploitation for calculating a physical field

The spectral representation of an electric field in a two-constituent composite medium is revisited. A theory is developed for calculating the electromagnetic (EM) eigenstates of Maxwell's equations for such a composite where the magnetic permeability, as well as the electric permittivity, have different uniform values in the two constituents. The physical electric field E(r) produced in the system either by a given incident field or by a given source current density is expanded in this set of biorthogonal eigenstates for any position r. If the microstructure consists of a cluster of separate inclusions in a uniform host medium, then the EM eigenstates of all the isolated inclusions can also be used to calculate E(r). Once all these eigenstates are known for a given host and a given microstructure then the calculation of E(r) only involves performing three-dimensional integrals of known functions and solving sets of linear algebraic equations.